Quantitative Demography and Health Estimates: Healthy Life Expectancy, Templates for Direct Estimates from Life Tables and other Applications 9783031286971, 3031286979

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The Springer Series on Demographic Methods and Population Analysis 55

Christos H Skiadas Charilaos Skiadas   Editors

Quantitative Demography and Health Estimates Healthy Life Expectancy, Templates for Direct Estimates from Life Tables and other Applications

The Springer Series on Demographic Methods and Population Analysis Volume 55

Series Editor Scott M. Lynch, Department of Sociology, Duke University, Durham, NC, USA

This series is now indexed in Scopus. In recent decades, there has been a rapid development of demographic models and methods and an explosive growth in the range of applications of population analysis. This series seeks to provide a publication outlet both for high-quality textual and expository books on modern techniques of demographic analysis and for works that present exemplary applications of such techniques to various aspects of population analysis. Topics appropriate for the series include: General demographic methods, Techniques of standardization, Life table models and methods, Multistate and multiregional life tables, analyses, and projections, Demographic aspects of biostatistics and epidemiology, Stable population theory and its extensions, Methods of indirect estimation, Stochastic population models, Event history analysis, duration analysis, and hazard regression models, Demographic projection methods and population forecasts, Techniques of applied demographic analysis, regional and local population estimates and projections, Methods of estimation and projection for business and health care applications, Methods and estimates for unique populations such as schools and students. Volumes in the series are of interest to researchers, professionals, and students in demography, sociology, economics, statistics, geography and regional science, public health and health care management, epidemiology, biostatistics, actuarial science, business, and related fields.

Christos H Skiadas • Charilaos Skiadas Editors

Quantitative Demography and Health Estimates Healthy Life Expectancy, Templates for Direct Estimates from Life Tables and other Applications

Editors Christos H Skiadas ISAST International Athens, Greece

Charilaos Skiadas Department of Mathematics and Department of Computer Science Hanover College Hanover, IN, USA

ISSN 1877-2560 ISSN 2215-1990 (electronic) The Springer Series on Demographic Methods and Population Analysis ISBN 978-3-031-28696-4 ISBN 978-3-031-28697-1 (eBook) https://doi.org/10.1007/978-3-031-28697-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

Part I Healthy Life Expectancy Estimates 1

2

3

4

5

6

Expanding the Life Tables to Include the Healthy Life Expectancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christos H. Skiadas and Yiannis Dimotikalis The Direct Healthy Life Expectancy Estimates from Life Tables to Support HALE Measures Done by the World Health Organization. A New Tool for a Standard Measure. . . . . . . . . . . . Christos H. Skiadas

3

13

Expanding the Life Tables for Companion Dogs in UK and Japan to Include the Healthy Life Expectancy . . . . . . . . . . . . . . . . . . . . . Christos H. Skiadas

33

Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan Extension: The Case of Brazil 2003 . . . . . . . . . . . . . . . . . . . . Yiannis Dimotikalis and Christos H. Skiadas

43

Assessment of the CASP-12 Scale Among People Aged 50+ in Europe: An Analysis Using SHARE Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bamicha Elena and Verropoulou Georgia

53

Possibilities of Creating New Health Indicators. . . . . . . . . . . . . . . . . . . . . . . . . Jana Vrabcová, Tomáš Fiala, and Jitka Langhamrová

61

Part II Health – Covid-19 7

Exploring Cross-National Comparability of Unidimensional Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anastasia Charalampi, Catherine Michalopoulou, and Clive Richardson

77

v

vi

8

Contents

A Stochastic Characterization of Omicron Variant of SARS-CoV 2 Virus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jesús E. García and V.A. González-López

91

9

Factors Associated with Direct and Indirect Aspects of Loneliness Among Europeans Aged 50 or Higher . . . . . . . . . . . . . . . . . . . 105 Eleni Serafetinidou

10

Neuropsychological Normed Measures for the Tinker Toy Test (TTT). Exploring Latent Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Franca Crippa, Luca Cesana, and Roberta Daini

11

A Tool for Measuring Alcohol Policy Scoring in Czechia and EU: The Innovative Alcohol Policy Indicator . . . . . . . . . . . . . . . . . . . . . . 131 Kornélia Svaˇcinová, Markéta Majerová, and Jana Vrabcová

Part III Population and Mortality 12

Analyzing Euler and Süßmilch’s Population Growth Model . . . . . . . . . . 141 Peter Pflaumer

13

Epidemic Models with Several Levels of Immunity . . . . . . . . . . . . . . . . . . . . 163 Flavius Guia¸s

14

Preventable Neonatal Deaths and Maternal and Child Factors in a Region of Brazil: Panel Data Modeling. . . . . . . . . . . . . . . . . . . . 175 Tiê Dias de Farias Coutinho and Neir Antunes Paes

15

Comparing the Mortality Regimes in 39 Populations . . . . . . . . . . . . . . . . . . 187 Konstantinos N. Zafeiris

16

Kane Tanaka’s 119 Birthday and the Supercentenarians’ Age Estimation. Further Remarks on the Oldest Old Record of 122 Years by Jeanne Calment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Christos H. Skiadas

17

Recent Changes in Human Mortality: The Case Study of Greece . . . . 217 Panagiotis Andreopoulos, Fragkiskos G. Bersimis, Kleomenis Kalogeropoulos, and Alexandra Tragaki

Part IV Data Analysis 18

Optimal Maintenance Policy for a Two-State System with Population Heterogeneity Under Partial Observation. . . . . . . . . . . . . . . . . . 235 Mizuki Kasuya and Lu Jin

19

Measuring Transition Smoothness into European Labour Market(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Maria Symeonaki, Dimitrios Parsanoglou, and Glykeria Stamatopoulou

Contents

vii

20

Could the Idea of Equitable Normal Pension Age Stabilize the Pension System? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Tomáš Fiala, Jitka Langhamrová, and Jana Vrabcová

21

The Use of Artificial Intelligence in Medical Imaging. Scientific Research and Opinions of Doctors and Radiologists Towards the Use of Artificial Intelligence in Radiology . . . . . . . . . . . . . . . . 271 Anna Sygletou and George Matalliotakis

Part V Demography and Society 22

A Topological Approach of Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Rafik Abdesselam

23

Semantic Integration of Data: From Theory to Social Research Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Aggeliki Kazani, George Filandrianos, Maria Symeonaki, and Giorgos Stamou

24

To Read on Not to Read? Examining the Relation Between Students’ Well-Being and Their Attitude Towards Reading. . . . . . . . . . . 315 Aliki Symeonaki and Maria Symeonaki

25

The Demographic, Social and Regional “Profile” of Peoples’ Perceptions of Their Social Class: Evidence from the Seventh Wave of the World Values Survey, 2017 –2020 . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Aggeliki Yfanti and Catherine Michalopoulou

Part I

Healthy Life Expectancy Estimates

Healthy Life Expectancy (HLE) estimates from the Life Tables with various applications and examples. The expanded form of full or abridged life tables provides the Life Expectancy (LE) but also the HLE. The Templates apply immediately to the life tables from WHO, HMD, Eurostat and other providers.

Chapter 1

Expanding the Life Tables to Include the Healthy Life Expectancy Christos H. Skiadas and Yiannis Dimotikalis

1.1 Introduction and Model Building We provide a method to expand the Life Tables in Czechia, to include the Healthy Life Years Lost to Disability (HLYL), to estimate the Proportion with Disability and then apply the Sullivan Method (Sullivan, 1971) to estimate the Disability Free Life Expectancy (DFLE) or the Healthy Life Expectancy (HLE) and the Healthy Life Years Lost (HLYL). The main part of the theory appears in: Skiadas, C. H., & Skiadas, C. (2020). Direct healthy life expectancy estimates from life tables with a Sullivan extension. Bridging the gap between HALE and Eurostat estimates. In The Springer series on demographic methods and population analysis 50. https://doi.org/ 10.1007/978-3-030-44695-6_3. The Life Tables are provided by the Human Mortality Database (HMD) at the related website https://www.mortality.org/. The first five columns are included in the HMD life table, and the rest sixteen columns are completed by the authors of this paper following the theory presented by Skiadas and Skiadas in (2018a, b, 2020a, b, c). The life table applications provide important information for the health of the population. However, more information is provided by estimating not only the life expectancy but also the healthy life expectancy and the healthy life years lost and the disability percentage, by expanding the provided life tables as we do in the present paper (Fig. 1.1). C. H. Skiadas () ManLab, Technical University of Crete, Crete, Greece e-mail: [email protected] Y. Dimotikalis Department of Management Science and Technology, Hellenic Mediterranean University, Crete, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_1

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C. H. Skiadas and Y. Dimotikalis

Fig. 1.1 Full Expanded Life Table with Disability Section and Sullivan Section for the Healthy Life Expectancy estimation for males in 2019 in Czechia. The Life Table is provided by the HMD. The first five columns are included in the HMD life table and the rest sixteen columns are completed by the authors of this paper following the theory presented by Skiadas and Skiadas in (2018a, b, 2020a, b, c)

1 Expanding the Life Tables to Include the Healthy Life Expectancy

5

The Life Table for Czechia is provided from the Human Mortality Database. Ten columns are provided starting from the age column, the number of persons dx died in the interval (x, x + 1), the probability qx dying in (x, x + 1), the Mean fraction ax of last year of life lived by persons died in (x, x + 1), the Number of personyears Lx lived in (x, x + 1), the Number of person-years Tx lived beyond x and the Life expectancy ex at x. This is the classical Life Table provided for the human population. A few years ago, we expanded this life table to include the estimates of the Proportion with Disability, followed by four columns for the Sullivan Method (see Jagger et al., 2014) to estimate the Healthy Life Expectancy (HLE) and the Healthy Life Years Lost (HLYL). First, we calculate the years of disability influence at age x (YDIx) as Y DI x =

(x + ax ) dx x 0 qx

Figure 1.2 illustrates the form of the curve expressing the years with disability influence adopted for persons in Czechia. Then the Healthy Life Years Lost Indicator bx is calculated by dividing the YDIx by lx, the numbers of people living at x. bx =

Y DI x lx

The last formula is equal to the following to calculate to proportion with disability to form the Healthy Life Years Lost Indicator: bx =

(x + ax ) qx x 0 qx

Fig. 1.2 Years of Disability Influence at age x to calculate bx

6

C. H. Skiadas and Y. Dimotikalis

Fig. 1.3 Healthy Life Years Lost Indicator bx and maximum level

This formula provides the average of dying probability qx over the mean probability at age x (Fig. 1.3). The next column provides the disability parameter kD so that the maximum of bx = 8.51 for males in Czechia in 2019 is the Healthy Life Years Lost (HLYL) = 8.51 at age (0–1) years. The proportion with disability (PxD) is P xD = kbx After this stage the Person Years Lived without Disability (LxD) are estimated with the Sullivan method as LxD = (1 − kbx ) Lx The Total Years Lived without Disability (TxD) are then provided in the next column. The Disability Free Life Expectancy or the Healthy Life Expectancy (HLE) at age x is given by H LEx =

T xD lx

And the Healthy Life Years Lost (HLYL) at age x are provided by H LY Lx = LEx − H LEx Where the life expectancy at age x is LEx = ex.

1 Expanding the Life Tables to Include the Healthy Life Expectancy

7

The Survival vs Mortality space graph is used to provide bx to form the Healthy Life Years Lost Indicator. More information and details for the formula needed to estimate the healthy life years lost appear in several papers by Skiadas and Skiadas (2018a, b, 2020a, b, c). The survival curve Lx and the disability-free survival LxD are provided in Fig. 1.1 and illustrated in Fig. 1.4 for males and females the 2019 in Czechia. The space between the survival curve and the disability free survival curve (with orange color) corresponds to the disability period for males, while the space below the disability free survival curve (blue curve) is the healthy period for males in 2019. Figure 1.5a illustrate the Life Expectancy and the Healthy Life Expectancy for males in Spain in the period 1908–2020. A clear decline appears in 1918 pandemic and the 1936–1939 period. The Healthy Life Years Lost are illustrated in Fig. 1.5b with a sharp decline in 1918 pandemic. Another decline in 2019–2020 is due to covid-19 pandemic (Figs. 1.6, 1.7, 1.8 and 1.9).

Fig. 1.4 Survival Curve and Disability Free Survival for males and females in Czechia, 2019

a

b

LE and HLE in Spain, males (1908-2020) 90,00

9,00

70,00 60,00 50,00

LE

40,00

HLE

30,00

Age x (Years)

Age x (Yeas)

80,00

20,00 1900

HLYL in Spain, males (1908-2020) 10,00

8,00 7,00 6,00 5,00 4,00 1900

1920

1940

1960 Year

1980

2000

1920

1940

1960

1980

2000

2020 Year

Fig. 1.5 (a) LE, HLE in Spain, males (1908–2020). (b) HLYL in Spain, males (1908–2020)

2020

8

C. H. Skiadas and Y. Dimotikalis

Fig. 1.6 Full Expanded Life Table with Disability Section and Sullivan Section for males in Spain, 1908

1 Expanding the Life Tables to Include the Healthy Life Expectancy

9

Fig. 1.7 Full Expanded Life Table with Disability Section and Sullivan Section for males in France, 1816

10

C. H. Skiadas and Y. Dimotikalis

Fig. 1.8 Full Expanded Life Table with Disability Section and Sullivan Section for females in Australia, 1921

1 Expanding the Life Tables to Include the Healthy Life Expectancy

11

Fig. 1.9 Full Expanded Life Table with Disability Section and Sullivan Section for males in Canada, 1921

12

C. H. Skiadas and Y. Dimotikalis

1.2 Summary and Conclusions Our study has produced the expanded life tables for Czechia and other countries (Spain, France, Australia and Canada), providing annual life expectancy and healthy life expectancy for the population. The construction and application of expanded form of life tables offers great support for the health and welfare sciences. Expanded life tables generated in the current study promote not only a better understanding of the life span and related health status, but also offer several applications for the healthy life estimation and research to improve the health and welfare professions. A main achievement was the presentation of the disability space for health state with characteristic graphs.

References Jagger, C., Van Oyen, H., & Robine, J.-M. (2014). Health expectancy calculation by the Sullivan method: A practical guide. Institute for Ageing, Newcastle University. Skiadas, C. H., & Skiadas, C. (2018a). The health-mortality approach in estimating the healthy life years lost compared to the global burden of disease studies and applications in world, USA and Japan. In Exploring the health state of a population by dynamic modeling methods (The Springer series on demographic methods and population analysis) (Vol. 45, pp. 67–124). Springer. https://doi.org/10.1007/978-3-319-65142-2_4 Skiadas, C. H., & Skiadas, C. (2018b). Demography and health issues: Population aging, mortality and data analysis (The Springer series on demographic methods and population analysis) (Vol. 46). Springer. https://doi.org/10.1007/978-3-319-76002-5 Skiadas, C. H., & Skiadas, C. (2020a). Relation of the Weibull shape parameter with the healthy life years lost estimates: Analytical derivation and estimation from an extended life table. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures (The Springer series on demographic methods and population analysis) (Vol. 50). Springer. https://doi.org/10.1007/978-3-030-44695-6_2 Skiadas, C. H., & Skiadas, C. (2020b). Direct healthy life expectancy estimates from life tables with a Sullivan extension. Bridging the gap between HALE and Eurostat estimates. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures (The Springer series on demographic methods and population analysis) (Vol. 50). Springer. https://doi.org/10.1007/978-3-030-44695-6_3 Skiadas, C. H., & Skiadas, C. (2020c). How the unsolved problem of finding the Healthy Life Expectancy (HLE) in the far past was resolved: The case of Sweden (1751–2016) with forecasts to 2060 and comparisons with HALE. https://doi.org/10.31235/osf.io/akf8v Sullivan, D. F. (1971). A single index of mortality and morbidity. Health Services Mental Health Administration Health Reports, 86, 347–354.

Chapter 2

The Direct Healthy Life Expectancy Estimates from Life Tables to Support HALE Measures Done by the World Health Organization. A New Tool for a Standard Measure Christos H. Skiadas

2.1 General Healthy life expectancy (HALE) at birth is an important indicator of health status and quality of life of a country’s population. The data provided by WHO for the years 2000, 2005, 2010, 2015 and 2016 for males and females and termed here as HALE-2016 are used for comparisons with the Direct HLE estimation. Later on, WHO provided updated estimates for the years 2000, 2010, 2015 and 2019 for males and females here termed as HALE-2019 see at https://apps.who.int/ gho/data/view.main.HALEXv?lang=eralen. Both estimates differ considerably for several countries in the HALE calculations. Another work providing HLE for the years 2005 and 2015 for males and females, here termed as HALE-2015, appears in The Lancet as “GBD 2015 DALYs and HALE Collaborators (2016). Global, regional, and national disability-adjusted lifeyears (DALYs) for 315 diseases and injuries and healthy life expectancy (HALE), 1990–2015: a systematic analysis for the Global Burden of Disease Study 2015. Lancet 2016; 388: 1603–58 (p 1620).” These three particular HALE measures, provided after continuous updates of the related methodology, are considered as the most appropriate to test our “Direct Methodology” for providing a standard measure for the Healthy Life Expectancy (HLE). We have used the country life table data sets from Human Mortality

C. H. Skiadas () ManLab, Technical University of Crete, Crete, Greece ISAST International, Athens, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_2

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Database (HMD) to estimate the Healthy Life Years Lost (HLYL) and then the HLE = LE-HLYL where (LE) is the Life Expectancy.

2.2 The Uncertainty Interval (UI) Particular importance is related to the uncertainty interval when estimating HALE. The 95% uncertainty interval usually adopted provides large deviations from the HALE value assessed. For Japanese females in 2005, the HALE is estimated at 75.43 years of age with (72.48–77.97) UIs from HALE-2015 paper, whereas from the same source, the HALE for females in Japan in 2015 is 76.28 years of age with a (73.33–78.85) UIs. The related estimates for males in Japan are 70.32 years for 2005 with (67.99–72.38) UIs and 71.54 years for 2015 with (69.14–73.67) UIs instead, our “Direct Estimates” based on HMD life tables provide a unique number for HLE as a standard measure, which is 74.49 and 75.20 years of age for Japanese females in 2005 and 2015 respectively, and HLE at 69.50 and 70.94 years of age for males in 2005 and 2015 respectively. Clearly, our estimates lie within the ULs provided by HALE-2015 estimates. Over the years, the HALE estimates have been closer and closer to the estimates of our method provided. It is expected, that due to the large number of diseases comprised in the Global Burden of Disease (GBD) methodology, and the many adaptations made at a reasonable level could stabilize at our estimates that provide simple, definite and reproductive figures.

2.3 The HLYL Estimation Method Retrieved from “Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan Extension: The case of Brazil 2003” https://osf.io/preprints/socarxiv/ 4x5et/. The “Direct” Healthy Life Years Lost (HLYL) methodology Skiadas and Skiadas (2020a, b, c) was based on averaging the Health State of a Population by taking into account the deaths/population from the mortality mx and the alive part of the population. A geometric approach of the methodology is presented in the following graph of mortality spaces where both mortality and survival are presented as corresponding areas. We use the Life Tables provided from the Human Mortality Database or any other related data base. Mortality is expressed by mx in these tables. In the above graph data from 2003 for the total population in Brazil (Romero et al., 2005) was used. mx is shown as the blue exponential curve. The main forms of Life Tables start with mx and then the survival forms of the population are estimated. This methodology leads to the calculation of a probability measure termed as life expectancy at age x or life expectancy at birth when considering the total life time. There are several differences between the graph with the survival space above and the survival curves

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

15

methodology. First of all, the vertical axis in the Survival-Mortality Space (SMS) diagram is the probability mx . Instead in the survival diagram the vertical axis represent population (usually it starts from 100.000 in most life tables and gradually slow down until the end). By the SMS diagram we have probability spaces for both survival and mortality. For the age x, the total space is (ABCOA) in the SMS diagrams, that is (OC).(BC) = x mx . The mortality space is the sum S(mx ) while the survival space is (xmx − S(mx )). Accordingly, the important measure of the Health State is simply the fraction (ABDOA)/(BCODB). It is simpler to use the fraction (ABCOA)/(BCODB) = xmx /S(mx ) that can be estimated from mx for every age x of the population. In modeling the healthy life years lost to disability some important issues should be realized. Mortality expressed by mx is important for modeling disability but more important is the cumulative mortality S (mx ) which, as an additive process, is more convenient for the estimation of the healthy life years lived with disability and the deterioration process causing deaths. The estimates for this type of mortality are included in the term bx S (mx ). The approach in previous publications (Skiadas & Skiadas, 2018a, b, c, 2020a, b, c) was to set a time-varying fraction bx for Health/Mortality of the form: xmx H LY L = bx = max  x 0 ms ds

.

This formula is immediately provided from Fig. 2.1a by considering the fraction: bx =

.

T otal Space OABCO xmx = = x Mortality Space ODBCO 0 ms ds

Fig. 2.1a Healthy Life Years Lost Estimates Survival vs Mortality space graph

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C. H. Skiadas

The main hypothesis is that the population involved in the deterioration process is a fraction of the total population at age x determined by the level of mortality mx at age x. Accordingly, the mortality process will have two alternatives expressed by the simple equation:  xmx = bx

x

.

ms ds ≈ bx

x

0

0

mx

(2.2)

Clearly, when collecting data by asking people to respond to disability related questions, the answers is expected to be influenced from the previous experience from 0 to x years of age including dead and alive. People comment on their disability in connection to their knowledge from the environment around. In a way, they respond after summarizing, averaging and assessing their knowledge in a way similar to the above methodology. Accordingly, it is not surprising to have similar results for Healthy Life Expectancy and Healthy Life Years Lost from both methods as the “Direct” and Health Adjusted Life Expectancy (HALE) applied by the World Health Organization (WHO). In the latter morbidity is adjusted by a specific parameter for every appropriate cause thus making the final estimate quite complicated. However, several decades of collecting data and applying data sets make HALE a classical tool for estimating the Health State of a Population. However, the HALE methodology turns only few decade years back as far as health data are already collected. For more unexplored health state periods in countries and territories the Direct methodology is appropriate as far as Life Table Data exist.

2.4 Applications Figure 2.1b presents Life Expectancy as a magenta curve from Human Mortality Database (HMD) and our estimates for Healthy Life Expectancy (HLE) for Japanese males from 1950 to 2019 by the Direct method from Life Tables. The WHO estimates for Healthy Life Expectancy termed as HALE are illustrated as well. Three options are provided. The WHO estimates for the years 2000, 2005, 2010, 2015 and 2016 as HALE-2016 in the graphs and for the years 2000, 2010, 2015 and 2019 termed as HALE-2019. The latter is the newer estimate to update-correct the previous one. However, a Standard estimates basis is needed to compare the new updates calculated. The HLE estimates from the life tables are based on the formula xmx H LY L = max  x 0 ms ds

.

Where mx is the mortality at age x and the HLE = LE-HLYL. Our proposed HLE provided by the blue curve in the graph is ideal as a standard basis. The HALE-2019 (red bullets) for Japanese males is closer to our HLE estimates than HALE-2016 (green bullets). Furthermore, the HALE-2015 estimates appear as blue squares. In

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

17

Japan, Complete life tables, Males 85

Years of Age

80 75 70 LE HLE HALE-2015 HALE-2016 HALE-2019

65 60 55

50 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020

Calendar Year Fig. 2.1b LE, HLE, HALE-2015, HALE-2016 and HALE-2019 estimates for Japanese males from 1950 to 2019

the following graphs for several countries, the two HALE options are demonstrated. In the majority of cases, an update based on HALE-2019 is needed. In almost all cases, both HALE-2016 and HALE-2019 do not cross the HLE curve. They stay on the same side of the HLE curve or in both sides following the HLE curve’s direction. In the latter case, the average of HALE-2016 and HALE-2019 tends to approach the HLE curve. The estimates are illustrated in Figs. 2.2 to 2.35 with related comments and summarized in Table 2.1 for males and females with data provided by the Human Mortality Database for the Life Tables. For every case of HALE, HALE-2015, HALE-2016 and HALE-2019 the mean distance from our estimate curve is calculated. In all cases, except USA females, the mean distance is lower than 1 year of age. The mean distance for males is lower than half of a year for 28 cases and larger than half a year and lower than 1 year for 5 cases. The mean distance for females is lower than half of a year for 27 cases and larger than half year and lower than 1 year for 5 cases. Only for United States females the mean distance is 1.315 years of age. Following these findings, our “Direct Estimates” are very close to the HALE measures, thus providing a simple and strong alternative for replacing the HALE measures not only when no available GBD data exists but also as a general estimate applied (Fig. 2.2). A slight improvement was made for Japanese male HALE-2015 whereas the related HALE-2019 for females (red bullets) fit almost perfectly to our direct estimates (see blue curve) (Fig. 2.2).

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C. H. Skiadas

Japan, Complete life tables, Females

Japan, Complete life tables, Males 73 71

Years of Age

Years of Age

72 70

69

HLE HALE-2015 HALE-2016 HALE-2019

68 67 66 1990

1995

2000

2005 Year

2010

2015

2020

(a)

78 77 76 75 74 73 72 71 70 1990

HLE HALE-2015 HALE-2016 HALE-2019

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.2 (a) HLE and HALE for Japanese males. (b) HLE and HALE for Japanese females Australia, Complete life tables, Females 75 74

Years of Age

Years of Age

Australia, Complete life tables, Males 73 72 71 70 69 68 67 66 65 64 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

72 71 HLE HALE-2015 HALE-2016 HALE-2019

70 69 68 67 1990

2020

(a)

73

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.3 (a) HLE and HALE for Australian males. (b) HLE and HALE for Australian females Austria, Complete life tables, Males

Austria, Complete life tables, Females

70 68 HLE HALE-2015 HALE-2016 HALE-2019

66 64 62 1990

(a)

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

72

2020

75 74 73 72 71 70 69 68 67 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.4 (a) HLE and HALE for Austrian males. (b) HLE and HALE for Austrian females

Australian male updates for HALE-2015 are very close to the HLE estimates (blue curve). A good correction should be the average of both HALE-2016 and HALE-2019. HALE-2016 is almost perfect for females, whereas the update for HALE-2019 is far away from the HLE curve (blue line) (Fig. 2.3). A perfect update with a HALE-2019 correction for Austrian males and a perfect HALE-2015 position for Austrian females (Fig. 2.4).

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

Belarus, Complete life tables, Females 71

61

69

59

Years of Age

Years of Age

Belarus, Complete life tables, Males 63

57 HLE HALE-2016 HALE-2019 HALE-2015

55 53

51 49 1990

1995

2000

2005 Year

2010

19

2015

65

HLE HALE-2016 HALE-2019 HALE-2015

63 61 59 1990

2020

(a)

67

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.5 (a) HLE and HALE for Belarusian males. (b) HLE and HALE for Belarusian females Belgium, Complete life tables, Females 74

70

73

69

72

68 67

HLE HALE-2015 HALE-2016 HALE-2019

66 65 64 1990

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

Belgium, Complete life tables, Males 71

71 70

HLE HALE-2015 HALE-2016 HALE-2019

69 68 67 1990

2020

1995

2000

2005

2010

2015

2020

Year

(a)

(b)

Fig. 2.6 (a) HLE and HALE for Belgian males. (b) HLE and HALE for Belgian females

64

69

63 62

HLE HALE-2016 HALE-2019 HALE-2015

61 60

59 58 1990

(a)

Bulgaria, Complete life tables, Females 70

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

Bulgaria, Complete life tables, Males 65

68 67

HLE HALE-2016 HALE-2019 HALE-2015

66 65

64 63 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.7 (a) HLE and HALE for Bulgarian males. (b) HLE and HALE for Bulgarian females

A perfect HALE-2016 and HALE-2016 for Belarusian males and a perfect HALE-2016 and HALE-2019 for Belarusian females (Fig. 2.5). A perfect update for Belgian males with HALE-2019 (see red bullets). Not needed update for Belgian females as the HALE-2016 estimates (green bullets) are very close to HLE (bleu curve) whereas HALE-2019 estimates are far away (see red bullets). Better is the HALE-2015 estimate (Fig. 2.6).

20

C. H. Skiadas

Canada, Complete life tables, Females 75

71

74

Years of Age

Years of Age

Canada, Complete life tables, Males 73

69 HLE HALE-2015 HALE-2016 HALE-2019

67 65 63 1990

1995

2000

2005 Year

2010

2015

73 72 71

HLE HALE-2015 HALE-2016 HALE-2019

70 69 68 1990

2020

(a)

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.8 (a) HLE and HALE for Canadian males. (b) HLE and HALE for Canadian females Croaa, Complete life tables, Females 72

66

71

65 HLE HALE-2016 HALE-2019 HALE-2015

64 63 62 2000

2005

2010 Year

2015

Years of Age

Years of Age

Croaa, Complete life tables, Males 67

69

HLE HALE-2016 HALE-2019 HALE-2015

68 67 66 2000

2020

(a)

70

2005

2010 Year

2015

2020

(b)

Fig. 2.9 (a) HLE and HALE for Croatian males. (b) HLE and HALE for Croatian females

(a)

Czechia, Complete life tables, Females

Years o f Age

Years of Age

Czechia, Complete life tables, Males 68 67 66 65 64 63 62 61 60 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

72 71 70 69 68 67 66 65 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.10 (a) HLE and HALE for Czech males. (b) HLE and HALE for Czech females

A perfect update for Bulgarian males with HALE-2019 (see red bullets). A perfect update for Bulgarian females as the HALE-2019 estimates (red bullets) are very close to HLE (bleu curve) (Fig. 2.7). A perfect update for Canadian males with HALE-2019 (see red bullets). Not needed update for Canadian females as the HALE-2016 estimates (green bullets)

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

Denmark, Complete life tables, Females

Denmark, Complete life tables, Males 72

HLE HALE-2015 HALE-2016 HALE-2019

66 64 62 1990

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

70

68

2020

(a)

21

74 73 72 71 70 69 68 67 66 65 1990

HLE HALE-2015 HALE-2016 HALE-2019

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.11 (a) HLE and HALE for Danish males. (b) HLE and HALE for Danish females Estonia, Complete life tables, Females

Estonia, Complete life tables, Males 68 72

64 62

HLE HALE-2016 HALE-2019 HALE-2015

60 58

56 54 1990

1995

2000

2005 Year

2010

2015

Years o f Age

Years of Age

66

HLE HALE-2016 HALE-2019 HALE-2015

68 66 64 1990

2020

(a)

70

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.12 (a) HLE and HALE for Estonian males. (b) HLE and HALE for Estonian females Finland, Complete life tables, Females

(a)

74 73

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

Years o f Age

Years of Age

Finland, Complete life tables, Males 71 70 69 68 67 66 65 64 63 62 1990

72 71 HLE HALE-2015 HALE-2016 HALE-2019

70 69 68 1990

2020

1995

2000

2005

2010

2015

2020

Year

(b)

Fig. 2.13 (a) HLE and HALE for males in Finland. (b) HLE and HALE for females in Finland

are very close to HLE (bleu curve) whereas HALE-2019 estimates are far away (see red bullets) (Fig. 2.8). A perfect HALE-2016 and HALE-2019 for Croatian males (see green and red bullets). Not needed update for Italian females as the HALE-2016 estimates (green

22

C. H. Skiadas

France, Complete life tables, Males

France, Complete life tables, Females

74

Years of Age

Years of Age

72 70

68 HLE HALE-2015 HALE-2016 HALE-2019

66 64 62 1990

1995

2000

2005 Year

2010

2015

2020

(a)

76 75 74 73 72 71 70 69 68 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.14 (a) HLE and HALE for French males. (b) HLE and HALE for French females Germany, Complete life tables, Females 74

70

72

Years of Age

Years of Age

Germany, Complete life tables, Males 72

68 HLE HALE-2016 HALE-2019 HALE-2015

66 64 62 60 1990

1995

2000

2005 Year

2010

2015

HLE HALE-2016 HALE-2019 HALE-2015

68 66 64 1990

2020

(a)

70

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.15 (a) HLE and HALE for German males. (b) HLE and HALE for German females

70

73

69 68

HLE HALE-2016 HALE-2019 HALE-2015

67 66 65 1990

(a)

Greece, Complete life tables, Females 74

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

Greece, Complete life tables, Males 71

72 71 HLE HALE-2016 HALE-2019 HALE-2015

70 69 68 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.16 (a) HLE and HALE for Greek males. (b) HLE and HALE for Greek females

bullets) and HALE-2019 (red bullets) are very close to HLE (bleu curve). The same is for HALE-2015 (Fig. 2.9). An almost perfect fit for Czech males for both HALE-2016 and HALE-2019. No need for an update for females as HALE-2016 provides a good fit (see green bullets) (Fig. 2.10).

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

23

Hungary, Complete life tables, Females

Hungary, Complete life tables, Males 71

66 Years of Age

Years of Age

70

64 62 HLE HALE-2016 HALE-2019 HALE-2015

60 58

56 1990

1995

2000

2005 Year

2010

2015

69 68

HLE HALE-2016 HALE-2019 HALE-2015

67 66

65 1990

2020

(a)

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.17 (a) HLE and HALE for Hungarian males. (b) HLE and HALE for Hungarian females Ireland, Complete life tables, Females 74 73

Years of Age

Years of Age

Ireland, Complete life tables, Males 72 71 70 69 68 67 66 65 64 63 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

72 71 70 HLE HALE-2015 HALE-2016 HALE-2019

69 68 67 66 1990

2020

(a)

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.18 (a) HLE and HALE for Irish males. (b) HLE and HALE for Irish females Israel, Complete life tables, Females

Israel, Complete life tables, Males 75

74

70

HLE HALE-2016 HALE-2019 HALE-2015

68 66 64 1990

(a)

1995

2000

2005 Year

2010

2015

Years o f Age

Years of Age

72

73 72 71

HLE HALE-2016 HALE-2019 HALE-2015

70

69 68 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.19 (a) HLE and HALE for Israeli males. (b) HLE and HALE for Israeli females

A slight update for Danish males (see red bullets for HALE-2019) The HALE2015 fits better. No need an update for Danish females as HALE-2016 (green bullets) almost perfectly fits with HLE (bleu curve) (Fig. 2.11).

24

C. H. Skiadas

Italy, Complete life tables, Females 75 74

Years of Age

Years of Age

Italy, Complete life tables, Males 73 72 71 70 69 68 67 66 65 64 1990

HLE

HALE-2015

1995

2000

2005 Year

73 72

70

HALE-2019

69

2010

2015

68 1990

2020

(a)

HLE HALE-2015 HALE-2016 HALE-2019

71

HALE-2016

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.20 (a) HLE and HALE for Italian males. (b) HLE and HALE for Italian females Latvia, Complete life tables, Females

Latvia, Complete life tables, Males 64

60 58

HLE HALE-2016 HALE-2019 HALE-2015

56 54 52 1990

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

62

2020

(a)

71 70 69 68 67 66 65 64 63 1990

HLE HALE-2016 HALE-2019 HALE-2015 1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.21 (a) HLE and HALE for Latvian males. (b) HLE and HALE for Latvian females Lithuania, Complete life tables, Females

Lithuania, Complete life tables, Males 71 70

61

59

HLE HALE-2016 HALE-2019 HALE-2015

57 55 1990

(a)

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

63

69 68

HLE HALE-2016 HALE-2019 HALE-2015

67 66 65 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.22 (a) HLE and HALE for Lithuanian males. (b) HLE and HALE for Lithuanian females

A slight update for Estonian males (see red bullets for HALE-2019) The HALE2015 fits better. A slight update for Estonian females is needed for both HALE-2016 (green bullets) and HALE-2019 (red bullets) (Fig. 2.12). A slight update for males in Finland (see red bullets for HALE-2019) The HALE-2015 fits better. A slight update for females in Finland is needed for both

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

Luxembourg, Complete life tables, Females 74 73

Years of Age

Years of Age

Luxembourg, Complete life tables, Males 72 71 70 69 68 67 66 65 64 63 1990

25

HLE HALE-2016

72 71 HLE HALE-2016 HALE-2019 HALE-2015

70

HALE-2019 69

HALE-2015 1995

2000

2005 Year

2010

2015

68 1990

2020

(a)

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.23 (a) HLE and HALE for Luxembourg males. (b) HLE and HALE for Luxembourg females

Netherlands, Complete life tables, Females

Netherlands, Complete life tables, Males 72

74 73

70

Years of Age

Years of Age

71 69

68

HLE HALE-2015 HALE-2016 HALE-2019

67 66

65 64 1990

1995

2000

2005 Year

2010

2015

72 71

HLE HALE-2015 HALE-2016 HALE-2019

70 69 68 1990

2020

(a)

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.24 (a) HLE and HALE for males in Netherlands. (b) Female HLE and HALE in Netherlands

Norway, Complete life tables, Females

Norway, Complete life tables, Males 73

69 HLE HALE-2015 HALE-2016 HALE-2019

67

65 63 1990

(a)

Years of Age

Years of Age

71

1995

2000

2005 Year

2010

2015

2020

75 74 73 72 71 70 69 68 67 66 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.25 (a) HLE and HALE for Norwegian males. (b) HLE and HALE for Norwegian females

26

C. H. Skiadas

Poland, Complete life tables, Females

Poland, Complete life tables, Males 72 71

64

HLE HALE-2016 HALE-2019 HALE-2015

62 60 58 1990

1995

2000

2005 Year

2010

2015

Years of Age

Years of Age

66

69

HLE HALE-2016 HALE-2019 HALE-2015

68 67 66 1990

2020

(a)

70

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.26 (a) HLE and HALE for Polish males. (b) HLE and HALE for Polish females Portugal, Complete life tables, Females

Years of Age

Years of Age

Portugal, Complete life tables, Males 71 70 69 68 67 66 65 64 63 62 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

(a)

75 74 73 72 71 70 69 68 67 66 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.27 (a) HLE and HALE for Portuguese males. (b) HLE and HALE for Portuguese females Slovakia, Complete life tables, Females 72

66

71

64

62

HLE HALE-2015 HALE-2016 HALE-2019

60 58 56 1990

(a)

Years of Age

Years of Age

Slovakia, Complete life tables, Males 68

1995

2000

2005 Year

2010

2015

70 69 HLE HALE-2015 HALE-2016 HALE-2019

68

67 66 65 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.28 (a) HLE and HALE for Slovak males. (b) HLE and HALE for Slovak females

HALE-2016 (green bullets) and HALE-2019 (red bullets). HALE-2015 fits better (Fig. 2.13). A slight update for French males (see red bullets for HALE-2019). The HALE2015 fits better. An update for French females is needed for both HALE-2016 (green bullets) and HALE-2019 (red bullets). HALE-2015 fits better (Fig. 2.14).

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

27

Slovenia, Complete life tables, Females

Slovenia, Complete life tables, Males 74

73

67

HLE HALE-2016 HALE-2019 HALE-2015

65 63 61 1990

1995

2000

2005 Year

2010

2015

Years o f Age

Years of Age

69

71

HLE HALE-2016 HALE-2019 HALE-2015

70 69

68 67 1990

2020

(a)

72

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.29 (a) HLE and HALE for Slovenian males. (b) HLE and HALE for Slovenian females Slovenia, Complete life tables, Females

Slovenia, Complete life tables, Males 74

73

67

HLE HALE-2016 HALE-2019 HALE-2015

65 63 61 1990

1995

2000

2005 Year

2010

2015

Years o f Age

Years of Age

69

71

HLE HALE-2016 HALE-2019 HALE-2015

70 69

68 67 1990

2020

(a)

72

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.30 (a) HLE and HALE for Slovenian males. (b) HLE and HALE for Slovenian females Spain, Complete life tables, Females

(a)

76 75

Years of Age

Years of Age

Spain, Complete life tables, Males 73 72 71 70 69 68 67 66 65 64 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

74

73 72

HLE HALE-2015 HALE-2016 HALE-2019

71 70 69 68 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.31 (a) HLE and HALE for Spanish males. (b) HLE and HALE for Spanish females

A slight update for German males (see red bullets for HALE-2019). The HALE2015 fits better. An update for German females is needed for both HALE-2016 (green bullets) and HALE-2019 (red bullets). HALE-2015 fits better (Fig. 2.15). A good update for Greek males (see red bullets for HALE-2019). The HALE2015 fits well. An update for Greek females is needed for both HALE-2016 (green bullets) and HALE-2019 (red bullets). HALE-2015 fits better (Fig. 2.16).

28

C. H. Skiadas

Sweden, Complete life tables, Females 74

73 Years of Age

Years of Age

Sweden, Complete life tables, Males 73 72 71 70 69 68 67 66 65 64 1990

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

72 HLE

70

HALE-2015 HALE-2016

69

HALE-2019

68 1990

2020

(a)

71

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.32 (a) HLE and HALE for Swedish males. (b) HLE and HALE for Swedish females Switzerland, Complete life tables, Females

Switzerland, Complete life tables, Males 74

75

74 Years of Age

Years of Age

72 70 HLE HALE-2015 HALE-2016 HALE-2019

68 66 64 1990

1995

2000

2005 Year

2010

2015

73 72

71

HLE HALE-2015 HALE-2016 HALE-2019

70 69

68 1990

2020

(a)

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.33 (a) HLE and HALE for Swiss males. (b) HLE and HALE for Swiss females United Kingdom, Complete life tables, Females 74

71

73

70

72

Years of Age

Years of Age

United Kingdom, Complete life tables, Males 72

69 68 HLE

67

HALE-2015

66 64 1990

2000

2005

2010

2015

66 1990

2020

Year

(a)

HLE HALE-2015 HALE-2016 HALE-2019

69 67

HALE-2019

1995

70 68

HALE-2016

65

71

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.34 (a) HLE and HALE for UK males. (b) HLE and HALE for UK females

A good update for Hungarian males (see red bullets for HALE-2019). The HALE-2015 fits well. An update for Hungarian females is done (see HALE-2019 red bullets) (Fig. 2.17).

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

United States, Complete life tables, Females 74 72 Years of Age

Years of Age

United States, Complete life tables, Males 69 68 67 66 65 64 63 62 61 60 1990

29

HLE HALE-2015 HALE-2016 HALE-2019 1995

2000

2005 Year

2010

2015

(a)

70 68 66

HLE HALE-2015 HALE-2016 HALE-2019

64 62

60 1990

2020

1995

2000

2005 Year

2010

2015

2020

(b)

Fig. 2.35 (a) HLE and HALE for US males. (b) HLE and HALE for US females Table 2.1 Three HALE updates compared Country

AUSTRALIA AUSTRIA BELARUS BELGIUM BULGARIA CANADA CROATIA CZECHIA DENMARK ESTONIA FINLAND FRANCE GERMANY GREECE HUNGARY IRELAND ISRAEL ITALY JAPAN LATVIA LITHUANIA LUXEMBOURG NETHERLANDS NORWAY POLAND

Males HALE2016 0.969 1.370 0.472 1.072 0.472 1.251 0.227 0.136 1.193 0.502 0.768 1.961 1.109 1.080 0.393 1.145 0.468 1.271 1.248 0.219 0.417 1.138 1.173 1.391 0.397

HALE2019 0.719 0.366 0.419 0.153 0.419 0.184 0.308 0.224 0.876 0.470 0.503 1.312 0.846 0.323 0.224 0.544 0.367 0.324 0.946 0.329 0.735 0.959 1.057 0.407 0.252

HALE2015 0.213 0.455 2.147 0.167 2.147 0.458 0.081 0.215 0.160 0.469 0.164 0.329 0.571 0.497 0.323 0.592 0.282 0.385 0.714 0.072 0.055 0.272 0.247 0.226 0.486

Females HALE2016 0.403 1.293 0.597 0.455 0.796 0.517 0.802 0.222 0.359 0.332 0.639 0.757 0.601 0.673 0.346 0.385 0.789 0.693 1.347 0.165 0.284 0.647 0.568 1.099 0.153

HALE2019 1.975 0.539 0.784 1.393 0.165 1.531 0.160 0.529 1.463 0.470 0.861 0.887 0.981 0.931 0.213 1.336 1.023 1.200 0.189 0.616 0.467 1.210 0.627 1.293 0.338

HALE2015 0.751 0.257 1.317 0.202 0.406 0.967 0.624 0.462 0.815 0.485 0.378 0.150 0.288 0.411 0.958 0.540 0.351 0.291 1.011 0.332 0.405 0.544 0.344 0.483 0.264 (continued)

30

C. H. Skiadas

Table 2.1 (continued) Country

PORTUGAL SLOVAKIA SLOVENIA SPAIN SWEDEN SWITZERLAND UK USA

Males HALE2016 1.247 0.141 0.556 1.504 1.337 1.387 0.991 0.269

HALE2019 0.400 0.247 0.385 0.325 1.065 0.852 0.247 1.885

HALE2015 0.281 0.424 0.114 0.532 0.694 0.853 0.338 0.607

Females HALE2016 0.585 0.691 0.292 1.202 0.484 0.859 0.338 1.315

HALE2019 1.493 0.157 0.366 1.280 0.928 0.640 1.947 4.045

HALE2015 0.743 0.613 0.728 0.462 0.205 0.592 0.374 2.039

A good update for Irish males (see red bullets for HALE-2019). No need an update for Irish females (see HALE-2016 green bullets). The HALE-2015 fits well (Fig. 2.18). A small update for Israeli males (see red bullets for HALE-2019). No need an update for Israeli females (see HALE-2016 green bullets). The HALE-2015 fits well (Fig. 2.19). A perfect update for Italian males with HALE-2019 (see red bullets). Not needed update for Italian females as the HALE-2016 estimates (green bullets) are very close to HLE (bleu curve) whereas HALE-2019 estimates are away (see red bullets). A good HALE-2015 fit (Fig. 2.20). A perfect update for Latvian males with HALE-2019 (see red bullets). Not needed update for Latvian females as the HALE-2016 estimates (green bullets) are very close to HLE (bleu curve) whereas HALE-2019 estimates are away (see red bullets). A good HALE-2015 fit (Fig. 2.21). A good update for Lithuanian males with HALE-2019 (see red bullets). Not needed update for Lithuanian females as the HALE-2016 estimates (green bullets) are very close to HLE (bleu curve) whereas HALE-2019 estimates are away (see red bullets). A good HALE-2015 fit (Fig. 2.22). A good update for Luxembourg males with HALE-2019 (see red bullets). Not needed update for Luxembourg females as the HALE-2016 estimates (green bullets) are very close to HLE (bleu curve) whereas HALE-2019 estimates are away (see red bullets). A good HALE-2015 fit (Fig. 2.23). No improvement for males in Netherlands. HALE-2015 fits better. The best update for females should be the average of HALE-2016 and HALE-2019 (Fig. 2.24). A perfect update for Norwegian males with HALE-2019 (see red bullets). HALE2015 perfectly fit. The best update for females should be the average of HALE-2016 and HALE-2019. HALE-2015 better fit (Fig. 2.25). A perfect update for Polish males with HALE-2019 (see red bullets). HALE2015 perfectly fit. The best update for females should be the average of HALE-2016 and HALE-2019. HALE-2015 better fit (Fig. 2.26).

2 The Direct Healthy Life Expectancy Estimates from Life Tables to Support. . .

31

A perfect update for Portuguese males with HALE-2019 (see red bullets). HALE-2015 perfectly fit. The best update for females should be the average of HALE-2016 and HALE-2019. HALE-2015 better fit (Fig. 2.27). A perfect update for Slovak males with HALE-2019 (see red bullets). HALE2015 perfectly fit. The best update for females is with HALE-2019 (Fig. 2.28). A perfect update for Slovenian males with HALE-2019 (see red bullets). HALE2015 perfectly fit. The best update for females is with HALE-2019 (Fig. 2.29). A perfect update for Slovenian males with HALE-2019 (see red bullets). HALE2015 perfectly fit. The best update for females is with HALE-2019 (Fig. 2.30). A perfect update for Spanish males with HALE-2019 (see red bullets). HALE2015 perfectly fit. The best update for females is with HALE-2015 (Fig. 2.31). No significant updates for Swedish males. HALE-2015 fits better. The best update for females should be the average of HALE-2016 and HALE-2019. HALE (Fig. 2.32). A good update for Swiss males (see red bullets for HALE-2019). HALE-2015 fit well. A good update for females after 2010 should be the average of HALE-2016 and HALE-2019. HALE-2015 best fit (Fig. 2.33). An almost perfect update for UK males (see red bullets for HALE-2019). No need for an update for females as HALE-2016 fit well (see green bullets) (Fig. 2.34). An almost perfect fit for US males (see green bullets for HALE-2016). No need for an update for females as HALE-2016 provides a good fit (see green bullets).

2.5 Summary and Conclusions With this work we further demonstrate the usefulness of the Direct estimation of Healthy Life Expectancy from life table data. With the two latest HALE-2016 and HALE-2019 estimates, it was possible to verify the need for use of the “Direct” HLE estimate. Further to the unique and standard estimates provided, thus used to verify the HALE measures, more information is updated when particular health information is missing or no related information can be retrieved from the past.

References GBD 2015 DALYs and HALE Collaborators. (2016). Global, regional, and national disabilityadjusted life-years (DALYs) for 315 diseases and injuries and healthy life expectancy (HALE), 1990–2015: A systematic analysis for the Global Burden of Disease Study 2015. Lancet, 388, 1603–1658. (p 1620). Romero, D. E., Leite, I. C., & Szwarcwald, C. L. (2005). Healthy life expectancy in Brazil: Applying the Sullivan method. SciELO – Scientific Electronic Library Online Cad. Saúde Pública, 21(suppl 1). https://doi.org/10.1590/S0102-311X2005000700002

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Skiadas, C. H., & Skiadas, C. (2018a). Exploring the health state of a population by dynamic modeling methods. In The Springer series on demographic methods and population analysis 45. Springer. https://doi.org/10.1007/978-3-319-65142-2 Skiadas, C. H., & Skiadas, C. (2018b). The Health-mortality approach in estimating the healthy life years lost compared to the global burden of disease studies and applications in world, USA and Japan. In Exploring the health state of a population by dynamic modeling methods (The Springer series on demographic methods and population analysis 45) (pp. 67–124). Springer. https://doi.org/10.1007/978-3-319-65142-2_4 Skiadas, C. H., & Skiadas, C. (2018c). Demography and health issues: Population aging, mortality and data analysis (The Springer series on demographic methods and population analysis 46). Springer. https://doi.org/10.1007/978-3-319-76002-5 Skiadas, C. H., & Skiadas, C. (2020a). Relation of the Weibull shape parameter with the healthy life years lost estimates: Analytical derivation and estimation from an extended life table. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures (The Springer series on demographic methods and population analysis) (Vol. 50). Springer. https://doi.org/10.1007/978-3-030-44695-6_2 Skiadas, C. H., & Skiadas, C. (2020b). Direct healthy life expectancy estimates from life tables with a Sullivan extension. Bridging the gap between HALE and Eurostat estimates. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures (The Springer series on demographic methods and population analysis) (Vol. 50). Springer. https://doi.org/10.1007/978-3-030-44695-6_3 Skiadas, C. H., & Skiadas, C. (2020c). How the unsolved problem of finding the healthy life expectancy (HLE) in the far past was resolved: The case of Sweden (1751–2016) with forecasts to 2060 and comparisons with HALE. https://doi.org/10.31235/osf.io/akf8v WHO. (2016). Life expectancy and healthy life expectancy data provided in Excel.http://apps.who.int/gho/athena/data/GHO/WHOSIS_000001,WHOSIS_000015, WHOSIS_000002,WHOSIS_000007?filter=COUNTRY:*&format=xml&profile=excel WHO. (2019). Provided updated estimates for the years 2000, 2010, 2015 and 2019 for males and females here termed as HALE-2019. See at https://apps.who.int/gho/data/ view.main.HALEXv?lang=eralen

Chapter 3

Expanding the Life Tables for Companion Dogs in UK and Japan to Include the Healthy Life Expectancy Christos H. Skiadas

3.1 Introduction and Model Building We provide a method to expand the Life Tables for Dogs in UK and Japan, to include the Healthy Life Years Lost to Disability (HLYL), to estimate the Proportion with Disability and then apply the Sullivan Method (Sullivan, 1971) to estimate the Disability Free Life Expectancy (DFLE) or the Healthy Life Expectancy (HLE) and the Healthy Life Years Lost (HLYL). The main part of the theory, applied in humans, appears in: Skiadas, C. H., & Skiadas, C. (2020b). Direct healthy life expectancy estimates from life tables with a Sullivan extension. Bridging the gap between HALE and Eurostat estimates. In The Springer series on demographic methods and population analysis 50. Springer. https://doi.org/10.1007/978-3-03044695-6_3. The Life Table is provided by Teng, K. Ty., Brodbelt, D.C., Pegram, C. et al., 2022 in the related paper. The first eight columns are included in the authors’ paper, and the rest eight columns are completed by the author of this paper following the theory presented by Skiadas and Skiadas in 2018a, b, 2020a, b, c. According to the authors (Teng et al., 2022) “Life tables generated by this study allowed a deeper understanding of the varied life trajectory across many types of dogs and offer novel insights and applications to improve canine health and welfare. The current study helps promote further understanding of life expectancy, which will benefit pet owners and the veterinary profession, along with many other sectors.”

C. H. Skiadas () ManLab, Technical University of Crete, Chania, Crete, Greece ISAST International, Athens, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_3

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C. H. Skiadas

Fig. 3.1 Full Expanded Life Table with Disability Section and Sullivan Section for the Healthy Life Expectancy estimation for Companion Dogs in UK. (The Life Table is provided by Teng, K.Ty., Brodbelt, D.C., Pegram, C. et al., 2022 in the related paper. The first eight columns are included in the authors’ paper and the rest eight columns are completed by the author of this paper following the theory presented by Skiadas and Skiadas in 2018a, b, 2020a, b, c)

Both life table applications in the UK and Japan provide important information for the health of dogs. However, more information is provided by estimating not only the life expectancy but also the healthy life expectancy and the healthy life years lost and the disability percentage, by expanding the provided life tables as we do in the present paper. The expanded life tables for companion dogs in the UK and Japan are presented in Fig. 3.1 for the UK and Fig. 3.2 for Japan. The first eight columns are included in the authors’ paper and the rest eight columns are completed by the author of this paper following the theory presented by Skiadas and Skiadas in 2018a, b, 2020a, b, c. The Life Table for companion dogs in the UK is provided in the paper from Teng, K. Ty., Brodbelt, D.C., Pegram, C. et al., 2022. Eight columns are provided starting from the age column, the number of dogs dx died in the interval (x, x + 1), the probability qx dying in (x, x + 1), the Mean fraction ax of last year of life lived by dogs died in [x, x + 1), the Number of dog-years Lx lived in [x, x + 1), the Number of dog-years Tx lived beyond x and the Life expectancy ex at x. This is the classical Life Table provided as well as for the human population. A few years ago we expanded this life table to include the estimates of the Proportion with Disability, followed by four columns for the Sullivan Method to estimate the Healthy Life Expectancy (HLE) and the Healthy Life Years Lost (HLYL). First, we calculate the years of disability influence at age x (YDIx) as Y DI x =

(x + ax ) dx x 0 qx

3 Expanding the Life Tables for Companion Dogs in UK and Japan to Include. . .

35

Fig. 3.2 Full Expanded Life Table with Disability Section and Sullivan Section for the Healthy Life Expectancy estimation for Companion Dogs in Japan. (The Life Table is provided by Inoue, M., Hasegawa, A., Hosoi, Y. & Sugiura, K, 2015 in the related paper. The first eight columns are included in the authors’ paper and the rest eight columns are completed by the author of this paper following the theory presented by Skiadas and Skiadas in 2018a, b, 2020a, b, c)

Years of Disability Influence at Age x 70000

YDIx (Years)

60000 50000 40000 30000 20000 10000 0 0

5

10 Age x (Years)

15

20

Fig. 3.3 Years of disability Influence at age x to calculate bx

Figure 3.3 illustrates the form of the curve expressing the years with disability influence adopted for dogs in the UK. Then the Healthy Life Years Lost Indicator bx is calculated by dividing the YDIx by lx, the numbers of dogs living at x. bx =

Y DI x lx

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C. H. Skiadas

Healthy Life Years Lost Indicator bx 4.000

Indicator bx (Years)

3.500 3.000

2.500 2.000

1.500

bx Indicator

1.000

Maximum bx

0.500 0.000 0

5

10 Age x (Years)

15

20

Fig. 3.4 Healthy life years lost indicator bx and maximum level

The last formula is equal to the following to calculate to proportion with disability to form the Healthy Life Years Lost Indicator: bx =

(x + ax ) qx x 0 qx

This formula provides the average of dying probability qx over the mean probability at age x (Fig. 3.4). The next column provides the disability parameter kD so that the maximum of bx = 3.63 for companion dogs in the UK is the Healthy Life Years Lost (HLYL) = 3.63 at age (0–1) years. The proportion with disability (PxD) is P xD = kbx After this stage the Person Years Lived without Disability (LxD) are estimated with the Sullivan method as LxD = (1 − kbx ) Lx The Total Years Lived without Disability (TxD) are then provided in the next column. The Disability Free Life Expectancy or the Healthy Life Expectancy (HLE) at age x is given by H LEx =

T xD lx

3 Expanding the Life Tables for Companion Dogs in UK and Japan to Include. . .

37

Survival vs Mortality Space for Companion Dogs in UK 1

P ro b ab ilit y o f d y in g q x

0.9 0.8 0.7

A

B

0.6 0.5 0.4

Survival Space

0.3

D

0.2 0.1

Mortality Space

0 1

2

3

4

5

6

7

8

C

9 10 11 12 13 14 15 16 Age x (Years)

Fig. 3.5 Healthy life years lost estimates. (Survival vs. Mortality space graph)

And the Healthy Life Years Lost (HLYL) at age x are provided by H LY Lx = LEx − H LEx Where the life expectancy at age x is LEx = ex (Fig. 3.5). The Survival vs. Mortality space graph is used to provide bx to form the Healthy Life Years Lost Indicator. More information and details for the formula needed to estimate the healthy life years lost appear in several papers by Skiadas and Skiadas in 2018a, b, 2020a, b, c. The survival curve Lx and the disability-free survival LxD are provided in Fig. 3.1 and illustrated in Fig. 3.6 for companion dogs in the UK. The space between the survival curve and the disability free survival curve (with orange color) corresponds to the disability period for dogs, while the space below the disability free survival curve (blue curve) is the healthy period for dogs.

3.2 Morbidity Data “According to “2004 pedigree dog health survey”, the median current age of all live dogs with a reported age (N = 35,907) was 4 years and 10 months (min = 1 month, max = 19 years). Health information was reported for 36,006 live dogs of which 22,540 (62.6%) were healthy and 13,466 (37.4%) had at least one reported health condition, resulting in a total of 22,504 reported conditions with a median of 1 condition/dog (min = 1, max = 14).”

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Survival Curve and Disability Free Survival for Dogs in UK 35,000

Dog Years Lx

30,000 25,000 20,000

Disability Space 32.34%

15,000 10,000

Free Space

5,000

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Disability Space

Age x (Years) Disability Free Space

Fig. 3.6 Survival curve and disability free survival for dogs in UK. (Data from Fig. 3.1)

Following our estimates from the expanded UK life table provided in Fig. 3.1 the dog’s percentage lived with disability is 32.35%. The related fraction for dogs in Japan is 32.65% (see Fig. 3.2). In both cases the disability percentage is extremely high compared to the case in humans, which is around 10% (it is 11.55% for the UK and 11.74% for Japan in 2019). Teng et al. (2022), provided 33 Life Tables for dogs in the UK. We have expanded these life tables to include mortality and morbidity and form the complete expanded life tables as in Fig. 3.1 above. All estimates for LE, HLE, HLYL are provided for every year of age for all the life period. The main companion dog breeds in UK are classified according to the Life Expectancy at birth in Table 3.1. In the same table the Healthy Life Expectancy, Healthy Life Years Lost and Disability Percentage for Companion Dogs in UK are included. The Jack Russell Terrier holds the Life Expectancy record of 12.72 years of age followed by Yorkshire Terrier with 12.54 years. Both are first and second for the Healthy Life Expectancy with 8.46 years for Jack Russell Terrier and 8.18 years for Yorkshire Terrier. French Bulldog is in the last place for life expectancy with 4.55 years of age and 3.00 years for the healthy life expectancy. English Bulldog, Pug and American Bulldog complete the last place group. Chihuahuas have the smaller disability percentage of 29.80%. The larger disability percentage is found in Boxers with 41.21%, followed by Springer Spaniels with 40.62%. Figure 3.7 illustrates the disability space for Chihuahuas (orange color) included between the survival curve and the disability free curve and the space without disability (blue color). The provided disability graph for Chihuahuas is that of a relatively smooth curve of the disability graph that could explain a good behavior in the disability period. Instead, the related disability space for Boxer dogs (Fig. 3.8) is extremely large and with not-so-smooth behavior for the disability survival curve. It is expected a heavy disability period for boxer dogs.

3 Expanding the Life Tables for Companion Dogs in UK and Japan to Include. . .

39

Table 3.1 Life expectancy, healthy life expectancy, healthy life years lost and disability percentage for companion dogs in UK Dog breeds Jack Russell Terrier Yorkshire Terrier Border Collie Terrier Springer Spaniel Crossbred Labrador Retriever Gundog Cocker Spaniel Staffordshire Bull Terrier Pastoral dog Shih-tzu Hound dog Toy dog Cavalier King Charles Spaniel German Shepherd Dog Utility dog Boxer Beagle Husky Working dog Chihuahua American Bulldog Pug English Bulldog French Bulldog

Life expectancy LE 12.72

Healthy life expectancy HLE 8.46

Healthy life years lost HLYL 4.26

Disability percentage (%) 33.46

12.54

8.18

4.36

34.70

12.09

7.65

4.44

36.71

12.03 11.93

8.07 7.08

3.96 4.85

32.88 40.62

11.82 11.78

7.74 7.08

4.02 4.70

34.49 39.88

11.67 11.33

7.16 7.11

4.53 4.22

38.71 37.24

11.33

7.38

3.96

34.90

11.20 11.06 10.71 10.67 10.46

7.44 6.89 6.50 7.36 6.65

3.76 4.17 4.21 3.32 3.81

33.60 37.73 39.28 31.09 37.98

10.19

6.24

3.94

38.69

10.06 10.04 9.84 9.50 9.14 7.93 7.84

6.66 5.90 6.63 6.36 5.70 5.64 4.82

3.39 4.14 3.21 3.14 3.44 2.29 3.02

33.75 41.21 32.65 33.09 37.61 28.90 38.56

7.62 7.39

4.99 4.58

2.62 2.81

34.47 37.98

4.55

3.00

1.55

34.09

40

C. H. Skiadas

Survival Curve and Disability Free Survival for Chihuahuas in UK 500

Dog Years Lx

400 300

Disability Space 28.90%

200

Free Space

100 0 -100

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Age x (Years) Disability Space

Disability Free Space

Fig. 3.7 Survival curve and disability free survival for Chihuahuas in UK. (Data from the expanded life table)

Dog Years Lx

Survival Curve and Disability Free Survival for Boxer dogs in UK 900 800 700 600 500 400 300 200 100 0

Disability Space 42.21%

Free Space

0

1

2

3

4

5

6

Disability Space

7 8 9 Age x (Years)

10

11

12

13

14

15

Disability Free Space

Fig. 3.8 Survival curve and disability free survival for boxer dogs in UK. (Data from the expanded life table)

Figures 3.9a–c illustrate a comparative study of Chihuahua and Boxer. Figure 3.9a results from the classical Life Table providing the Life Expectancy and Fig. 3.9b, c from the expanded life table providing the Healthy Life Expectancy and the Healthy Life Years Lost. The Life Expectancy starts from high levels for Boxer and drops fast compared to Chihuahua’s life expectancy starting from lower level but drops slowly, keeping higher values from boxer after 4 years of age. The clear difference appears in Fig. 3.9b providing the Healthy Life Expectancy where Boxer and Chihuahua start at almost the same level and then the HLE is dropping fast for Boxer while it is almost linear for Chihuahua. This is further demonstrated in Fig. 3.9c where the Healthy Life Years Lost start from high levels for Boxers contrary to Chihuahua starting from low levels for HLYL.

3 Expanding the Life Tables for Companion Dogs in UK and Japan to Include. . .

HLE (Years)

L E ( Y ea r s )

10.00 8.00 6.00 4.00

Healthy Life Expectancy (HLE)

Healthy Life Years Lost (HLYL)

8.00

5.00

HLYL (Years)

Life Expectancy (LE) 12.00

6.00 4.00 2.00

2.00 0

5

10

15

4.00 3.00 2.00 1.00

0.00

0.00

41

0

5

10

Age x (Years)

Age x (Years)

15

0.00 0

5

10

15

Age x (Years) Boxer

Chihuahua

Boxer

Chihuahua

Boxer

Chihuahua

Fig. 3.9 (a) Life expectancy. (b) Healthy life expectancy. (c) Healthy life years lost

3.3 Summary and Conclusions Our study has produced the first expanded life tables for dogs in the UK and Japan, providing annual life expectancy and healthy life expectancy for the UK and Japan companion dog population, and breed groups, and also for 18 breeds and crossbred dogs in the UK. The construction and application of expanded form of life tables offers great support for companion animal health and welfare sciences. Expanded life tables generated in the current study promote not only a better understanding of the life span of dogs and related health status, but also offer several applications for the veterinary profession and research to improve the health and welfare of dogs. A main achievement was the presentation of the disability space for dog health state with characteristic graphs.

References Inoue, M., Hasegawa, A., Hosoi, Y., & Sugiura, K. (2015). A current life table and causes of death for insured dogs in Japan. Preventive Veterinary Medicine, 120, 210–218. Skiadas, C. H., & Skiadas, C. (2018a). The health-mortality approach in estimating the healthy life years lost compared to the global burden of disease studies and applications in world, USA and Japan. In Exploring the health state of a population by dynamic modeling methods (The springer series on demographic methods and population analysis 45) (pp. 67–124). Springer. https://doi.org/10.1007/978-3-319-65142-2_4 Skiadas, C. H., & Skiadas, C. (2018b). Demography and health issues: Population aging, mortality and data analysis. In The springer series on demographic methods and population analysis 46. Springer. https://doi.org/10.1007/978-3-319-76002-5 Skiadas, C. H., & Skiadas, C. (2020a). Relation of the Weibull shape parameter with the healthy life years lost estimates: Analytical derivation and estimation from an extended life table. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures (The springer series on demographic methods and population analysis, vol 50). Springer. https:/ /doi.org/10.1007/978-3-030-44695-6_2 Skiadas, C. H., & Skiadas, C. (2020b). Direct healthy life expectancy estimates from life tables with a Sullivan extension. Bridging the gap between HALE and Eurostat estimates. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures (The springer series on demographic methods and population analysis, vol 50). Springer. https:/ /doi.org/10.1007/978-3-030-44695-6_3

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Skiadas, C. H., & Skiadas, C. (2020c). How the unsolved problem of finding the healthy life expectancy (HLE) in the far past was resolved: The case of Sweden (1751–2016) with forecasts to 2060 and comparisons with HALE. https://doi.org/10.31235/osf.io/akf8v Sullivan, D. F. (1971). A single index of mortality and morbidity. Health Services Mental Health Administration Health Reports, 86, 347–354. Teng, K. T., Brodbelt, D. C., Pegram, C., et al. (2022). Life tables of annual life expectancy and mortality for companion dogs in the United Kingdom. Scientific Reports, 12, 6415. https:// doi.org/10.1038/s41598-022-10341-6

Chapter 4

Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan Extension: The Case of Brazil 2003 Yiannis Dimotikalis and Christos H. Skiadas

4.1 The HLYL Estimation Method The “Direct” Healthy Life Years Lost (HLYL) methodology Skiadas and Skiadas (2020a, b, c) was based on averaging the Health State of a Population by taking into account the deaths/population from the mortality mx and the alive part of the population. A geometric approach of the methodology is presented in the following graph of mortality spaces where both mortality and survival are presented as corresponding areas. We use the Life Tables provided from the Human Mortality Database or any other related data base. Mortality is expressed by mx in these tables. In the above graph data from 2003 for the total population in Brazil was used. mx is shown as the blue exponential curve. The main forms of Life Tables start with mx and then the survival forms of the population are estimated. This methodology leads to the calculation of a probability measure termed as life expectancy at age x or life expectancy at birth when considering the total life time. There are several differences between the graph with the survival space above and the survival curves methodology. First of all, the vertical axis in the Survival-Mortality Space (SMS) diagram is the probability mx . Instead in the survival diagram the vertical axis represent population (usually it starts from 100.000 in most life tables and gradually slow down until the end). By the SMS diagram we have probability spaces for both survival and mortality. For

Y. Dimotikalis Hellenic Mediterranean University, Department of Management Science and Technology, Agios Nikolaos, Crete, Greece e-mail: [email protected] C. H. Skiadas () ManLab, Technical University of Crete, Chania, Crete, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_4

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Y. Dimotikalis and C. H. Skiadas

the age x, the total space is (ABCOA) in the SMS diagrams, that is (OC).(BC) = x mx . The mortality space is the sum S(mx ) while the survival space is (xmx -S(mx )). Accordingly, the important measure of the Health State is simply the fraction (ABDOA)/(BCODB). It is simpler to use the fraction (ABCOA)/(BCODB) = xmx /S(mx ) that can be estimated from mx for every age x of the population. In modeling the healthy life years lost to disability some important issues should be realized. Mortality expressed by mx is important for modeling disability but more important is the cumulative mortality S (mx ) which, as an additive process, is more convenient for the estimation of the healthy life years lived with disability and the deterioration process causing deaths. The estimates for this type of mortality are included in the term bx S (mx ). The approach in previous publications (Skiadas & Skiadas, 2018a, b, c, 2020a, b, c) was to set a time-varying fraction bx for Health/Mortality of the form: xmx bx =  x 0 ms ds

(4.1)

This formula is immediately provided from Fig. 4.1 by considering the fraction: bx =

Total Space OABCO xmx = = x Mortality Space ODBCO 0 ms ds

Fig. 4.1 Survival vs Mortality space graph

4 Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan. . .

45

The main hypothesis is that the population involved in the deterioration process is a fraction of the total population at age x determined by the level of mortality mx at age x. Accordingly, the mortality process will have two alternatives expressed by the simple equation:  xmx = bx

x

ms ds ≈ bx

0

x 0

mx

(4.2)

Clearly when collecting data by asking people to respond to disability related questions, the answers is expected to be influenced from the previous experience from 0 to x years of age including dead and alive. People comment on their disability in connection to their knowledge from the environment around. In a way, they respond after summarizing, averaging and assessing their knowledge in a way similar to the above methodology. Accordingly, it is not surprising to have similar results for Healthy Life Expectancy and Healthy Life Years Lost from both methods as the “Direct” and Health Adjusted Life Expectancy (HALE) applied by the World Health Organization (WHO). In the latter morbidity is adjusted by a specific parameter for every appropriate cause thus making the final estimate quite complicated. However, several decades of collecting data and applying data sets make HALE a classical tool for estimating the Health State of a Population. However, the HALE methodology turns only few decade years back as far as health data are already collected. For more unexplored health state periods or territories the Direct methodology is appropriate as far as Life Table Data exist.

4.2 Program for the Estimates We have developed an Excel program for the Direct Estimates of bx which is provided free of charge. One version can be downloaded from the Demographics 2019 Workshop website at www.asmda.es. The program uses full life tables to provide the Healthy Life Year Lost estimator bx from the general equation form (4.1): xmx bx =  x 0 ms ds The Cumulative Mortality Mx is given by  Mx =

x 0

ms ds ≈

x  dx  0

lx

(4.3)

Where dx expresses the death population at age x in the life tables and lx is the remaining population at age x in the same life tables. Note that the starting population at age x = 0 is set at 100000.

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Y. Dimotikalis and C. H. Skiadas

The average mortality Mx/x is estimated by Mx Mx = ≈ x

x  dx 0

lx

x

Then the Person Life Years Lost (PLYL) are provided by PLYL =

dx Mx

=

xdx Mx

The final estimate for bx is given by xdx PLYL xdx xmx = ≈ bx =  x = x  dx lx l M m ds l x x s x 0 lx 0

(4.4)

The methodology is presented in Fig. 4.2 that follows. The full life table from the HMD is followed by 4 more columns for theestimation of bx . In the first, x the cumulative x mortality is estimated from M= . 0 mx . The average mortality .(M/x) = provided 0 mx /x is in the next column whereas the Person Life Years x Lost (PLYL) = x .dx / m 0 x are calculated in the next column. dx is provided by the column indicated by dx in the life table. For this very important information, an interesting graph is provided. The graph follows a growth process until a high level and a decline in the remaining lifespan period. It the next column the Healthy

Fig. 4.2 The extended Life Table for the HLYL estimates. (Download full program from http:// www.smtda.net/demographics2020.html)

4 Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan. . .

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Life Years Lost estimator bx is provided by dividing the PLYL by the lx from the life table. The results are presented in an illustrative graph with the growing trend for bx to reach a maximum and a decline at higher ages. This high level can be also estimated by fitting the Weibull model (Weibull, 1951; Skiadas and Skiadas, 2020a, b, c). Another option added in this Excel is the estimates of the World Health Organization from 2000–2016 for Life Expectancy at birth and at 60 years of age for all the member countries whereas information for the Healthy Life Expectancy (HALE) at birth and at 60 years of age are provided for the years 2000, 2005, 2010, 2015 and 2016. We have added a small Table to present comparatively the WHO estimates with our estimates for the direct method. What is only needed after that is to copy and paste the life table and to select the name of the country in 11th column and the gender (male, female or both sexes) in cell below in the Excel sheet. To avoid mistakes we have used the list of the WHO countries with their official names.

4.3 A Further HLE Estimate Based on the Sullivan Method The classical Sullivan method is a standard tool to estimate the healthy life expectancy (see Sullivan, 1971; Jagger et al., 1999). The simplicity of this method and the possibility to use it as a continuation or extension of the life table gave us the opportunity to add a Sullivan extension to the above-extended life table. By this extension, we have estimated the Healthy Life Years Lost (HLYL) for all the life span along with the Healthy Life Expectancy (HLE). The main part of the estimate is based on the proportion lived with disability. This is generated from the bx indicator from the previous columns multiplied with a discount Health Parameter. This is estimated directly from the program for our “direct” estimates and for WHO as well. For Eurostat estimates it is necessary to add the Healthy Life Expectancy at Birth in the appropriate box at the top of Fig. 4.3. Another opportunity is by selecting the “Equal” option which automatically provides an estimate higher than HALE and closer to Eurostat. Every one of these options should be selected manually in the “Select” and “Parameter” places. The “Other” selection is set by the program user if needed. After selecting the appropriate Health Parameter, the next estimates follow automatically the Sullivan method, first for estimating the personyears lived without disability, then the total years lived without disability and finally the Disability Free Life Expectancy. The column of Health Life Years Lost follows. An alternative method based on the Sullivan system is presented in the columns on the right-hand side of Fig. 4.3. The estimates are based on the Person Years Lost to Disability and the direct estimates of the person-years lived without disability, the total years lived without disability and the Disability Free Life Expectancy with similar results with the previous approach. The estimated Healthy Life Years from

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Fig. 4.3 The extended Life Table for the HLYL estimates with the Sullivan method

two methods are presented in the appropriate graph of Fig. 4.4a, b. The Health Parameters are estimated as follows: Direct Parameter = sumproduct (Lx.bx) / (Tx − (LE − HLYL) .lx) WHO Parameter = sumproduct (Lx.bx) / (Tx − (HALE) .lx) Eurostat Parameter = sumproduct (Lx.bx) / (Tx − HLE.lx) The inverse of the Equal Parameter corresponds to the Healthy Life Years Lost, that is: HLYL = 1/Equal For the application for Brazil in 2003 the related estimates are included in the next Table (Table 4.1): Clearly the estimates for the HLE and the HLYL for males and females are similar for the Direct and the SKI-6 method. The latter is based on the model proposed by J. Janssen and Ch. Skiadas in 1995. As it is also found from the estimate based on the SKI-6 program (see Fig. 4.5) presented in previous publications, both

4 Direct Healthy Life Expectancy Estimates from Life Tables with a Sullivan. . .

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Healthy Life Years Lost Indicator bx for Brazil 2003

Parameter bx

10.0 Males

8.0

Females

6.0 4.0 2.0 0.0

0

20

40

60

80

100

Age (Years)

Fig. 4.4 (a, b) Healthy Life Years Lost for males and females (a) and total % Disabled (b) in Brazil in 2003 Table 4.1 LE, HLE and HLYL for males, females and total in Brazil in 2003 Method Direct SKI-6 Severe & Moderate SKI-6 moderate SKI-6 severe

LEmales 67.3 67.3

HLEmales 60.9 52.7

67.3

61.4

67.3

58.5

HLYLmales 6.5 14.6

LEfemales 75.0 75.0

HLEHLYLfemales females 67.3 7.7 58.6 16.4

LEtotal 71.2 71.2

HLEtotal 64.1 55.8

HLYLtotal 7.1 15.3

5.9

75.0

66.7

8.3

71.2

64.4

6.7

8.8

75.0

66.9

8.1

71.2

62.5

8.5

estimates (Direct and SKI-6) are close to Severe disability cases. To this end, the Direct and SKI-6 estimates refer to an important part of the life span with the life years lost to disability governing the development of everyday life. Our Direct method, in addition to estimating the Healthy Life Expectancy, has the advantage of providing the Healthy Life Years Lost at every year of age via the bx parameter as is illustrated in Fig. 4.4. Males and females show similar behavior for the age period 0–50 years of age with the exception of the years from 17–30 where an excess of life years lost to disability appear with the form of a higher bx for males than for females. After 50 years of age, the bx for females becomes higher with a maximum level at 95 years of age (b = 7.74) with a decline for the higher age years. For males, the maximum is at 95 years (b = 6.49) with a decline at higher ages. Romero et al. (2005) explored the Healthy Life Expectancy in Brazil in 2003 by applying the Sullivan method. The data collected by the 2003 survey. Fig. 4.4b illustrates the proportion of disabled persons estimated by Romero et al. from the survey disability data (red curve) while the green curve represents our estimate with the “Direct” method from the complete 2003 Brazilian life table. Both methods provide similar results though the direct method explore the disability in more details.

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Fig. 4.5 The main view of the SKI-6 Excel Program and the Healthy Life Years Lost estimates. (Download from: http://www.smtda.net/demographics2020.html) Person Life Years Lost for Brazil 2003 20000 Males 15000

Females

10000

5000 0 0

20

40

60

80

100

Age (Years)

Fig. 4.6 (a, b) Person Life Years Lost for males and females (a) and total population (b) in Brazil in 2003.

The Person Life Years Lost for males and females in Brazil in 2003 as constructed from Fig. 4.3 data in the Excel program are illustrated in Fig. 4.6a. The highest level for males is at 68 years of age while an excess of mortality is at 17–30 years. Females present a maximum mortality level at 72 years of age. Both males and females follow a declining process after the maximum level. The results for the total population with both Direct and Self-evaluation methods appear in Fig. 4.6b. The self-evaluation estimates come from Romero et al. paper (Table 2) after appropriate calculations.

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4.4 Conclusions and Further Study We have provided an analytic explanation of the behavior of a parameter bx related to the healthy life years lost. We have also presented an analytic formulation for the observations made along the development of appropriate extensions of the classical life tables in order to give a valuable tool for estimating the Healthy Life Years Lost. We have also demonstrated that the results found for the general HLYL parameter that we proposed provide results similar to those provided by the Healthy Adjusted Life Expectancy and the corresponding HLYL estimates. An analytic derivation of the mathematical formulas is presented along with an easy to apply Excel program. A further extension of the Excel program based on the Sullivan method provides estimates of the Healthy Life Expectancy at every year of the lifespan by a Direct method. Estimates for Brazil in 2003 are presented. The latest versions of this program appear in the Demographics2020 Workshop website at http://www.smtda. net/demographics2020.html.

References Jagger, C., Van Oyen, H. and Robine, J. M. (1999). Health expectancy calculation by the Sullivan method: A practical guide. Janssen, J., & Skiadas, C. H. (1995). Dynamic modelling of life-table data. Applied Stochastic Models and Data Analysis, 11(1), 35–49. Romero, D. E., Leite, I. C., & Szwarcwald, C. L. (2005). Healthy life expectancy in Brazil: applying the Sullivan method. SciELO – Scientific Electronic Library Online. Cad. Saúde Pública, 21(suppl 1). https://doi.org/10.1590/S0102-311X2005000700002 Skiadas, C. H., & Skiadas, C. (2018a). Exploring the health state of a population by dynamic Modeling methods (The springer series on demographic methods and population analysis 45). Springer. https://doi.org/10.1007/978-3-319-65142-2 Skiadas, C.H. and Skiadas, C. (2018b). The health-mortality approach in estimating the healthy life years lost compared to the global burden of disease studies and applications in world, USA and Japan. In Exploring the health state of a population by dynamic Modeling methods. The springer series on demographic methods and population analysis 45, Springer, , pp. 67–124. https://doi.org/https://doi.org/10.1007/978-3-319-65142-2_4 Skiadas, C. H., & Skiadas, C. (2018c). Demography and health issues: Population aging, mortality and data analysis. In The springer series on demographic methods and population analysis 46. Springer. https://doi.org/10.1007/978-3-319-76002-5 Skiadas, C. H., & Skiadas, C. (2020a). Relation of the Weibull shape parameter with the healthy life years lost estimates: Analytical derivation and estimation from an extended life table. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures. The springer series on demographic methods and population analysis (Vol. 50). Springer. https://doi.org/10.1007/978-3-030-44695-6_2 Skiadas, C. H., & Skiadas, C. (2020b). Direct healthy life expectancy estimates from life tables with a Sullivan extension. Bridging the gap between HALE and Eurostat estimates. In C. H. Skiadas & C. Skiadas (Eds.), Demography of population health, aging and health expenditures. The springer series on demographic methods and population analysis (Vol. 50). Springer. https://doi.org/10.1007/978-3-030-44695-6_3

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Skiadas, C. H., & Skiadas, C. (2020c). How the unsolved problem of finding the healthy life expectancy (HLE) in the far past was resolved: The case of Sweden (1751-2016) with forecasts to 2060 and comparisons with HALE. https://doi.org/10.31235/osf.io/akf8v Sullivan, D. F. (1971). A single index of mortality and morbidity. Health Services Mental Health Administration Health Reports, 86, 347–354. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18(3), 293–297. WHO Life Expectancy and Healthy Life Expectancy Data provided in Excel. http://apps.who.int/ gho/athena/data/GHO/WHOSIS_000001,WHOSIS_000015,WHOSIS_000002,WHOSIS_000 007?filter=COUNTRY:*&format=xml&profile=excel .

Chapter 5

Assessment of the CASP-12 Scale Among People Aged 50+ in Europe: An Analysis Using SHARE Data Bamicha Elena and Verropoulou Georgia

5.1 Background Over the past decades, older adults’ quality of life has grown into a prevalent social issue as population aging challenges social policies across the globe (Ghosh & Dinda, 2020; Borrat-Besson et al., 2015). As a consequence, the measurement of quality of life in elderly people has become of great importance, since it helps health professionals and policy makers comprehend what factors are associated with ameliorating or deteriorating the quality of life in order to adopt proper policy interventions aiming to enhance elderly’s quality of everyday life and promote active and healthy ageing (Gyu Ri Kim et al., 2015). Undoubtedly, quality of life amongst older people consists a convoluted and multi-faceted concept which incorporates several dimensions (physical, psychological, social and environmental) including, in this way, each and every aspect of an individual’s life (Higgs et al., 2003; Walker & Mollenkopf, 2007). The CASP scale, which was specifically designed to evaluate the quality of life in older people, reflects all the above-mentioned perspectives. More precisely, this scale of quality of life is based on Maslow’s hierarchy of needs, which suggests that all humans share a certain set of needs that are hierarchically organized (Mathes, 1981). Physiological and safety needs are on the bottom of the hierarchy. On the one hand, physiological needs include all biological requirements necessary for human survival, such as hunger, thirst, clothing, warmth, shelter, sexual desire as well as the need for activity, exercise, sleep and rest. On the other hand, safety and security needs involve stability, protection, and freedom from fear, anxiety, and chaos. Once the physiological and safety needs are gratified, belongingness

B. Elena · V. Georgia () Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_5

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and love needs emerge; belongingness refers to a human emotional need for interpersonal relationships, affiliating, connectedness, and being a part of the group. Esteem needs are the fourth level in Maslow’s hierarchy and include self-worth, accomplishment and respect. Maslow classified esteem needs into two categories: (i) esteem for oneself (dignity, achievement, mastery, independence) and (ii) the desire for reputation or respect from others (desire for recognition, dignity, and appreciation). When all prior needs are sufficiently satisfied, the desire for selfactualization makes its appearance referring to the realization of a person’s full potential, and self-fulfillment (Maslow, 1970). Maslow (1943) describes this class of needs as the desire to “accomplish everything that one can, to become the most that one can be”. The original CASP scale was composed of 19 items (CASP-19); it was developed by Martin Hyde and his colleagues, working with a group of UK adults aged between 65 and 75 years old. The questionnaire was focused on the higher psychological and self-fulfillment needs targeting older adults living in developed countries, where it is assumed that basic needs, such as food and shelter, are generally met. These higher needs were translated into four different domains of quality of life: (1) Control, (2) Autonomy, (3) Self-Realization, and (4) Pleasure (Hyde et al., 2003). The combination of these four domains is seen as an accurate measure of the positive and beneficial aspects of ageing, and of subjective quality of life in later life (Diener, 2006). Due to its questionable psychometric properties, though, a shorter version of the scale has been proposed (CASP-12) (Wiggins et al., 2008). It is important to stress that a thorough examination of the CASP-12 scale has shown a better performance of this particular scale compared to the performance of its extended version (CASP-19) (Wiggins et al., 2008; Sim et al., 2011; Vanhoutte, 2012; Sexton et al., 2013). However, in our study, we use the SHARE (Survey of Health, Ageing and Retirement in Europe) version of the CASP-12 scale, which differs slightly from the 12-item version suggested by Wiggins et al. (2008) (Borrat-Besson et al., 2015). The main objective of this paper is not only to analyze the psychometric properties of the European version of the CASP-12 scale used in the SHARE project, but also reappraise the structure of this scale, using both Confirmatory and Exploratory Factor Analysis, since further investigation of this instrument is warranted.

5.2 Materials and Methods 5.2.1 Measurement Instrument The CASP-12 self-report instrument, which was constructed purposely to be used in the SHARE Survey with the intention of quantifying and measuring the quality of life amongst people aged 50 years and older in Europe, comprises of 4 latent variables (Control, Autonomy, Self-Realization, and Pleasure) each defined by 3

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Table 5.1 List pf the CASP-12 items by dimensions, used in the SHARE project Latent variables/factors Control

Autonomy

Pleasure

Self-realization

Items/indicators My age prevents me from doing the things I would like to do I feel that what happens to me is out of control I feel left out of things I can do the things I want to do Family responsibilities prevent me from doing the things I want to do Shortage of money stops me from doing things I want to do I look forward to each day I feel that my life has meaning On balance, I look back on my life with a sense of happiness I feel full of energy these days I feel that life is full of opportunities I feel that the future looks good for me

items. Each item is scored on a 4-point Likert-type scale with response categories ranging from “Often” to “Never” (1 = “Often”, 2 = “Sometimes”, 3 = “Rarely”, and 4 = “Never”). Table 5.1 presents the SHARE version of the CASP-12 scale.

5.2.2 Participants The analysis is applied on data from the eighth wave of the Survey of Health, Ageing and Retirement in Europe (SHARE), carried out in 2019/20. SHARE is a longitudinal survey; particular individuals are repeatedly interviewed every 2 years, which enables comparison of the dynamics of their life situation (Caruana et al., 2015), and is conducted since 2004. It collects information on health, economic, demographic and psychological aspects of European citizens aged 50 and above (Borrat-Besson et al., 2015). Twenty-seven countries participated in wave eight: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, German, Greece, Hungary, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Romania, Slovakia, Slovenia, Spain, Sweden, and Switzerland, along with Israel. Participants with missing values on one or more of the CASP items were excluded from the analysis. Hence, the initial sample consisted of 46,500 individuals aged 50 and over; 3799 subjects were removed due to missing data, as they omitted some items of the CASP-12 scale. As a result, the final sample consisted of 42,701 subjects.

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5.2.3 Statistical Analysis Both internal consistency and factor structure were examined. Factor structure was tested using exploratory and confirmatory factor analysis (EFA, CFA).

5.2.3.1

Confirmatory Factor Analysis

Confirmatory factor analysis is habitually used as a deductive approach as it allows the researcher to test the hypothesis that a relationship between the observed variables/items and their underlying latent construct exists. In other words, it is used in order to evaluate a latent structure which has been developed a priori and is driven by a theoretical basis (Lance & Vandenberg, 2002). At this point, it is crucial to note that confirmatory factor analysis can be performed only when there is an association between the items with a minimum of .30 correlation coefficient allowing them to be distributed among the factors (Tabachnick & Fidell, 2001). Given the predominant use of Likert-type scales in the social and behavioral sciences, the indicators are often ordinal in nature. Thus, a number of authors argued that Likert items should be treated as ordinal variables and should be analyzed accordingly, particularly when the number of response levels is smaller than five (Allen & Seaman, 2007; Jakobsson, 2004). Hence, their association should be measured based on the Polychoric Correlation Matrix, which does not underestimate the magnitude of the association (Holgado-Tello et al., 2010). The hypothesized model which was examined is a four-factor correlated model composed of four domains: Control, Autonomy, Self-realization and Pleasure. A good fit between the existing data and the latent variables reassures the hypothesized structure (Sim et al., 2011). The indices that we used as measures of goodnessof-fit are the following: Comparative Fit Index (CFI), Tucker Lewis Index (TLI, also known as Non-Normed Fit Index, NNFI), and Root Mean Square Error of Approximation (RMSEA). An acceptable fit was indicated by CFI ≥ .95, TLI ≥ .95 (Hu & Bentler, 1999), and RMSEA ≤ .08 (Browne & Cudeck, 1993).

5.2.3.2

Exploratory Factor Analysis

Exploratory factor analysis has been used to explore the possible underlying structure of a set of interrelated variables without imposing any preconceived structure on the outcome (Child, 1990). In fact, by performing exploratory factor analysis, the number of constructs and the underlying factor structure are uncovered. Conventionally, a factor loading >.30 is recommended (Martinez-Vizcaino et al., 2010).

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Internal Consistency

Reliability was based on internal consistency (Ordinal Cronbach’s alpha). An Ordinal Cronbach’s alpha value ranging from .70 to .80 was considered satisfactory (DeVellis, 2003).

5.3 Results 5.3.1 Confirmatory Factor Analysis The implementation of the Polychoric Correlation Coefficient indicates that item “Family responsibilities prevent me from doing the things I want to do” and item “Shortage of money stops me from doing things I want to do” correlate weakly with the vast majority of the observed variable s. Thus, we eliminated these two items from our analysis rendering the Autonomy dimension poorer as it consists now only of one item, “I can do the things I want to do”. Moreover, the four-factor correlated model for the CASP-12 scale had relatively poor fit, as illustrated by the goodness-of-fit indices. CFI (= .915) and TLI (= .883) values were less than the accepted value of .95. Only one indicator, the RMSEA (=. 067) is inside the accepted value of .08 or less.

5.3.2 CASP-12 Reliability Table 5.2 reveals that the reliability coefficient is unacceptably weak for the Autonomy dimension and satisfactory for the Pleasure dimension and the Selfrealization subscale. The internal consistency of the Control dimension is considered respectable while the CASP-12 scale shows a high level of consistency. Given the low correlations of the items “Family responsibilities prevent me from doing the things I want to do” and “Shortage of money stops me from doing things I want to do” with most of our dataset’s items and the low level of Table 5.2 Ordinal Cronbach’s alpha coefficient of internal consistency reliability Dimensions Control Autonomy Self-realization Pleasure Scale CASP-12

Number of items 3 3 3 3 Number of items 12

Ordinal Cronbach’s alpha 0.77 0.43 0.81 0.86 Ordinal Cronbach’s alpha 0.88

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internal consistency in the Autonomy dimension, we opted these weakly correlated indicators to become candidates for removal. Removing, though, these two items from our analysis the value of ordinal alpha for the Autonomy dimension still remains low (α = 0.46). Given the above-mentioned results, we considered the CASP-12 scale problematic, and hence, we proceeded with applying exploratory factor analysis aiming to challenge its conceptual construct.

5.3.3 Exploratory Factor Analysis After employing exploratory factor analysis, ten items having a significant loadings weight from .30 and above remained. These items were distributed into three factors: Self-realization, Pleasure, and Control, while the Autonomy factor disappeared and its remaining indicator, “I can do the things I want to do”, was added into the Self-realization dimension (Table 5.3). As it is apparent, the item “My age prevents me from doing the things I would like to do” loads into two factors, Pleasure and Control with almost the same loadings weight. Based on the international literature concerning cross-loadings and how researchers should deal with them, we would opt for eliminating this particular item. Based, though, on the literature regarding the indicators of the CASP-12 scale, such a thing is not suggested. Thus, we decided not to remove the “My age prevents me from doing the things I would like to do” item from the analysis, and thus, it was loaded into the factor which presented the heavier weight, the Control factor.

Table 5.3 Factor loadings per dimension for the CASP-10 scale Items My age prevents me from doing the things I would like to do I feel that what happens to me is out of control I feel left out of things I feel full of energy these days I feel that life is full of opportunities I feel that the future looks good for me I can do the things I want to do I look forward to each day I feel that my life has meaning On balance, I look back on my life with a sense of happiness

Factor loadings Self-realization

Pleasure −0.440

Control 0.468 0.838 0.724

0.735 0.721 0.667 0.352 0.714 0.828 0.589

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Table 5.4 Construct validity of the CASP-10 scale Index CFI (Comparative Fit Index) TLI (Tucker-Lewis Index) RMSEA (Root Mean Square Error of Approximation)

Value .966 .952 .047

Criterion ≥.95 ≥.95 ≤.08

5.3.4 Construct Validity of the CASP-10 Scale Results from a three-factor confirmatory factor analysis provided evidence that the CASP-10 scale fits adequately the data in contrast to the CASP-12 scale which revealed to have poor fit, as it is shown in Table 5.4.

5.4 Conclusion The present analysis aimed at exploring the robustness of the CASP-12 scale proposed in the SHARE study. The findings of the confirmatory and exploratory factor analysis indicate that omission of two questions out of the twelve and of one factor out of the four improves the construct validity of the instrument. The modified version of the CASP-12 scale we suggest, presents sufficient psychometric properties and a well-fitting three factor structure.

References Allen, E., & Seaman, C. A. (2007). Likert scales and data analyses. Quality Progress, 40(7), 64–65. Borrat-Besson, C., Ryser, V.-A., & Gonçalves, J. (2015). An evaluation of the CASP-12 scale used in the Survey of Ageing and Retirement in Europe (SHARE) to measure quality of life among people aged 50+ (FORS Working Paper Series, paper 2015-4). FORS. Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models. Sage. Child, D. (1990). The Essentials of Factor Analysis (2nd ed.). London: Cassel Educational Limited. Caruana, E. J., Roman, M., Hernández-Sánchez, J., & Solli, P. (2015). Longitudinal studies. Journal of Thoracic Disease, 7(11), 537–540. DeVellis, R. F. (2003). Scale development: Theory and applications (Vol. 26, 2nd ed.). Sage. Diener, E. (2006). Guidelines for national indicators of subjective well-being and ill-being. Journal of Happiness Studies: An Interdisciplinary Forum on Subjective Well-Being, 7(4), 397–404. Ghosh, D., & Dinda, S. (2020). Determinants of the quality of life among elderly: Comparison between China and India. The International Journal of Community and Social Development, 2(1), 71–98. Gyu Ri, K., Netuveli, G., Blane, D., Peasey, A., Malyutina, S., Simonova, G., Kubinova, R., Pajak, A., Croezen, S., Bobak, M., & Pikhart, H. (2015). Psychometric properties and confirmatory factor analysis of the CASP-19, a measure of quality of life in early old age: The HAPIEE study. Aging & Mental Health, 19(7), 595–609.

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Higgs, P., Hyde, M., Wiggins, R., & Blane, D. (2003). Researching quality of life in early old age: The importance of the sociological dimension. Social Policy and Administration, 37(3), 239–252. Holgado-Tello, F. P., Chacón-Moscoso, S., Barbero-García, I., & Vila-Abad, E. (2010). Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables. Quality & Quantity, 44(1), 153–166. Hu, L.-T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. Hyde, M., Wiggins, R. D., Higgs, P., & Blane, D. B. (2003). A measure of quality of life in early old age: The theory, development and properties of a needs satisfaction model (CASP-19). Aging and Mental Health, 7(3), 186–194. Jakobsson, U. (2004). Statistical presentation and analysis of ordinal data in nursing research. Scandinavian Journal of Caring Sciences, 18(4), 437–440. Lance, C. E., & Vandenberg, R. J. (2002). Confirmatory factor analysis. In F. Drasgow & N. Schmitt (Eds.), Measuring and analyzing behavior in organizations: Advances in measurement and data analysis. Jossey-Bass. Martínez-Vizcaíno, V., Martínez, M. S., Aguilar, F. S., Martínez, S. S., Gutiérrez, R. F., Sánchez López, M., Martínez, P. M., & Rodríguez-Artalejo, F. (2010). Validity of a single-factor model underlying the metabolic syndrome in children: A confirmatory factor analysis. Diabetes Care, 33(6), 1370–1372. Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50(4), 370–396. Maslow, A. H. (1970). Motivation and personality. Harper & Row. Mathes, E. W. (1981). Maslow’s hierarchy of needs as a guide for living. Journal of Humanistic Psychology, 21(4), 69–72. Sexton, E., King-Kallimanis, B. L., Conroy, R. M., & Hickey, A. (2013). Psychometric evaluation of the CASP-19 quality of life scale in an older Irish cohort. Quality of Life Research, 22(9), 2549–2559. Sim, J., Bartlam, B., & Bernard, M. (2011). The CASP-19 as a measure of quality of life in old age: Evaluation of its use in a retirement community. Quality of Life Research, 20(7), 997–1004. Tabachnick, B. G., & Fidell, L. S. (2001). Using multivariate statistics (4th ed.). Allyn and Bacon. Vanhoutte, B. (2012). Measuring well-being in later life: A review (CCSR Working Paper 201206). CCSR, University of Manchester. Walker, A., & Mollenkopf, H. (2007). International and multi-disciplinary perspectives on quality of life in old age: Conceptual issues. In H. Mollenkopf & A. Walker (Eds.), Quality of life in old age (Social indicators research series) (Vol. 31). Springer. Wiggins, R. D., Netuveli, G., Hyde, M., Higgs, P., & Blane, D. (2008). The evaluation of a self-enumerated scale of quality of life (CASP-19) in the context of research on ageing: A combination of exploratory and confirmatory approaches. Social Indicators Research, 89, 61– 77.

Chapter 6

Possibilities of Creating New Health Indicators Jana Vrabcová, Tomáš Fiala, and Jitka Langhamrová

6.1 Introduction There is an ageing population in all developed countries of the world. “The ageing of the population brings many challenges for European countries, both economic and non-economic in nature . . . These challenges are not unsurpassed, but they just require a different way of thinking, especially by politicians about what ageing actually means. Economic challenges include the future sustainability of public social security systems.” (Walker & Zaidi, 2021). For example, the Turner’s pension commission in the UK (Pensions Commission, 2004) suggested increasing the retirement age to reflect prolonging life expectancy, but some experts point out that the population’s health indicators would be more appropriate because work capacity determines health and not age. Monitoring and recording the health status of the population is important not only because of understanding the causes and consequences of health differences but also because of the measurement of the effectiveness of the medical intervention, evaluation of the quality of care or estimating future needs of the population (Ware et al., 1981). In the Czech Republic, there has been a significant prolongation of life expectancy in the last 30 years, mainly due to the reduction of death from premature cardiovascular and cerebrovascular disease – one of the most important disability

J. Vrabcová () Department of Statistics and Probability, Prague University of Economics and Business, Prague, Czech Republic e-mail: [email protected] T. Fiala · J. Langhamrová Department of Demography, Prague University of Economics and Business, Prague, Czech Republic e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_6

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factors (Fihel & Pechholdová, 2017; Rychtaˇríková, 2004). A significant decrease in mortality is expected in the future (Pechholdová, 2019). With increasing age, there is a greater probability of certain health disabilities and the proportion of persons with disability increases. If a person affects any type of disability, there may be incapacity for work that has negative consequences not only for individuals but also for society (Stucki et al., 2015). This is associated with difficulties not only with participation in the labour market but also in social and cultural activities (Restrepo, 2015). The indicators of the health status of the population are constructed based on the subjective assessment of the citizens’ own health and are based on a wide range of health aspects and perceptions of people about their quality of life. Therefore, expectations of health can be important indicators of potential demand for health services and long-term care services, especially in older generations of the population. These indicators, unlike the concept of life expectancy, emphasize not only the entire length of life but also its quality, expressed in health (Vrabcová et al., 2017). For the proposal of the prevalence of a new health indicator, the structure of the so-called minimum European health module was analyzed, i.e. on the subjective assessment of one’s own health, chronic diseases, and long-term limitation of activities. Everything was created based on individual data from the European Selection on Health in 2008, 2014 and 2019. All outputs are published on common unit numbers of respondents. The investigation also provides the values “weighted” on the population of the Czech Republic, but because people living in institutions are not included in the EHIS survey, this transport is not without error and this data will not be presented here. The future aim of this work is to use the prevalence of the newly proposed health indicator (variable “healthy vs. ill”) for the calculation of a new indicator of the health status of the population and its comparison with already known indicators based on subjective health assessment, chronic disease, and long-term limitation of activities.

6.2 Summary Measures of Population Health Summary measures of population health (SMPH) are indicators to characterize the health of the population using one value. However, before these indicators were defined, it took quite a long time. The first efforts to create an indicator that will link the quantitative and qualitative character of health are known from the 1960s (Sanders, 1964). This issue was dealt with very intensively and is still dealing with the expert Group REVES, which by their projects Ehleis (1994–2002), EuroREVES (1994–2002), Ehemu (2004–2007) and JA:EHLEIS is increasingly and more refines the definitions of individual health indicators and seeks to spread awareness of them not only among the professional public. All of the abovementioned projects have long been involved in life expectancy analysis, public

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Fig. 6.1 Scheme of the breakdown of selected indicators of the health status of the population. (Source: Vrabcová et al., 2017; Anglické a cˇ eské termíny pro souhrnné ukazatele zdravotního stavu obyvatelstva, 2010)

health strategies at the national and international level and monitoring of the differences between countries. SMPH can be divided into three wide groups: life expectancy, life expectancy according to health and health deficiency. While life expectancy according to health is the area under the curves of survival, health deficits try to quantify the difference between the current health of the population and a certain norm or aim (Mathers, 2003). The calculation of life expectancy is based on unambiguous death, but the calculation of health indicators differs from the definition of health/ disease/disability. So, as there are many ways of assessing health, there are also many different life expectancies in health, for clarity, there is a scheme with selected variables, see Fig. 6.1. As Hrkal and Daˇnková state, the interpretation of the results based on health indicators must be cautious: “The health-length indicator is a combination of the life expectancy that is based on complete statistics of the deceased, and the characteristics of health assessed based on answers obtained from surveys. These investigations are performed in a standardized manner in all countries and can be considered comparable from this point of view. However, complications may occur with how to interpret the correct results (i.e. what the health concept they describe), as these data are subject to subjective influences that are subject to the cultural and social environment in which people live. This can then be significantly manifested especially in the international comparison of indicators. On the other hand, the

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data can be appreciated as a reflection of a subjective feeling of health and as such thinking” (Hrkal & Daˇnková, 2005). This paper will focus on the prevalence needed to calculate LE in very good and good perceived health, LE without chronic morbidity and DFLE. These prevalences can be obtained based on respondents’ answers to Minimum European Health Module questions.

6.3 Minimum European Health Module The EHIS survey contains a Minimum European Health Module (MEHM), which includes three questions about self-rated health, chronic morbidity and long-term limitation of activities and can be used as a basic set of indicators for an overall health assessment (Vrabcová et al., 2017). As the indicator indicates, self-rated health is taken as a variable of subjective nature, on the other hand, chronic/longterm disease and disability are referred to as variables that evaluate the health status objectively. Self-reported health/self-rated health (SRH) is represented here by the question: • How is your health in general? Is it . . . • Very good /Good /Fair/Bad/Very bad; As Daˇnková & Otáhalová (2017) states: “This question monitors a truly subjective feeling of individual’s health, regardless of comparison with others, peers, etc.” As stated by Saito et al. (2014), people are likely to evaluate their health holistically and take into account several social, physical and emotional factors that affect their health and specific cultural factors. Figure 6.2 shows the responses of EHIS 2008, 2014 and 2019 respondents to the question of subjective assessment of health status by age and gender. The number of answers when the respondent stated that he did not know, did not want to answer, or left the answer blank is minimal (in 2008, only 2 people, 0.1% of respondents; 2014, 125 people, 1.86% of respondents; 2019, 109 people, 1, 36% of respondents). With increasing age, health problems increase and there is a logical shift from a very good and good assessment of one’s health to the “worse” one. In analyzes working with the SRH, it is customary to combine the answer categories “very good” + “good” as a certain positive evaluation of health and “bad” and “very bad” as a negative evaluation of the health status. The answer category “fair” can be assigned to this negative or, on the contrary, rather positive health assessment, and this results in a division into only two categories. The effect of assigning this middle category to good or bad SRH will be shown later. In the EHIS surveys from all three investigated years, it is evident (see Fig. 6.2) that the prevalence of a negative assessment of one’s health increases with increasing age. As a rule, these prevalences are higher in women (Gijsbers van Wijk et al., 1991; Zimmer et al., 2000), but in the results of this research, in some age groups, men have a higher proportion of negative evaluation of their health. As can be seen at

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100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+ 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

EHIS 2008

men

women

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15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+ 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

EHIS 2014

men

women

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+ 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

EHIS 2019

men

women 1

2

3

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Fig. 6.2 Prevalence of self-rated health in the EHIS survey 2008, 2014, 2019, by respondent’s age and gender in the Czech Republic (Note: 1 – very good, 2 – good, 3 – fair, 4 – bad, 5 – very bad). (Source: EHIS 2008, 2014, 2019, own processing)

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100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

men

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84

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women 2008

women 2014

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women 2019

Fig. 6.3 Prevalence of chronic morbidity/longstanding illness or health problem in the EHIS survey 2008, 2014, 2019, by respondent’s age and gender in the Czech Republic. (Source: EHIS 2008, 2014, 2019, own processing)

first glance, the fluctuation of values is influenced by the size of the sample (in 2008 there were 3 times and 4 times fewer respondents than in 2014 and 2019) and also by the distribution of respondents depending on age and gender. The question of chronic morbidity is in the EHIS survey as follows: • Do you have any longstanding1 illness or health problem? • Yes/No; In the case of this health indicator, the number of incomplete or rejected answers is minimal (in 2008, there were 11 people, i.e. 0.6% of respondents; 2014, 1 person, 0.01% of respondents; 2019, none of the respondents refused to answer and each chose either a “yes” or “no” answer). As can be seen from Fig. 6.3, the proportion of people who declare chronic morbidity or a long-term health problem increases with increasing age. As in the

1 Longstanding means an illness or health problem that lasts or is expected to last 6 months or more.

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case of the SRH, there are no clear trends from the point of view of gender. In 2014 and 2019, in the EHIS survey, women had a higher prevalence of long-term illness in almost all age groups, but as is clear, men reach very similar (or higher) values in older age groups. The question related to long-term limitation of activities (disability) is presented in the following wording: • For at least the past 6 months, to what extent have you been limited because of a health problem in activities people usually do? Would you say you have been ... • severely limited/limited but not severely or/not limited at all? This question is referred to as a long-term limitation of activities (Global Activity Limiting Indicator/Instrument, GALI). GALI is interested in the respondent’s limitation, whether it is due to health reasons and whether it is of a long-term nature (lasts at least 6 months) and how serious it is. “This is a very subjective indicator that depends, among other things, on the individual’s ability to deal with the health problem they have.” (Daˇnková & Otáhalová, 2017). When calculating the indicator of healthy life expectancy, GALI is an important component related to morbidity. In 2019 and 2014, there were no rejected or incomplete answers to this question, in 2008 there were 25 people, i.e. 1.25% of respondents. Even in the case of this indicator, the prevalence increases with increasing age, see Fig. 6.4.

6.4 Analysis of Sensitivity for the Middle Category of Self-Rated Health and a Proposal for a New Variable An auxiliary variable summarizing information about the answers of each respondent on SRH, long-term illnesses and GALI questions was created. For clarity, there is Table 6.1, where new codes are listed for individual answers. The new variable consists of a three-digit code consisting of only 0 and 1, where the first position of the code corresponds to SRH, the second long-term illness and the third GALI. To maintain clarity, the outputs for this new variable were illustrated only for EHIS 2019 in the Czech Republic and expressed relatively for better comparability, see Fig. 6.5. The upper graphs show the distribution of men’s and women’s responses if the third category of SRH is assigned to a good and very good SRH. The lower pair of graphs shows the assignment of the third category to the bad and very bad SRH. At first glance, it is evident that in all cases in younger age groups the answers 000 prevail, i.e. the respondent evaluates his/her health well, is without chronic illness and long-term limitation of activities. If category 3 SRH is assigned to good health assessment, then the code 011 prevails in higher age groups of women and men, which means that people feel good, but declare chronic disease and long-term limitation of activities. After recoding category 3 SRH for a

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100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

men

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84

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women 2008

women 2014

85+

women 2019

Fig. 6.4 Prevalence of long-term limitation of activities (GALI) in the EHIS survey 2008, 2014, 2019, by respondent’s age and gender in the Czech Republic. (Source: EHIS 2008, 2014, 2019, own processing)

bad health evaluation, the representation of responses will change and in older age groups increase the number of answers 111, i.e. persons subjectively feel bad and at the same time declare chronic disease and long-term limitation of activities. Thus, more sense makes the middle category SRH to bad health, but in the construction of a new variable “healthy” vs. “ill”, this does not necessarily mean that the respondent will be included in the “ill” category. Several sorting of respondents into these two groups was tested, but in the end, it was the best division described below and illustrated in Table 6.2. Based on answers to the questions from the MEHM module, a new variable was created to include the respondent either in the category “healthy” or “ill”. If the respondent responded in the EHIS to the GALI question – “severely limited”, then was always included among the ill people. If the answer to the question was “limited but not severely” or “not limited at all”, then it depended on the answers to SRH and long-term morbidity. If the answer GALI was “limited but not severely”, then the

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Table 6.1 Assigning the middle category subjectively evaluated health to the category “good” or “bad” health

Answers Very good Good Fair Bad Very bad Longstanding illness or health problem Yes No Global activity limitation indicator (GALI) Severely limited Limited but not severely Not limited at all Self-perceived/rated health (SRH)

New code name “Good Health” 0

New code name “Bad Health” 0 1

1 1 0 1

1 0 1

0

0

Source: Own processing

Fig. 6.5 Distribution of respondents according to their responses in SRH, long-term illness and GALI in the EHIS survey 2019 in the Czech Republic, by age and gender. (Source: EHIS 2019, own processing)

respondent in most cases was included among the ill people, only in the absence of long-term morbidity and good subjective health assessment among healthy. In the case of answering the question of GALI “not limited at all”, on the other hand, the respondent is usually included among healthy persons, only in the case of long-

No

Yes

Self-perceived / rated health (SRH)

Source: Own processing Note: A total of 16,420 respondents from EHIS 2008, 2014 and 2019

Longstanding illness or health problem

Table 6.2 Variables defining a new variable “healthy vs. ill”

Very bad Bad Fair Good Very good Very bad Bad Fair Good Very good Ill(98)

Healthy(171)

Ill(10)

Ill(1373)

Ill(8)

Ill(128)

Healthy(5879)

Healthy(678)

Healthy(2443)

Global Activity Limitation Indicator (GALI) Severely limited Limited but not severely Not limited at all Ill(1543) Ill(2927) Ill(1543)

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Fig. 6.6 Prevalence of very good and good perceived health, without chronic morbidity and activity limitation in the EHIS survey 2008, 2014, 2019, by respondent’s age and gender in the Czech Republic. (Source: EHIS 2008, 2014, 2019, own processing)

term morbidity and bad self-rated health falls into the group of ill. It was made on answers from 16,420 respondents of the EHIS survey from 2008–2019 in the Czech Republic. On the other hand, in the case of 265 respondents, there was no answer to one or more of these MEHM questions, so they were not included. Based on this sorting, a prevalence for a new variable was created for each year of the EHIS survey (see Fig. 6.6). It is the prevalence of certain good health (without restrictions in usual activities, without long-term diseases and with subjectively well-rated health). So, it is logical that the curve with increasing age decreases, unlike the prevalence of the previously displayed (there was displayed a share of negative health evaluation, proportion of persons with disabilities, etc.). These prevalences are compiled in such a way as to correspond to the construction of the three health indicators mentioned in the introduction: LE in very good and good perceived health, LE without chronic morbidity and DFLE. Everything is supplemented by a prevalence suitable for the calculation of a new variable (healthy vs. ill) that attempts to use the potential of three variables (SRH, chronic morbidity, GALI) that are normally published separately. The curves have not been smoothed in any way, in the next research the plan is to smooth them out using suitable models.

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This new variable aims to combine information from the subjective and objective responses of respondents to their health. Because the fact that someone has a longterm illness does not necessarily mean that he/she feels sick and is limited in normal activities. Conversely, the fact that the respondent does not allow the disease (or does not know about it) but feels bad and is more or less limited in normal activities is unlikely to include it among persons without a disability. This new variable can also be used to model the future development of the share of persons limited in healthrelated points of view.

6.5 Challenges and Limitations in Data Collection The size of the selected sample, its structure, the data collection period, or the data collection method itself can be problematic for the health-related survey. The ideal would be if the target population consisted of all individuals, who are in a given area, and all households or institutionalized residents (in hospitals, hotels, homes for seniors, and prisons). People living in private homes form the basis of most surveys, but it would be advisable to expand these surveys in such a way as to include people living in institutions because especially in older populations, the health of institutionalized persons, is worse than households (Buratta & Egidi, 2003; Deeg et al., 2003). Another distortion factor may be the elimination of homeless respondents who are not included in household-based surveys or institutions and whose health status can generally be considered worse than those of the same age resident (Buratta & Egidi, 2003). In some countries, the survey includes interviews in different seasons (often quarterly) to monitor the development of morbidity specific to the season. In other countries, interviews do not repeat and take place on a specific date. Data on the prevalence of chronic diseases collected by the selection survey are influenced by seasonality because the symptoms of the disease may be more evident in different seasons and therefore affect the perception of the individual (Buratta & Egidi, 2003).

6.6 Conclusions Based on data from the EHIS survey in 2008, 2014 and 2019 in the Czech Republic, a new health indicator “healthy vs. ill” was proposed. The new variable was created based on a combination of responses to the three questions from the MEHM module. Health indicators based on the prevalence of very good and good perceived health, without chronic morbidity and activity limitation, are commonly published. Based on them, life expectancy in very good and good perceived health, life expectancy without chronic morbidity and disability-free life expectancy are calculated. But it is always a health indicator based solely on the prevalence of one question, it is never a combination. By combining the information for these three questions together, it

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is possible to get a more comprehensive view of the respondent’s health, and this could be used for further calculations or an estimate of future development. In the long run, improvement (increased prevalence of good health) can be assumed, but due to the Covid pandemic, there will undoubtedly decrease, which we will catch up in the coming years. A limitation of this research is undoubtedly the fact that the EHIS survey in the Czech Republic only takes place in private households and institutionalized people are not included in the survey. Another limitation is the small number of harmonized surveys over time. ˇ 19Acknowledgement This article was supported by the Czech Science Foundation No. GA CR 03984S under the title Economy of Successful Ageing.

References Anglické a cˇ eské termíny pro souhrnné ukazatele zdravotního stavu obyvatelstva (English and ˇ Czech terms for summary indicators of the health status of the population). (2010). Ceská demografiká spoleˇcnost. https://www.natur.cuni.cz/geografie/demografie-a-geodemografie/ ceska-demograficka-spolecnost/aktualni-informace/ukazatele-zdravotniho-stavu-obyvatelstva Buratta, V., & Egidi, V. (2003). Data collection methods and comparability issues. In Determining health expectancies (pp. 187–201). Wiley. Daˇnková, Š., & Otáhalová, H. (2017). Zdravotní stav cˇ eské populace podle výbˇerového šetˇrení o zdraví Ehis (Health status of the Czech population according to the Ehis sample health survey). Demografie, 59(3) https://www.czso.cz/documents/10180/46203816/Prehledy+Dankova.pdf Deeg, D. J. H., Verbrugge, L. M., & Jagger, C. (2003). Diability measurement. In Determining health expectancies (pp. 203–219). Wiley. Fihel, A., & Pechholdová, M. (2017). Between ‘pioneers’ of the cardiovascular revolution and its ‘late followers’: Mortality changes in The Czech Republic and Poland since 1968. European Journal of Population, 33(5), 651–678. https://doi.org/10.1007/s10680-017-9456-y Gijsbers van Wijk, C. M. T., van Vliet, K. P., Kolk, A. M., & Everaerd, W. T. A. M. (1991). Symptom sensitivity and sex differences in physical morbidity: A review of health surveys in the United States and The Netherlands. Women & Health, 17(1), 91–124. https://doi.org/ 10.1300/J013v17n01_06 Hrkal, J., & Daˇnková, Š. (2005, July 10). ANALÝZA: Zdravá délka života u obyvatel EU (ANALYSIS: Healthy life expectancy for EU residents). Demografický Informaˇcní Portál. http://www.demografie.info/?cz_detail_clanku=&artclID=107 Mathers, C. (2003). Cause-deleted health expectancies. In Determining health expectancies (pp. 149–174). Wiley. Pechholdová, M. (2019). Mortality assumptions and forecasting methodology: Population projection of The Czech Republic from the Czech statistical office, 2018–2100. Demografie, 61(4), 261–280. Pensions Commission. (2004). Pensions: Challenges and choices—The first report of the Pensions Commission. The Stationery Office. Restrepo, J. F. A. (2015). Disability, living conditions and quality of Life. University of Oslo. Rychtaˇríková, J. (2004). The case of The Czech Republic: Determinants of the recent favourable turnover in mortality. Demographic Research, S2, 105–138. https://doi.org/10.4054/ DemRes.2004.S2.5

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Saito, Y., Robine, J.-M., & Crimmins, E. M. (2014). The methods and materials of health expectancy. Statistical Journal of the IAOS, 30(3), 209–223. https://doi.org/10.3233/SJI140840 Sanders, B. S. (1964). Measuring community health levels. American Journal of Public Health and the Nations Health, 54(7), 1063–1070. https://doi.org/10.2105/AJPH.54.7.1063 Stucki, G., Brage, S., Homa, D., & Escorpizo, R. (2015). Conceptual framework: Disability evaluation and vocational rehabilitation. In Handbook of vocational rehabilitation and disability evaluation: Application and implementation of the ICF (Springer International Publishing) (1st ed., pp. 3–10). Springer. https://doi.org/10.1007/978-3-319-08825-9 Vrabcová, J., Daˇnková, Š., & Faltysová, K. (2017). Healthy life years in The Czech Republic: Different data sources, different figures. Demografie, 59(4), 315–331. Walker, A., & Zaidi, A. (2021). Strategie aktivního stárnutí v Evropˇe (Strategies for active aging in Europe). In Budoucnost stárnutí v Evropˇe: Dlouhovˇekost jako kapitál (pp. 31–55). Zdenˇek Susa. Ware, J. E., Brook, R. H., Davies, A. R., & Lohr, K. N. (1981). Choosing measures of health status for individuals in general populations. American Journal of Public Health, 71(6), 620–625. Zimmer, Z., Natividad, J., Lin, H.-S., & Chayovan, N. (2000). A cross-National Examination of the determinants of self-assessed health. Journal of Health and Social Behavior, 41(4), 465–481. https://doi.org/10.2307/2676298

Part II

Health – Covid-19

Health state cases are presented along with Covid-19 cases.

Chapter 7

Exploring Cross-National Comparability of Unidimensional Constructs Anastasia Charalampi, Catherine Michalopoulou, and Clive Richardson

7.1 Introduction Standardization of measurement is a prerequisite for cross-national and/or overtime comparative analyses (Kish, 1994). In the case of scales that have been developed as a unidimensional or multidimensional measurement of an underlying construct, scaling theory requires investigation of the scales’ structure and assessment of their psychometric properties before their application (Michalopoulou, 2017). As the literature contains instances where the validation of constructs produced scales (or subscales) defined differently from the proposed theoretical structure and also across countries (Carey, 2000; Charalampi et al., 2020), there is a need for creating overall standardized measurements for cross-national and/or overtime research (Charalampi et al., 2021). In this paper, an empirical methodology for exploring the standardization of unidimensional constructs to be used in cross-national comparative analyses is presented. First, the inclusion of items for further analyses is investigated at country level and the most common items are used to define the overall measurements, followed by validation of their structure. Based on the results of Confirmatory Factor Analysis (CFA), their psychometric properties are assessed (Charalampi et al., 2021). For the demonstration of the suggested methodology, and in order to facilitate practical applications, we used an 8-item scale that measures functioning as a determinant of wellbeing; this was included in the 2012 European

A. Charalampi () · C. Michalopoulou Department of Social Policy, Panteion University of Social and Political Sciences, Athens, Greece e-mail: [email protected]; [email protected] C. Richardson Department of Economic and Regional Development, Panteion University of Social and Political Sciences, Athens, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_7

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Social Survey (ESS) questionnaire for 17 European countries. These measurements serve as a good example because they are defined as unidimensional and are provided at country level. Moreover, a cross-national mean scores comparison of the overall measurements of functioning with satisfaction with life and happiness is illustrated. We now present briefly the ESS measurement of wellbeing. A module on personal and social wellbeing was first introduced in 2006 (Round 3 of the ESS) and was repeated with certain changes in 2012 (Round 6). Based on a combination of theoretical models and statistical analyses, the 2012 ESS measurement of personal and social wellbeing (European Social Survey, 2013, 2015; Jeffrey et al., 2015; New Economics Foundation (2009) is comprised of 35 items defined in six key-dimensions: evaluative wellbeing (two items), emotional wellbeing (six items), functioning (14 items), vitality (four items), community wellbeing (five items) and supportive relationships (four items). The present study focuses on the dimension of functioning, a determinant of wellbeing (Charalampi et al., 2021) which is described by “feelings of autonomy, competence, engagement, meaning and purpose, self-esteem, optimism and resilience” (Jeffrey et al., 2015; Brown, 2015: 4). Similarly, Panek (2015) describes positive functioning as comprising of competence, autonomy, engagement, meaning and purpose of life. The current paper aims at a cross-national comparison of functioning as a determinant of wellbeing. Standardized overall measurements of unidimensional constructs are created and their psychometric properties are investigated for 17 European countries. To decide on the inclusion of items in further analyses, item analysis was carried out using IBM SPSS Statistics Version 20. Then the resulting overall measurements were validated by performing CFA on the full samples using Mplus Version 8.6. Based on the CFA results, their psychometric properties were assessed. In order to demonstrate how these measurements may be used in additional analyses, a cross-national comparison of mean scores of the resulting overall measure of functioning was conducted in relation to measures of satisfaction with life and happiness.

7.2 Methods 7.2.1 Participants The analysis was based on the ESS Round 6 data (2018) for the following 17 countries: Belgium, Denmark, Finland, France, Germany, Hungary, Ireland, Netherlands, Norway, Poland, Portugal, the Russian Federation, Slovenia, Spain, Sweden, Switzerland and the UK. The ESS implements all the strict methodological prerequisites for comparability over time and cross-nationally (Kish, 1994; Carey, 2000) by applying probability sampling, minimum effective achieved sample sizes

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Table 7.1 The demographic and social characteristics of participants: European Social Survey, 2012

Country Belgium Denmark Finland France Germany Hungary Ireland Netherlands Norway Poland Portugal Russian Fed Slovenia Spain Sweden Switzerland UK

N 1869 1650 2197 1968 2958 2014 2628 1845 1624 1898 2151 2484 1257 1889 1847 1493 2286

Men (%) 48.7 50.5 48.9 44.8 50.4 44.8 47.6 46.4 52.8 47.9 39.6 38.3 45.9 48.3 51.3 50.0 42.6

Women (%) 51.3 49.5 51.1 55.2 49.6 55.2 52.4 53.6 47.2 52.1 60.4 61.7 54.1 51.7 48.7 50.0 57.4

Age Mean (SD) 47.3 (19.1) 48.7 (19.0) 49.8 (18.9) 51.8 (18.5) 48.7 (18.6) 47.2 (18.2) 47.3 (17.9) 51.2 (18.0) 46.0 (18.2) 46.1 (18.8) 52.3 (19.0) 46.0 (18.1) 48.3 (18.8) 47.6 (18.0) 47.8 (19.0) 47.4 (18.8) 51.8 (19.1)

Married (%) 50.1 52.2 48.1 43.3 54.2 43.1 48.4 47.2 48.1 57.6 49.4 42.9 48.3 53.6 45.6 54.1 48.7

Secondary education or lower (%) 58.8 58.8 58.7 70.9 60.1 76.4 59.8 66.6 54.4 75.4 89.2 35.7 76.6 72.8 57.4 66.1 63.4

In paid work (%) 48.3 50.8 49.9 47.0 48.9 45.5 40.1 48.6 61.1 48.2 39.1 56.5 40.6 43.6 54.1 57.5 45.5

Note. The reference period for the respondent’s main activity was defined as during the last 7 days

in all participating countries and a maximum target non-response rate of 30% (The ESS Sampling Expert Panel, 2016). The ESS defines the survey population in all rounds as all individuals aged 15+ residing within private households in each country, regardless of their nationality, citizenship or language. The realized samples and a summary of the participants’ demographic and social characteristics are presented in Table 7.1. As shown, gender was almost equally distributed in most countries with the exception of Portugal and the Russian Federation – and to a lesser extent the UK, Hungary, France and Slovenia – where the samples included more women than men. The mean age was between 46 and 52 years in every country. By country, more than 42.9% of the participants were married, the majority had completed secondary education or lower (except in the Russian Federation) and at least 39.1% were in paid work.

7.2.2 Measures and Item Selection The structure of the functioning dimension consisting of eight common items from both Rounds of the ESS is presented in Table 7.2. The response categories range from 1 to 5 and are defined as follows: 1 (agree strongly); 2 (agree); 3 (neither

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Table 7.2 The 2012 European Social Survey (ESS) measurement of functioning as a determinant of wellbeing Items of the functioning scale Free to decide how to live my life Little chance to show how capable I am Feel accomplishment from what I do Feel what I do in life is valuable Always optimistic about my future Feel very positive about myself At times I feel as if I am a failure When things go wrong in my life it takes a long time to get back to normal

Identifier on ESS questionnaire 2006 2012 E23 D16

Aligned scale 1–5 (R)

Item label F1

E25

D17

1–5

F2

E27

D18

1–5 (R)

F3

E40 E4

D23 D2

1–5 (R) 1–5 (R)

F4 F5

E5 E6

D3 D4

1–5 (R) 1–5

F6 F7

E29

D19

1–5

F8

R = these items were reversed before analysis. The response categories for each item were defined as follows: 1 = agree strongly; 2 = agree; 3 = neither agree nor disagree; 4 = disagree; 5 = disagree strongly

agree nor disagree); 4 (disagree); 5 (disagree strongly). Having emphasized in previous work (Charalampi, 2018; Charalampi et al., 2019, 2020) the importance of ascertaining the items’ level of measurement in the application of the appropriate methods, the items is considered as pseudo-interval, i.e. having at least five response categories (Bartholomew et al., 2008). The scale is comprised of five positively (F1 and F3-F6) and three negatively (F2, F7 and F8) worded items. The scoring of positively worded items was reversed before the analysis in order to achieve correspondence between the ordering of the response categories. Since items are considered as pseudo-interval, the corrected item-total correlations must be computed for each country. Internal construct validity is assessed using the criterion of corrected item-total correlations >.30 (Nunnally & Bernstein, 1994) as the cut-off for adequate correlation (Chin et al., 2015) in order to decide which items to include in the analysis. The most common items satisfying this criterion cross-nationally define the overall measurements of unidimensional constructs. The labeling of these measurements is based on theoretical and empirical considerations. For additional statistical analyses, the association of overall measurements of functioning with the subjective satisfaction with life and general happiness scales was explored. The satisfaction with life question in the ESS questionnaire is worded as follows: “All things considered, how satisfied are you with your life as a whole nowadays, on a scale 0–10 where 0 means extremely dissatisfied and 10 means extremely satisfied?”. The question on happiness is worded as follows: “Taking all

7 Exploring Cross-National Comparability of Unidimensional Constructs

81

things together, how happy would you say you are, on a scale 0–10 where 0 means extremely unhappy and 10 means extremely happy?”

7.2.3 Statistical Analyses 7.2.3.1

Preliminary Decisions

Since the case of unidimensional constructs is under consideration, the structure of the overall measurements was validated by performing CFA on the full sample of adequate size that is, 300 cases or more (Tabachnick & Fidell, 2007) for each country. Initially, missing data analysis and data screening for outliers and unengaged responses was performed for all samples. Only cases with missing values on all items were excluded automatically from the analysis (Muthén & Muthén, 1998–2017). In addition, cases were eliminated if they exhibited low standard deviation ( 0 .∀v ∈ A, by theorem 3 of García et al. (2018) and also from Fernández et al. (2020), n1 n2 1. .P (v|r) = Q(v|r)∀v ∈ A ⇔ dr (x1,1 , x2,1 )

2. .∃v0 ∈ A : .P (v0 |r) = Q(v0 |r) ⇔

−→

0,

min(n1 ,n2 )→∞ n1 n2 dr (x1,1 , x2,1 ) −→ min(n ,n )→∞ 1

∞.

2

Those relations show that increasing the sample sizes increases the ability of .dr of to detect discrepancies or similarities between the stochastic laws. Obviously, the comparison between sequences state by state could be a way to be followed, but our goal is to provide global comparisons that take into account the entire state space .S. To do so, we must first identify a single state space, that is, an order (memory o) for all sequences will be established, in order to define a single state space that allows such a global comparison between the sequences. We appeal to a notion derived from the metric. In addition, we will use this global notion to introduce an index that helps to identify the more or less representative sequences, since we know that the genomic sequences tend to present heterogeneity.

8.1.2 Classifying Samples from Markov Processes Consider now n1 n2 n1 n2 dmax(x1,1 , x2,1 ) = max{ds (x1,1 , x2,1 ), s ∈ S}

(8.4)

.

dmax has some useful asymptotic properties (consistency), see Fernández et al. n1 n2 , x2,1 ) it follows that, under the (2020). From the properties observed for .dr (x1,1 assumption of Definition 8.1.1, if .{P (v|s)}v∈A,s∈S and .{Q(v|s)}v∈A,s∈S are the sets of transition probabilities of .(X1,t )t∈N and .(X2,t )t∈N , respectively, consider the state .s ∈ S such that .Nni (s) = 0, for .i = 1, 2, .P (v|s) > 0 and .Q(v|s) > 0 .∀v ∈ A, n1 n2 1. .P (v|s) = Q(v|s) ∀v ∈ A, ∀s ∈ S ⇔ dmax(x1,1 , x2,1 )

−→

min(n1 ,n2 )→∞

0,

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n1 n2 2. .∃v0 ∈ A : P (v0 |s) = Q(v0 |s) for some s ∈ S ⇔ dmax(x1,1 , x2,1 )

∞.

−→

min(n1 ,n2 )→∞

The following notion, introduced by Fernández et al. (2020), allows us to classify sequences, let’s see. n

j m Definition 8.1.2 Given a finite collection .{xj,1 }j =1 of samples from the indepenm dent processes .{Xj,t }j =1 with probabilities .{Pj }m j =1 , over the finite alphabet .A, with state space .S = Ao (.o < ∞). For a fixed .i ∈ {1, 2, . . . , m} define

n

ni ni j V (xi,1 ) = median{dmax(xi,1 , xj,1 ) : j = i, 1 ≤ j ≤ m}.

.

(8.5)

According to the properties of the Definition 8.1.2, widely identified in theorem 1 and corollary 1 of Fernández et al. (2020), we highlight the following, ni 1. If all the samples follow the same law, .V (xi,1 )

−→

min{n1 ,··· ,nm }→∞

0, i = 1, . . . , m.

2. If .Ji = {j : 1 ≤ j ≤ m, Pj = Pi }, then, for each .i, .1 ≤ i ≤ m, ni (a) .V (xi,1 ) ni (b) .V (xi,1 )

−→

0 ⇔ |Ji | > m2 .

−→

∞ ⇔ |Ji | ≤ m2 .

min{n1 ,··· ,nm }→∞ min{n1 ,··· ,nm }→∞

Where . r represents the smallest integer which is also larger than .r. Theorem 2 of Fernández et al. (2020), shows that as long as there is a nj m }j =1 , that is, under the assumption predominant law in the collection of samples .{xj,1 that the majority (.>50%) of the samples share the same law, the indicator V can classify the samples by representativeness, attributing the lowest V index to the most representative sample and attributing the highest V value to the least representative sample. In the following section, we introduce the data used in this paper, as well as, provide all the information so that the interested reader can identify them in the database that has provided them to us.

8.2 SARS CoV 2 Sequences The paper is based on groups of sequences of the Omicron (B.1.1.529) variant subtypes 1 (BA.1), 2 (BA.2) and 3 (BA.3). All the sequences that we treat are found in their FASTA expressions, that is, concatenation of elements of the alphabet .A = {a, c, g, t}. All of them come from the GISAID source, see https://www.gisaid. org/. In this article we specifically deal with 3 subtypes of Omicron SARS CoV 2 variant, since these have been the predominant ones at the end of 2021 and the beginning of 2022.

8 A Stochastic Characterization of Omicron Variant of SARS-CoV 2 Virus

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This study deals with 31 sequences coming from the BA.1 subtype, 28 sequences coming from the BA.2 subtype, and 24 sequences coming from the BA.3 subtype. 1. BA.1 (alias of B.1.1.529.1) https://cov-lineages.org/lineage.html?lineage=BA.1.1 Below are the sequences of this subtype, used in the study, ordered by laboratory (submitting and originating), see Sect. 8.4. (1) sequences: 102557x, x=01, 02, 05, 07, 08, 09, 24, 42, 46, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 65 and 102556y, y=77, 79, 80, 81, 99; (2) sequences: 10248244, 10248248; (3) sequence 10235431; 2. BA.2 (alias of B.1.1.529.2) https://cov-lineages.org/lineage.html?lineage=BA.2.2 Below are the sequences of this subtype, used in the study, ordered by laboratory (submitting and originating), see Sect. 8.4. (4) sequences: 102556x, x = 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, and 102557y, y = 14, 15, 16, 18, 20, 26, 29, 33, 34, 36, 43, 44, 45; (5) sequence 10271217; (6) sequence 10104443; 3. BA.3 (alias of B.1.1.529.3) https://cov-lineages.org/lineage.html?lineage=BA.3.3 Below are the sequences of this subtype, used in the study, ordered by laboratory (submitting and originating), see Sect. 8.4. (7) sequence 9845041; (8) sequences 97934x, x = 28, 29, 30, 31, 32, 102118y, y = 41, 42, 43, 44; (9) sequences: 8925410, 9512507, 9614593, 9614639, 9791112, 9791175, 10014520, 10255696, 10255727, 10255728, 10255750; (10) sequences: 9551718, 9275180; (11) sequence: 9404691. We use in this paper the FASTA format of each sequence which is composed of around 29,900 bases: .a, c, g, t. For the construction of the model, we must choose a memory .o. In a discrete Markov process with a discrete alphabet, the criterion considered here (the naive one) is .o < log|A| (n) − 1. For the alphabet .A = {a, c, g, t} with .n = 29,900, we have the restriction .o < 6 (the bases in a DNA structure are organized in triples), then the only reasonable option which remains is .o = 3. We use the metric, with .α = 2 (value stated in Schwarz (1978)) and .o = 3, to identify discrepancies/similarities between pair of sequences. In the results (next section), we first present a classification of the sequences via the notion .V , (1) by subtype, BA.1, BA.2 and BA.3 and then (2) considering the 3 subtypes together. Now, in a second moment, we use the notion dmax to visualize through dendrograms the way in which the sequences are grouped. We do this study in two ways (3) by subtype, BA.1, BA.2, and BA.3 and then (4) by considering the 3 subtypes together. Finally we present a global analysis of distance between the subtypes, also using the notion .dmax.

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J. E. García and V. A. González-López Table 8.1 Classification (see classifier given by Definition 8.1.2) of sequences of Omicronvariant (B.1.1.529) by subtype. From left to right BA.1, BA.2 and BA.3, in increasing order of V values, from top to bottom. In bold is the most representative sequence per subtype, and underlined the least representative sequence per subtype Sequence (BA.1) 10255746 10255707 10255724 10255751 10255749 10255702 10255754 10255679 10255748 10255752 10255701 10255756 10255677 10255705 10255753 10255742 10255755 10255699 10255758 10255681 10255709 10255708 10255757 10255680 10255763 10255762 10255761 10255765 10248248 10235431 10248244

V 0.00454 0.00475 0.00527 0.00534 0.00535 0.00542 0.00555 0.00561 0.00583 0.00589 0.00597 0.00598 0.00599 0.00606 0.00611 0.00618 0.00622 0.00625 0.00690 0.00693 0.00696 0.00697 0.00705 0.00708 0.00729 0.00737 0.00770 0.00771 0.00878 0.00948 0.01091

Sequence (BA.2) 10255683 10255687 10255684 10255690 10255685 10255691 10255693 10255718 10255686 10255689 10255694 10255715 10271217 10255726 10255720 10255695 10255733 10255716 10255697 10255714 10255734 10255692 10255743 10255744 10255736 10255745 10255729 10104443

V 0.00158 0.00175 0.00176 0.00181 0.00187 0.00195 0.00196 0.00204 0.00209 0.00209 0.00209 0.00209 0.00227 0.00227 0.00233 0.00240 0.00241 0.00249 0.00254 0.00274 0.00276 0.00288 0.00341 0.00343 0.00368 0.00375 0.00382 0.00962

Sequence (BA.3) 9845041 9793429 9793428 8925410 9793430 9614593 9551718 10255696 10211841 9793431 10211842 10211843 9793432 10211844 9791112 10014520 9404691 9614639 10255750 10255727 9512507 10255728 9275180 9791175

V 0.00245 0.00291 0.00291 0.00291 0.00291 0.00293 0.00345 0.00368 0.00368 0.00368 0.00368 0.00368 0.00368 0.00368 0.00368 0.00378 0.00383 0.00490 0.00514 0.00582 0.00623 0.00634 0.00729 0.00787

8.3 Results In the results that we show in Table 8.1, we present the classification of the sequences via the notion V (Definition 8.1.2) from left to right by subtype BA.1, BA.2, and BA.3, respectively. Highlighted in bold letter the sequence that receives the lowest value of .V , that is, the sequence that is considered the most representative of each subtype: BA.1, BA.2, BA.3. Also, the sequence that least represents the

23

80 10

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02

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5677

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99 556 102

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102557

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10255709

8 A Stochastic Characterization of Omicron Variant of SARS-CoV 2 Virus

54

102

10255

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10255748

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10 1 75

56

10

4 25572

Fig. 8.1 Dendrogram by Average, using dmax (Eq. (8.4)) between sequences of BA.1

subtype, or the most discrepant sequence when compared with those of the subtype is underlined. Then, for the BA.1 case, the most representative sequence is 10255746 (.V = 0.00454) and the least representative sequence is 10248244 (.V = 0.01091). In the case of BA.2, the most representative sequence is 10255683 (.V = 0.00158) and the least representative sequence is 10104443 (.V = 0.00962). While, for the case BA.3 the most representative sequence is 9845041 (.V = 0.00245) and the least representative sequence is 9791175 (.V = 0.00787). In Fig. 8.1, we visualize a dendrogram constructed with the values of dmax (see Eq. (8.4)) between the sequences of the BA.1 subtype. It is possible to verify that the most discrepant sequence, 10248244, according to .V , is also identified by dmax as being one of the most discrepant. While the most representative sequence 10255746

7 57

28

250

25

95 1

979

1

10211843

8

5

8

342

95

1 17

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504

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10255733

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29

J. E. García and V. A. González-López 10255734

100

Fig. 8.2 Dendrogram by Average, using dmax (Eq. (8.4)) between sequences of BA.2 (left), between sequences of BA.3 (right)

is positioned (below) in a group of 17 sequences, out of a total of 31 of the BA.1 type. In Fig. 8.2 (left), we see a dendrogram built with the values of dmax (see Eq. (8.4)) between the sequences of the BA.2 subtype. Note that the most discrepant sequence, 10104443, according to V is also identified by dmax as being the most discrepant. While the most representative sequence 10255683 is positioned in a group of 12 sequences (below), out of a total of 28 of the BA.2 subtype. While in Fig. 8.2 (right), we see a dendrogram built with the values of dmax (see Eq. (8.4)) between the sequences of the BA.3 subtype. The most discrepant sequence, 9791175, according to .V , is also identified by dmax as being the most discrepant. While the most representative sequence, 9845041, is positioned in a group of 8 sequences (left), out of a total of 24 of the BA.3 subtype. Table 8.2 shows the classification attributed by the V index (Definition 8.1.2), when considering the three subtypes, BA.1, BA.2, and BA.3 together. And Fig. 8.3 shows the dendrogram between all of them, via the use of dmax (Eq. (8.4)). We found that when considering the three subtypes together, BA.1, BA.2, and BA.3, the most representative sequence is of type BA.3, sequence 10255696.BA3, being the least representative sequence of type BA.1 sequence 10248244.BA1. From this comparison, possible through indicator .V , we rescue that BA.3 could be considered closer to BA.1 and BA.2, which leads us to measure this discrepancy/similarity. In Table 8.3, we see evidence that points to this possibility. We verify that the least representative sequences by subtype BA.1, BA.2 and BA.3, and underlined in Table 8.1 also receive higher classifications (attributed by V ) in the global comparison (sequences with * on the right, see Table 8.2), which indicates that globally they are not the most representative.

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Table 8.2 Classification (see classifier given by Definition 8.1.2) of sequences of Omicronvariant (B.1.1.529). From left to right in increasing order of V value. Each sequence shows the subtype indicator in the postfix. In bold is the most representative sequence, and underlined the least representative sequence. With ** we indicate the most representative sequence by subtype, BA.1, BA.2 and BA.3 respectively, with * we indicate the least representative sequence by subtype, BA.1, BA.2 and BA.3 respectively (see Table 8.1) Sequence 10255696.BA3 10014520.BA3 10255709.BA1 10255702.BA1 10255708.BA1 10271217.BA2 10255677.BA1 10255699.BA1 10255727.BA3 10255679.BA1 10235431.BA1 10255705.BA1 10255695.BA2 10255728.BA3 10255750.BA3 10255686.BA2 10255689.BA2 10255707.BA1 10255692.BA2 10255680.BA1 10255701.BA1 10255693.BA2 10255694.BA2 10255691.BA2 10255681.BA1 10255685.BA2 9793429.BA3 10255684.BA2

V 0.00479 0.00489 0.00533 0.00543 0.00568 0.00573 0.00578 0.00589 0.00620 0.00634 0.00639 0.00651 0.00651 0.00652 0.00659 0.00660 0.00660 0.00679 0.00696 0.00701 0.00712 0.00716 0.00716 0.00719 0.00721 0.00728 0.00733 0.00746

Sequence 10255729.BA2 8925410.BA3 10255743.BA2 9404691.BA3 10255744.BA2 9614593.BA3 10255734.BA2 9845041.BA3** 10255690.BA2 9791112.BA3 10255697.BA2 10255687.BA2 10255716.BA2 10255726.BA2 10255715.BA2 9793430.BA3 10255718.BA2 10211841.BA3 9793431.BA3 10211842.BA3 10211843.BA3 10211844.BA3 9793428.BA3 10255720.BA2 9793432.BA3 10255733.BA2 10255736.BA2 10255745.BA2

V 0.00747 0.00747 0.00747 0.00747 0.00747 0.00747 0.00747 0.00751 0.00754 0.00779 0.00786 0.00787 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00803 0.00804

Sequence 10255683.BA2** 10255724.BA1 9614639.BA3 9551718.BA3 10255714.BA2 10255742.BA1 10255746.BA1** 10255751.BA1 10255754.BA1 9512507.BA3 9275180.BA3 9791175.BA3* 10255757.BA1 10255749.BA1 10255748.BA1 10248248.BA1 10255755.BA1 10255753.BA1 10255752.BA1 10255758.BA1 10255756.BA1 10255762.BA1 10255761.BA1 10255765.BA1 10255763.BA1 10104443.BA2* 10248244.BA1*

V 0.00815 0.00818 0.00821 0.00823 0.00826 0.00838 0.00845 0.00846 0.00901 0.00911 0.00917 0.00937 0.00948 0.00949 0.00954 0.01013 0.01013 0.01015 0.01019 0.01027 0.01041 0.01103 0.01161 0.01253 0.01265 0.01313 0.01498

8.4 Concluding Remarks In this paper, we investigate the behavior of genomic sequences coming from three subtypes BA.1, BA.2, and BA.3 of the Omicron variant of the SARS CoV 2 virus. This variant has dominated contaminations by the SARS CoV 2 virus in late 2021 and early 2022, representing a challenge for the global health because, despite the fact that the contingent of vaccinated has grown, this variant has been shown to be efficient in continuing to contaminate the population, and has even been shown to be

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Fig. 8.3 Dendrogram by Average, using dmax (Eq. (8.4)), between sequences of subtypes BA.1, BA.2, and BA.3. In blue, the subtype BA.1, in red, the subtype BA.2, and in green, the subtype BA.3. Marked with an oval and in the color of the subtype the most representative sequence of the subtype. Underlined in the color of the subtype the least representative sequence per subtype (Color figure online)

capable of evolving. Today there are already records of two more recently emerged subtypes, BA.4 and BA.5. From all this context arises the need to study and establish how these subtypes are related. To carry out such a comparison, in this paper, we propose to use inferential tools developed in the context of finite order Markovian stochastic processes on finite alphabets. The comparison is made possible by establishing that the sequences in FASTA format can be considered samples coming from stochastic processes on the alphabet .A = {a, c, g, t}, which is the genomic alphabet. A metric essentially designed to compare samples coming from stochastic processes is used, see Definition 8.1.1. Based on such a notion, it is possible to compare the sequences in relation to

8 A Stochastic Characterization of Omicron Variant of SARS-CoV 2 Virus

103

Table 8.3 Comparison between subtypes: mean (left) and median (right) value between the dmax values BA.1 BA.2 BA.3

BA.1 0.00667 – –

BA.2 0.01080 0.00303 –

BA.3 0.00893 0.00826 0.00434

BA.1 BA.2 BA.3

BA.1 0.00623 – –

BA.2 0.01075 0.00249 –

BA.3 0.00846 0.00840 0.00375

the transition probabilities that each sequence show in .S = Ao state space (with .o = 3). Two notions, dmax (see Eq. (8.4)) and V (see Definition 8.1.2), are derived from such a metric. dmax allows a global comparison between the sequences (small values indicate great proximity), V allows determining each sequence’s representativeness in relation to its subtype and globally (small values indicate greater representativeness). V identifies which are the most and least representative sequences by subtype, and these findings appear in the dendrograms by subtype, see Table 8.1 and Figs. 8.1 and 8.2. For BA.1, the most representative sequence is 10255746, and the least representative sequence is 10248244. For BA.2, the most representative sequence is 10255683, and the least representative sequence is 10104443. For BA.3, the most representative sequence is 9845041, and the least representative sequence is 9791175. We can see that the sequences considered least representative by subtype, also are the least representative in the whole set, see Table 8.2, sequences with * on the right. The comparative study that includes the three subtypes points to the following evidence. From Fig. 8.3, we conclude that dmax captures the separation between the subtypes. dmax forms several groups with a predominance of one subtype per group, In blue, the subtype BA.1, in red, the subtype BA.2, and in green, the subtype BA.3. From Table 8.2 we see that V shows that the sequence 10255696.BA3 can be considered the most representative sequence of the whole set (with three subtypes), and V shows that the sequence 10248244.BA1 can be considered the most discrepant sequence of the whole set (with three subtypes). According to the table that records the mean and median values of dmax, intra subtypes and extra subtypes (Table 8.3) we see that there is greater heterogeneity in type BA.1 sequences, and, it is possible to more easily discriminate BA.1 from BA.2 than BA.1 from BA.3 or BA.2 from BA.3. With this preliminary study of Omicron subtypes (composed by BA.1, BA.2 and BA.3), we hope to contribute in the attempt to measure the discrepancy and similarity between the subtypes. Establish a comparison framework regarding the subtypes that can help to understand the evolution of the new subtypes of Omicron, as BA.4 and BA.5. Acknowledgments The authors thank GISAID (https://www.gisaid.org/) for making available the genomic sequences investigated in this paper. Below we list the responsible laboratories (submitting and originating), related to each sequence (omitting the prefix EPI_ISL_). BA.1: (1) sequences: 102557x, x = 01, 02, 05, 07, 08, 09, 24, 42, 46, 48, 49, 51, 52, 53, 54, 55,

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56, 57, 58, 61, 62, 63, 65 and 102556y, y = 77, 79, 80, 81, 99; Originating lab: Laboratorium Diagnostyki Medycznej (ul. Debinki 4, 80-211 Gda´nsk); Submitting lab: Wojewódzka Stacja Sanitarno-Epidemiologiczna w Gda´nsku (Debinki 4, 80-211 Gda´nsk). (2) sequences: 10248244, 10248248; Originating lab: GH A.CHENEVIER-H.MONDOR (51 avenue du Maréchal de Lattre de Tassigny,94010,CRETEIL Cedex); Submitting lab: Department of Virology, Henri Mondor University Hospital, Assistance Publique Hôpitaux de Paris, Université Paris-Est Créteil, INSERM U955 (51 avenue du Maréchal de Lattre de Tassigny, 94010 Créteil, France) (3) sequence 10235431; Originating lab: TN DOH Lab Services (630 Hart La, Nashville TN 37216); Submitting lab: TN DOH Lab Services (630 Hart La, Nashville TN 37216). BA.2: (4) sequences: 102556x, x = 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, and 102557y, y = 14, 15, 16, 18, 20, 26, 29, 33, 34, 36, 43, 44, 45; Originating lab: Laboratorium Diagnostyki Medycznej (ul. Debinki 4, 80-211 Gda´nsk); Submitting lab: Wojewódzka Stacja Sanitarno-Epidemiologiczna w Gda´nsku (Debinki 4, 80-211 Gda´nsk). (5) sequence 10271217; Originating lab: WSSE w Krakowie (31-202 Kraków, ul. Pradnicka 76); Submitting lab: Wojewódzka Stacja Sanitarno-Epidemiologiczna w Katowicach (Raciborska 39, 40-074 Katowice). (6) sequence 10104443; Originating lab: Allergy, Immunology and Cell Biology Unit (AICBU) (Department of Immunology and Molecular Medicine, Faculty of Medicine, University of Sri Jayewardenepura, Sri Lanka); Submitting lab: Allergy, Immunology and Cell Biology Unit (AICBU) (Department of Immunology and Molecular Medicine, Faculty of Medicine, University of Sri Jayewardenepura, Sri Lanka). BA.3 (7) sequence 9845041; Originating lab: Institute of Molecular and Translational Medicine/Laboratory of Experimental Medicine, Faculty of Medicine and Dentistry, Palacky University (Hnˇevotinská 5, 77900 Olomouc, Czech Republic); Submitting lab: Institute of Molecular and Translational Medicine/Laboratory of Experimental Medicine, Faculty of Medicine and Dentistry, Palacky University (Hnˇevotinská 5, 77900 Olomouc, Czech Republic). (8) sequences 97934x, x = 28, 29, 30, 31, 32, 102118y, y = 41, 42, 43, 44; Originating lab: CERBALLIANCE CHARENTES (2 Rue du Dr Rene Laennec, 17100 Saintes); Submitting lab: CERBA HealthCare (7-11 rue de l’equerre 95230 Saint-Ouen l’Aumone). (9) sequences: 8925410, 9512507, 9614593, 9614639, 9791112, 9791175, 10014520, 10255696, 10255727, 10255728, 10255750; Originating lab: Laboratorium Diagnostyki Medycznej (ul. Debinki 4, 80-211 Gda´nsk); Submitting lab: Wojewódzka Stacja Sanitarno-Epidemiologiczna w Gda´nsku (Debinki 4, 80-211 Gda´nsk). (10) sequences: 9551718, 9275180; Originating lab: Laboratorium Medyczne GynCentrum – Oddzial Sosnowiec (SLASKIE, Sosnowiec, 41-208, ul. Wojska Polskiego 8A); Submitting lab: Wojewódzka Stacja Sanitarno-Epidemiologiczna w Katowicach (Raciborska 39, 40-074 Katowice). (11) sequences: 9404691; Originating lab: Medyczne ´ Laboratorium Diagnostyczne Centrum Medyczne Femina Kapu´sniak Waleczek sp.j (SLASKIE, Katowice, Katowice, 40-703, ulica: Kłodnicka, nr domu: 23); Submitting lab: Wojewódzka Stacja Sanitarno-Epidemiologiczna w Katowicach (Raciborska 39, 40-074 Katowice).

References Csiszár, I., & Talata Z. (2006). Context tree estimation for not necessarily finite memory processes, via BIC and MDL. IEEE Transactions on Information Theory, 52(3), 1007–1016. Fernández, M., García, J. E., Gholizadeh, R., & González-López, V. A. (2020). Sample selection procedure in daily trading volume processes. Mathematical Methods in the Applied Sciences, 43(13), 7537–7549. García, J. E., & González-López, V. A. (2017). Consistent estimation of partition Markov models. Entropy, 19(4), 160. García, J. E., Gholizadeh, R., & González-López V. A. (2018). A BIC-based consistent metric between Markovian processes. Applied Stochastic Models in Business and Industry, 34(6), 868– 878. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.

Chapter 9

Factors Associated with Direct and Indirect Aspects of Loneliness Among Europeans Aged 50 or Higher Eleni Serafetinidou

9.1 Introduction Loneliness is considered as a major problem for individuals, with emphasis to those in older ages. Perlman and Peplau (1981), defined loneliness as “a subjective, unwelcome feeling of lack or loss of companionship that happens when it is observed dissimilarity between the quantity and quality of social relationships we have and those we want”. As authors suggest, loneliness is a different condition that should not be confused with social isolation. In this study, the focus is on the subjective emotional experience of loneliness instead of social isolation, which is related to the objective experience of how often we are alone (Office for National Statistics, 2018) and the lack of social contacts or relationships (Hawkley & Cacioppo, 2010). Past literature supports studies detecting factors and mechanisms that contribute to the feeling of loneliness. Even though the sense is observed in people of all ages, researchers have pointed that firstly, loneliness tends to increase with age (Neto, 2014a; Hansen & Slagsvold, 2016), especially for individuals over 80 years who are more vulnerable, and secondly, that women report significantly higher percentages of this feeling compared to men (Demakakos et al., 2006; Beutel et al., 2017). Possible predictors of loneliness are poor health, infrequent social contact and isolation, and the experience of divorce (Neto, 2014a) or widowhood as well (Theeke, 2010). In particular, individuals suffering from cardiovascular or coronary heart disease, stroke, physical illness and depression or other mental disorder, not only are expected being alone more frequently compared to healthy persons but also tend to have an increased mortality risk (Singer, 2018; Grover et al.,

E. Serafetinidou () Department of Statistics and Insurance Science, University of Piraeus, Athens, Greece © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_9

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2018). Researchers consider that there is an evident link between loneliness and depression (Beutel et al., 2017; Taube et al., 2013) as patients suffering from depression or somatic symptoms tend to be more vulnerable to loneliness (Grover et al., 2018). Moreover, persistent difficulties including activities of daily living (adl), instrumental activities of daily living (iadl) and poor subjective health (self – perceived health) are associated to feeling lonely in later life (Yeh & Lo, 2004; Theeke, 2010; Hansen & Slagsvold, 2016). Further, cognitive decline (Boss et al., 2015; Nikmat et al., 2015) and the potential risk of Alzheimer’s disease are strongly associated with being lonely (Office for National Statistics, 2018) while the opposite does not necessarily hold (Okely & Deary, 2019). Contrasting to previous results, being married or having a partner or cohabiting assist in reducing the emptiness of loneliness whereas being single widens this feeling (Phaswana-Mafuya & Peltzer, 2017; Grover et al., 2018). Demakakos et al. (2006) agree that contact with others and having children (Beutel et al., 2017) are very important factors which eliminate this disorder. For instance, families’ relationships, including substantial contact with partner or children, contribute to the limitation of being alone whereas not being close to members of the family widens the distance among them. Hansen and Slagvold (2016) included the number of children in their study as a protective factor against loneliness empowering the social contact and support for the elderly. Additionally, Sundström et al. (2009) in their analysis found that living with a partner is beneficial to eliminate the prevalence of loneliness and this holds across all European countries. Moreover, they supported that for respondents living alone and having poor health the odds of feeling lonely were ten times higher compared to individuals having good health and staying with someone. Regarding economic hardship, findings highlight that frequency of economic problems leading to deprivation and poverty result in the enhancement of loneliness in adults over 65 years old (Ausín et al., 2017). Another study illustrated that lower socioeconomic status is strongly associated with that feeling and this holds for the majority of Europeans aged 60–80 resident in 11 countries (Hansen & Slagsvold, 2016). As an offset to this serious and harmful experience, good quality of life and the sense of satisfaction with life may limit the prevalence of loneliness (Ausín et al., 2017; Taube et al., 2013). Indeed, there is a reverse relationship between life satisfaction and the sense of loneliness indicating that as life satisfaction increases, the estimated level of loneliness decreases (Akhunlar, 2010). Additionally, having a good educational attainment contributes to the restriction of this feeling. The latter factor is significant as the higher the education the less likely for an individual to feel lonely (Neto, 2014b; Vakili et al., 2017). Finally, physical inactivity, smoking, sleeping problems and low self-esteem create paths and linkages guiding to the experience of loneliness (Office for National Statistics, 2018). Loneliness was evaluated and measured under the development of a 20-item general measure scale of loneliness, known as UCLA (University of California, Los Angeles) Loneliness Scale. The construction of the measure gave evidence that scale items are internally highly consistent (coefficient alpha = 0.96) (Russell et al., 1978). Since then, Hughes et al. (2004) introduced a short version of the UCLA

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Loneliness Scale including only three items i.e. companionship, being left out and being isolated and thus measuring the indirect aspect of loneliness. Nevertheless, based on the Survey of Health, Aging and Retirement in Europe (SHARE), the above-mentioned items can be replaced with a direct over-all item measuring selfassessment of loneliness (Mehrbrodt et al., 2017). Aims of the Study The purpose of this study is to estimate the effect of predictors of loneliness covering different domains of life on the three indirect items of the loneliness scale and the fourth item, separately. The analysis is structural and, based on a holistic process, focuses on the factors of health, economic conditions and demographic characteristics in order to examine the magnitude of their association with the items of loneliness. Results will inform psychologists regarding special characteristics of the items giving the chance to deal with the harmful condition of loneliness that makes people of all ages suffer, particularly the older ones.

9.2 Data and Methods Sample Data included in the present analysis were derived from the database of SHARE giving information of respondents’ life histories aged 50 or higher, resident in different European countries. SHARE is a longitudinal and cross-national database, providing material regarding health, socioeconomic status and demographic factors for individuals (Börsch-Supan et al., 2013). Collection of data was carried out in different time points and information was gathered and classified in corresponding waves referring to the specific year of the survey. In particular the data used in the present study comes from the sixth wave of the survey conducted in 2015, including 64,670 respondents dwelling in the countries mentioned below: Austria, Germany, Sweden, Spain, Italy, France, Denmark, Greece, Switzerland, Belgium, Israel, Czech Republic, Poland, Luxembourg, Portugal, Slovenia, Estonia and Croatia. The initial sample included 68,188 individuals but 3518 persons (5.15%) were excluded as missing values. Based on Jakobsen et al. (2017), as the percentage of missing cases is close to 5%, the analysis was performed without replacing them applying an imputation technique. Measures Dependent variables The outcome factors in the current analysis involve the three-item scale of loneliness, referring to the indirect dimension of this condition, and the fourth item as well, corresponding to the direct measure of loneliness. In particular, the indirect dependent variables of interest are “How much of the time do you feel you lack companionship”, “How much of the time do you feel left out” and “How much of the time do you feel isolated from others” and the direct one is “How much of the time do you feel lonely”. For all items, the answers of respondents are grouped in three

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categories according to the Likert scale i.e. (1) “often”, (2) “some of the time” and (3) “hardly ever or never”; the latter is the reference category. Although the score of measurement for the indirect items varies from 3, indicating “no lonely status”, to 9, indicating “very lonely status”, the literature does not support a threshold in order to categorize respondents as “lonely” and “not lonely” individuals. Due to this reason, the direct measure provides further information concerning loneliness, based on the self-assessment of respondents. Independent variables Health predictors included in the analysis are a variable indicating whether individuals are limited or not in their activities (gali), the number of instrumental activities of daily living respondents had to deal with, the number of mobility limitations and the subjective measure of self-perceived health (1: excellent status – 5: poor status). The last factor has been used by Richard et al. (2017) in their analysis as well, whereas Jagger et al. (2010) support that gali measures functional ability across European countries. Instrumental activities of daily living include the following items: (1) using a map to figure out how to get around in a strange place, (2) preparing a hot meal, (3) shopping for groceries, (4) making telephone calls, (5) taking medications, (6) doing work around the house or garden and (7) managing money, such as paying bills and keeping track of expenses. Further, mobility limitations correspond to the number of limitations with respect to an individual’s mobility, arm function and fine motor function. All of the above factors were measured in discrete form apart from gali that is binary (0: not limited as reference category and 1: limited). Additionally, depression, referring to the mental health status of respondents, is measured through the “eurod” scale, counting the total number of symptoms out of a 12 list including (1) depression, (2) pessimism, (3) suicidality, (4) guilt, (5) sleep, (6) interest, (7) irritability, (8) appetite, (9) fatigue, (10) concentration, (11) enjoyment and (12) tearfulness. Above variables are described in detail in the Release Guide 2.6.0 for Waves 1&2 of SHARE (Release Guide 2.6.0 Waves 1&2, 2013). Cognitive function is measured through “orienti”, describing orientation in time and, in particular, orientation to date, month, year and day of week as well as memory, writing and reading tests. Concerning orientation, the score ranges from 0 to 4; the higher the score the better oriented the respondents are. For all the remaining components of cognitive ability the score ranges from 1 (excellent performance) to 5 (poor performance). Similarly to our analysis, other researchers have measured cognitive function considering memory, orientation, attention, comprehension, new learning, perception and calculation (Donovan et al., 2017; Evans et al., 2019). The socioeconomic status of individuals is represented by the ordinal qualitative variable of “fdistress” showing whether the household was able to make ends meet. Possible answers of individuals are ‘with great difficulty’, being the reference category, ‘with some difficulty’, ‘fairly easily’ and ‘easily’. The perspective of life is measured through “lifesat”, a discrete scale estimating the amount of persons’ life satisfaction. Lower values of the scale indicate dissatisfaction, especially the zero value, reporting complete dissatisfaction. Higher values of the scale indicate the opposite status˙ the upper value is ten showing complete satisfaction. Finally, a

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binary risk factor reporting the daily smoking status of respondents has been used (0: never smoked as reference category and 1: smoked in the past or presently). Previous studies for loneliness have included this factor as well (Richard et al., 2017; Stickley & Koyanagi, 2018). Demographic predictors include age of the respondents at the time of interview and years of education (which evaluates their educational attainment), both measured in discrete form. Further, a variable showing whether the respondent had a partner (reference category) or was alone and the number of an individuals’ children are included in the analysis. Finally, country – as a control variable – and gender have been used to examine differences (corresponding reference categories are Austria and males). Statistical Analysis The analysis was carried out using the gologit2 routine, written for Stata, version 13. Gologit2 is a program that estimates generalized logistic regression models for ordinal dependent variables (Williams, 2005a, b) and comprises a development of gologit routine, being inspired by Vincent Fu (Williams, 2016). A major advantage of this method is that it can estimate a partial proportional odds model which is less restrictive compared to a proportional odds model (or parallel lines model) being estimated by the ologit model (ordinal logit model) but more interpretable than models estimated through a non-ordinal method, for instance the mlogit model (multinomial logistic regression model). In the present analysis all of the ordinal outcome variables have three categories, so the generalized ordered model for each of them can be written (Williams, 2005b) as.   exp aj + Xi βj  j = 1, 2   P (Yi > j ) = (9.1) 1 + exp aj + Xi βj pointing out that the gologit model will have two sets of coefficients. The ordered logit model is a special case of the gologit model where the betas are the same for each j. In a partial proportional odds model as the one being applied in this study, some of the beta coefficients are the same for values 1 and 2 of j, while others can differ. As a consequence, the powerful mark of this method is that it has the option to restrict variables where it is functional to meet the parallel lines assumption, letting the others free from that constraint (Williams, 2016). The interpretation of the results is achieved through binary logistic regression comparisons between the first category of j versus the second and third and the first and second category of j versus the third. Based on the assumption of proportional odds model the effect of X on Y is the same among all comparisons (Williams, 2016) while based on the partial proportional odds model this does not hold for few X, being the fundamental difference between the models. The reliability of the gologit2 method bears out through autofit, pl and lrforce available options. Under the autofit option, which is an iterative process, a series of Wald tests for each variable is accomplished in order to examine whether variables

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fulfil the parallel lines assumption. Whether the result of Wald test is statistically insignificant for one or more variables, the one with the least significant value is constrained to have equal effects among equations. Afterwards, the model is reestimated with previous constraints and the process is repeated until there are not other variables meeting the parallel lines assumption. Finally, a global Wald test is done where a statistically insignificant test value indicates that the assumption is not violated by the final model. The pl option sets the constraints for the specific explanatory variables to satisfy the parallel lines assumption whereas for the remaining variables there is no need for that. Finally, the lrforce option is used for the performance of a Likelihood Ratio Statistic for the constrained model (Williams, 2005a, b).

9.3 Results Table 9.1 shows predictors having constraints in order to meet the parallel lines assumption or partial proportional odds model. We distinguish differences among indirect items and between direct and indirect as well. Gali, instrumental activities of daily living and reading are constrained predictors among all items of the loneliness scale whereas orientation in time, memory, whether household was able to make ends meet, age at the time of interview, years of educational attainment and number of children meet the parallel lines assumption for two of the three indirect items, not necessarily the same, and the direct one. Being satisfied with life and the smoking status of respondents are restricted factors for the feelings of isolation and lack of companionship respectively. By contrast, mobility limitations, selfperceived health, depression and whether individuals were single are not constrained predictors, regarding all indirect items and the direct as well. Further, smoking status and gender are free of parallel lines assumption considering the direct measure. The line before the last of Table 9.1 informs about the total number of variables meeting this assumption; the rest not inscribing in the table refer to selected countries participating in the analysis. Showing the coefficients in Tables 9.2 and 9.3 respectively, we observe that partial proportional odds model restricts βκ coefficients to be the same among the two categories of dependent variables, i.e., often and some of the time, while letting other variables free to vary. A series of Wald tests is conducted on each variable individually in order to see whether coefficients among the categories often and some of the time are the same. Finally, a statistical insignificant global Wald test for the final model in the latter table line indicates that the final model does not violate the parallel lines assumption. In other words, showing the two last table lines, for instance, we can see that, regarding the lack of companionship item, fourteen constraints have been imposed to the final model, eight of them referring to selected predictors whereas the rest of them to selected countries, not included in Table 9.1, having their effects meet the parallel lines assumption.

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Table 9.1 P-values for constraints imposed for parallel lines assumption regarding predictors measuring loneliness directly and indirectly (selected countries are constrained) Indirect measure Direct measure Companionship Left out Isolated Feeling lonely Health factors Gali Instrumental activities of daily living Mobility limitations Self-perceived health Depression Cognitive factor Orientation in time Memory skills Reading skills Writing skills Factor of perspective of life Life satisfaction Risk factor Smoking status Factor of socioeconomic status Household able to make ends meet With some difficulty Fairly easily Easily Demographic factors Age at the time of interview Gender (ref. cat.: Males) Years of education Single (ref. cat.: Yes) Number of children Number of variables being constrained Global Wald test for the final model

0.0927 0.0910

0.9364 0.5869 0.6214

0.4083 0.4789

0.0861

0.0659 0.3987

0.2281 0.1726

0.1474 0.1159 0.7898 0.2891

0.8507 0.5912 0.5711 0.3035

0.1631

0.4904

0.2690

0.3459

0.3998 0.3832

0.2342

0.9075

14 0.1407

0.8886 0.8252 0.5632 0.9452

0.2675

0.6676 0.7922

0.2803

0.0728 16 0.2859

0.3207 20 0.0572

0.8422 16 0.7236

Feelings of indirect measures include (1) How much of the time someone feels lack of companionship, (2) How much of the time someone feels left out and (3) How much of the time someone feels isolated from others. Feeling of direct measure includes How much of the time someone feels lonely

Tables 9.2 and 9.3 give information regarding the coefficients of the model and standard errors in parenthesis for two separate equations, taking into consideration the categories ‘often’ and ‘some of the time’. As we described earlier – in the data and methods section – the comparisons are between (i) the category “often” versus the categories “some of the time” and “hardly ever or never” and (ii) the categories “often” and “some of the time” versus the category “hardly ever or never”. The interpretation of the results is much more straightforward for variables meeting the parallel lines assumption, having the same coefficients across equations.

Category often Health factors Gali Instrumental activities of daily living Mobility limitations Self-perceived health Depression Cognitive factor Orientation in time Memory skills Reading skills Writing skills Factor of perspective of life Life satisfaction Risk factor Smoking status Factor of socioeconomic status Household able to make ends meet With some difficulty Fairly easily Easily Demographic factors Age at the time of interview Gender (ref. cat.: Males) −0.1258*** (0.0260) −0.0138 (0.0095) −0.0566*** (0.0094) −0.1036*** (0.0259) −0.3191*** (0.0087) 0.1378*** (0.0298) −0.0305 (0.0214) −0.0423** (0.0169) −0.0871*** (0.0225) 0.2041*** (0.0108) −0.0712* (0.0418)

0.2183*** (0.0467) 0.2235*** (0.0356) 0.2578*** (0.0380) −0.0037*** (0.0012) 0.1352*** (0.0442)

−0.0134(0.0184) −0.0174*(0.0104) −0.0772***(0.0150) 0.0318*(0.0190)

0.1250***(0.0089)

−0.0101(0.0187)

0.0357(0.0397) 0.1005**(0.0455) 0.0409(0.0340)

−0.0047***(0.0010) 0.0640*(0.0338)

Left out

−0.0783***(0.0222) 0.0189**(0.0087) −0.0387***(0.0076) −0.1079***(0.0205) −0.2934***(0.0071)

Indirect measure Companionship

0.0005 (0.0022) 0.0334 (0.0250)

0.1315*** (0.0333) 0.2158*** (0.0379) 0.1405** (0.0639)

−0.1537*** (0.0445)

0.1887*** (0.0068)

0.0532** (0.0210) −0.0641*** (0.0128) −0.0566*** (0.0182) −0.0339* (0.0179)

−0.2032*** (0.0286) −0.0672*** (0.0096) −0.0555*** (0.0099) −0.1001*** (0.0284) −0.3403*** (0.0090)

Isolated

−0.0031*** (0.0011) −0.0415 (0.0404)

0.1301*** (0.0446) 0.1724*** (0.0511) 0.0539 (0.0372)

−0.0770** (0.0379)

0.1957*** (0.0063)

0.0037 (0.0198) −0.0291** (0.0115) −0.0827*** (0.0166) 0.0019 (0.0163)

−0.0564**(0.0251) 0.0113(0.0092) −0.0344*** (0.0085) −0.0910*** (0.0232) −0.3555*** (0.0079)

Direct measure Feeling lonely

Table 9.2 Coefficients and standard errors in parenthesis for the indirect and direct items measuring loneliness for the category “Often”

112 E. Serafetinidou

0.0068(0.0043) −1.2448***(0.0327) −0.0335***(0.0107) 4.6284***(0.1722)

−0.0079*** (0.0029) −0.4556*** (0.0419) 0.0176** (0.0079) 4.5835*** (0.2219)

−0.0079** (0.0031) −0.6539*** (0.0447) 0.0623*** (0.0086) 5.1392*** (0.2240)

−0.0030 (0.0028) −1.5682*** (0.0376) 0.0430*** (0.0076) 4.6912*** (0.1676)

All models were controlled for country of residence. Feelings of indirect measures include (1) How much of the time someone feels lack of companionship, (2) How much of the time someone feels left out and (3) How much of the time someone feels isolated from others. Feeling of direct measure includes How much of the time someone feels lonely Bold coefficients represent variables meet the parallel lines assumption *** p-value 0 for .1 ≤ k ≤ m, while .η0 = 0, that is, on level 0 there occurs no further decay of immunity. The general theory of Markov jump processes and the characterization of their dynamics in terms of the infinitesimal generator .Λ can be found in Ethier and Kurtz (1986). In general, for a Markov jump process X with state space .(E, d) (a polish space, e.g. .Rn or space of Radon measures) and transition kernel .r(·, ·), the transitions can be described by X → X at rate r(X, dX ).

.

The infinitesimal generator is the operator .Λ defined on the space of bounded continuous functions .Ψ on the space E by 

(Ψ (X ) − Ψ (X))r(X, dX )

(ΛΨ )(X) =

.

(13.1)

E

Then, according to Ethier and Kurtz (1986), we have the dynamics  Ψ (X(t)) = Ψ (X(0)) +

t

.

(ΛΨ )(X(s))ds + MΨ (t)

(13.2)

0

where the deterministic trend is driven by the infinitesimal generator .Λ, to which we add a trendless stochastic noise .MΨ which is a martingale, i.e. .E[Mψ (t) | Fs ] = Mψ (s) for .s ≤ t. In our case with only a finite number of possible transitions, the integral in the formula for the infinitesimal generator reduces to a sum and therefore we have (ΛΨ )(X) =



.

X→X

(Ψ (X ) − Ψ (X))r(X, X )

(13.3)

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where the rates .r(X, X ) correspond to the four possible transition types described above: infection, vaccination, decay of immunity and recovery and depend further on the components k. By considering the continuous bounded functions .Ψk (X) = X˜ k which are equal to the k-th component .Xk if .|Xk | ≤ M and equal to M otherwise, for a sufficiently large constant M (noting that due to our assumption we have .0 ≤ Xk ≤ 1), we obtain the following integral equations which describe the deterministic trend of the process: 

t

Sk (t) = Sk (0) +

.

−βk · I (s) · Sk (s) − γk · I p (s) · Sk (s) − ηk · Sk (s)

0

for 0 ≤ k ≤ m − 1 +ηk+1 Sk+1 (s) ds  t m−1  α · I (s) + γk · I p (s) · Sk (s) − ηm · Sm (s) ds Sm (t) = Sm (0) + 0



t m−1 

I (t) = I (0) +

k=0

βk · I (s) · Sk (s) − α · I (s) ds

(13.4)

0 k=0

which means that the dynamics of the Markov jump process is a stochastic perturbation with a trendless noise of the following system of ordinary differential equations: .

dSk = −βk · I · Sk − γk · I p · Sk − ηk · Sk + ηk+1 Sk+1 , 0 ≤ k ≤ m − 1 dt

 dSm = α·I + γk · I p · Sk − ηm · Sm dt m−1 k=0

dI = dt

m−1 

βk · I · Sk − α · I

(13.5)

k=0

In the next section we will present the algorithm for numerical simulations of the considered stochastic process, while in Sect. 13.4 we will show that the second moments of the martingale parts are scaling like .1/N, meaning that for large N the magnitude of the random fluctuations becomes small. Moreover, based on this property, we can prove that for .N → ∞ a convergence result of the family of Markov jump processes towards the solution of (13.4) or (13.5) holds in the mean square sense.

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13.3 The Algorithm for Numerical Simulations m+2 Given the state .X = (S, I ) ∈ R≥0 with .S = (Sk )m k=0 at time t:

1. Simulate the waiting distributed random variable with  time .Δt as exponentially  parameter .λ = X→X RX→X = 4i=1 Ri , with m−1 • .R1 = N · I · k=0 β ·S m−1 k k • .R2 = N ·  I p · k=0 γk · Sk • .R3 = N · m η · S k k k=1 • .R4 = N · α · I 2. 3. 4. 5.

Sample the transition step of type i with probability proportional to .Ri .  (i) (i) Within step i with .Ri = k Qk sample k with probability proportional to .Qk .  Perform the transition .X → X according to i and k. Set .t = t + Δt.

13.4 The Convergence Result The following lemma states the properties of the martingale terms .Mj (t) := MΨj (t) for the functions .Ψj defined above, being essentially the projection on the j -th component of a vector in .Rm+2 . Lemma 13.1 For the martingales .Mj (·), .0 ≤ j ≤ m + 1, we have the estimates Ex [Mj2 (t)] ≤

.

Cj t N

with a suitable constant .Cj depending only on m and on the coefficients of the system (13.5), where .Ex [·] denotes the conditional expectation with respect to the initial condition .X(0) = x. Proof By standard techniques, we obtain similarly as in Guia¸s (2010):  2 .Ex [Mj (t)]

=

t

0

X→X

−2  =

   2 Xj (s) − Xj (s) + Mj (s) − Mj2 (s) − Ex 

Xj (s) − Xj (s)

t

Ex 0







Mj (s) · R

X→X

ds

2   Xj (s) − Xj (s) · RX→X

X→X

ds

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F. Guia¸s

 = 0

1 = N

t

m+1 4  1  2 −(ek )j + (ek  )j · N · ri (X(s)) ds Ex N2 k=0 i=1



t

m+1 4   2 −(ek )j + (ek  )j · ri (X(s)) ds Ex

0

k=0 i=1

where .k  is the new state into which the process jumps from state k (the infectious state  I corresponds to .Xm+1 and .Sk to .Xk for .0 ≤ k ≤ m, while .Ri = N · Sect. 13.3. Since in our model we have .Xk ∈ [0, 1] with k ri (X(s)) are defined in the conservation property . Xk = 1 and due to the assumptions on the coefficients .βk , γk , ηk , α, the form of .ri implies that the random process inside the expectation is uniformly bounded by a constant .Cj depending on m and on the parameters of the model. Therefore we conclude that Ex [Mj2 (t)] ≤

.

Cj t N



which proves the statement of the lemma.

The convergence result of the family of stochastic processes towards the solution of the deterministic differential equation is given in the following Theorem 13.1 Denoting by .X(t) the solution of (13.4) and by .X(N ) (t) the Markov jump process depending on the scaling parameter N, if .X(0) − X(N ) (0)1 → 0 in mean square as .N → ∞, then .supt≤T X(t) − X(N ) (t)1 → 0 in mean square as  m+2 , that is, .x = .N → ∞. By . · 1 we denote the 1-norm on .R |xi |. 1 Proof The structure of the equations in (13.4) is similar, so we consider exemplarily only estimates for the equations for .0 ≤ k ≤ m−1. For the equations corresponding to .k = m and .k = m + 1 (equation for I ) the computations are similar. Noting that  Sk (t) = Sk (0) +

t

.

−βk · I (s) · Sk (s) − γk · I p (s) · Sk (s) − ηk · Sk (s)

0

+ηk+1 Sk+1 (s) ds  t (N ) (N ) (N ) (N ) −βk · I (N ) s) · Sk (s) − γk · (I (N ) (s))p · Sk (s) Sk (t) = Sk (0) + 0

−ηk · Sk(N ) (s) (N )

(N )

+ηk+1 Sk+1 (s) ds + Mk (t) we have: (N )

(N )

|Sk (t) − Sk (t)| ≤ |Sk (0) − Sk (0)| +

.

 0

t

(N )

βk |I (s) · Sk (s) − I (N ) s) · Sk (s)|

13 Epidemic Models with Several Levels of Immunity

169 (N )

(N )

+γk |I p (s) · Sk (s)−(I (N ) (s))p · Sk (s)|+ηk |Sk (s)−Sk (s)| (N ) +ηk+1 |Sk+1 (s) − Sk+1 (s)| ds + |Mk(N ) (t)|

(13.6)

By using the estimate |I p · Sk − (I (N ) )p · Sk(N ) | ≤ |I p · Sk − I p · Sk(N ) | + |I p · Sk(N ) − (I (N ) )p · Sk(N ) |

.

applied to the terms in (13.6) with .I p and factor .γk as well as for .p = 1 to the terms with factor .βk and using the conservation property of the stochastic process and of the differential equation system (13.5) which implies that every component lies between 0 and 1, we obtain that (N )

(N )

|I p · Sk − (I (N ) )p · Sk | ≤ |Sk − Sk | + |I p − (I (N ) )p |.

.

Inserting this type of estimate in (13.6) (noting that for components m and .m + 1 we obtain similar estimates) and summing up over the index k we obtain: X(t) − X(N ) (t)1 ≤ X(0) − X(N ) (0)1 +

m+1 

.

|Mk(N ) (t)|

k=0



t

+ C1 0

X(s) − X(N ) (s)1 ds

where the constant .C1 depends only on m and on the parameters of the system. By taking supremum over .t ∈ [0, T ] and applying Gronwall’s inequality we obtain

.

sup X(t) − X t≤T

(N )

(t)1 ≤ X(0) − X

(N )

(0)1 +

m+1 

(N ) sup |Mk (t)| t≤T k=0

 · eC1 T

  By taking the second moments on each side, using .( ni=1 ai )2 ≤ n ni=1 ai2 and (N ) (N ) Doob’s maximal inequality .E[supt≤T |Mk (t)|2 ] ≤ 4E[|Mk (T )|2 ], together with Lemma 13.1, we obtain

   C (T )  2 (N ) 2 ·eC1 T .Ex (sup X(t) − X (t)1 ) ≤ Ex (X(0) − X(N ) (0)1 )2 + N t≤T from which the statement of the theorem directly follows.



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13.5 Numerical Simulations In this section we present the results of numerical simulations. The settings considered are the following: m=3 S0 (0) = 0.99, I (0) = 0.01, Si (0) = 0, 1 ≤ i ≤ 3 −1 = 4 days) .α = 0.25 (average time of being in the infectious state: . Tinf = α .R0 > 1 (basic reproduction number, infection related to immunity level 0) α · R0 , 0 ≤ k ≤ m − 1, βm = 0 • .βk = k+1 0.038 , 0 ≤ k ≤ m − 1, γm = 0 , i.e. the average time of staying • .γk = (k + 1)2 nonvaccinated on immunity level 0 is .1/0.038 ≈ 263 days • .ηk = 0.015 · k,i.e. the average time of complete decay of immunity from level −1 m to level 0 is . m k=1 ηk ≈ 122 days • • • •

. .

Figure 13.1 illustrates the convergence behaviour of the Markov process for a large value of .N = 104 towards the solution of (13.5). In Fig. 13.2 one can see that for a smaller value of N, the randomness of the model induces also another effect, beyond the fluctuation of the martingale

Fig. 13.1 Convergence to the solution of the deterministic ODE, .R0 = 3, N = 104 , p = 1 (vaccination proportional to I )

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171

Fig. 13.2 Fluctuations around the deterministic equilibrium, .R0 = 4, N = 103 , p = 1 (vaccination proportional to I )

components: namely the main profile of the paths exhibits an oscillatory behaviour around the components of the deterministic solution. Numerical simulations suggest that the system (13.5) has at least two equilibrium states: one with .I = 0 (which can be computed also explicitly as the solution of a linear system of equations) and an endemic equilibrium with .I > 0 (which can be computed numerically as the solution of a nonlinear system). However, starting with the initial condition which we considered, even if the deterministic solution approaches the endemic equilibrium, as can be seen in Fig. 13.3, some paths of the Markov process converge to the equilibrium with .I = 0 (left), while other paths converge to the endemic equilibrium (right). The statistics of convergence towards different equilibrium points (starting always from the same initial condition) is illustrated in Fig. 13.4 for three different scenarios: .γ = 0 (no vaccination), .p = 0 (vaccination independent on I ) and .p = 1 (vaccination rate depends on the size of the infected population). The other values considered are .N = 103 , .R0 = 3 (left picture) and .R0 = 4 (right picture). One can note that a significant amount of the paths converge to the equilibrium with .I = 0 only in the case .R0 = 3, while for .R0 = 4 this happens only in the case .p = 0. If we consider the stochastic model for the simulation of a real scenario, with a value of N on the one hand not too large, in order to have some significant stochastic effects, on the other hand not too small, in order that the random fluctuations don’t predominate, the conclusions which can be drawn from the numerical simulations

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Fig. 13.3 Paths of the Markov process converging to different equilibrium states. .R0 = 3, N = 103 , p = 0 (vaccination independent on I ). Left: equilibrium with .I = 0, right: endemic equilibrium with .I > 0

Fig. 13.4 Percentage of paths of the Markov processes converging to different equilibria with = 0 and .I = 0 respectively. Left: .R0 = 3, right: .R0 = 4

.I

are the following. Even if the solution of the deterministic system starting from the same initial value converges towards the endemic equilibrium with .I > 0, for a value of .R0 = 3 there is a significant probability that the stochastic model converges to the equilibrium with .I = 0 that is, the epidemy can vanish. This is a hint towards the fact that the endemic equilibrium is in this case not globally stable. However, for the larger value .R0 = 4, the simulations show that the epidemy vanishes only in the case .p = 0, that is, if the vaccination rate is independent on I . At this basic reproduction number but in the other situations, that is, no vaccination or vaccination proportional to I , the paths converge with high probability (100% in the simulations) towards the endemic equilibrium. Of course, this fact is not sufficient to infer the global stability of the endemic equilibrium.

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Table 13.1 Values of I at the endemic equilibrium in different scenarios .R0

2

=0 .p = 1 .p = 0 .Ip=0 /Iγ =0

.3.14

.γ

· 10−2 −2 .2.96 · 10 0 0

3 · 10−2 −2 .4.97 · 10 −2 .2.24 · 10 0.43 .5.12

4 · 10−2 −2 .6.56 · 10 −2 .4.87 · 10 0.73 .6.68

5 · 10−2 −2 .7.79 · 10 −2 .6.61 · 10 0.84 .7.90

The values of I at the endemic equilibrium (computed numerically) are shown in Table 13.1: Based on these data, we can make the following remarks: • The cases .p = 1 (vaccination rate proportional to I ) and .γ = 0 (no vaccination) have a similar behaviour at equilibrium. • For .p = 0 (vaccination independent on I ) and .R0 < R0∗ ≈ 2.43 there is no endemic equilibrium with .I = 0. In this case the epidemy will vanish. • If .p = 0 with increasing .R0 the advantage of vaccination diminishes (the proportion .Ip=0 /Iγ =0 increases towards 1).

13.6 Conclusions In this paper we introduce an extension of the classical SIR model in epidemiology in order to include vaccination with a temporary protection effect and several immunity levels, through which a fully immune individual (recovered or vaccinated) passes successively until he gets back at the initial level of lowest immunity. The approach is a stochastic model with dynamics driven by a Markov jump process. Under suitable conditions we showed convergence of this model towards the solution of a deterministic system of differential equations. Finally, we performed numerical simulations of the stochastic model and compared their behaviour to that of the deterministic model. The conclusion was that, due to stochastic effects, under suitable conditions the epidemy can vanish (i.e. convergence towards the trivial equilibrium with .I = 0 occurs with a positive probability), even if we start from an initial condition from which the corresponding deterministic solution converges towards the endemic equilibrium. In such a situation, the endemic equilibrium turns out to be not globally stable.

References Bhattacharya, S., & Adler, F. R. (2012). A time since recovery model with varying rates of loss of immunity. Bulletin of Mathematical Biology, 74, 2810–2819. Brauer, F. (2008). Compartmental models in epidemiology. In: F. Brauer, P. van den Driessche, & J. Wu (Eds.), Mathematical Epidemiology (pp. 19–79). Berlin, Heidelberg: Springer, Chapter 2.

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Brauer, F., & Castillo-Chávez, C. (2001). Mathematical models in population biology and epidemiology. New York: Springer. Ehrhardt, M., et al. (2019). SIR-based mathematical modeling of infectious diseases with vaccination and waning immunity. Journal of Computational Science, 37, 101027. https://doi. org/10.1016/j.jocs.2019.101027 Ethier, S., & Kurtz, T. G. (1986). Markov processes: Characterization and convergence. New York: Wiley. Guia¸s, F. (2010). Direct simulation of infinitesimal dynamics of semi-discrete approximations for convection-diffusion-reaction problems. Mathematics and Computers in Simulation, 81, 820– 836. Nakata, S., et al. (2014). Stability of epidemic models with waning immunity. SUT Journal of Mathematics, 50(2), 205–245.

Chapter 14

Preventable Neonatal Deaths and Maternal and Child Factors in a Region of Brazil: Panel Data Modeling Tiê Dias de Farias Coutinho and Neir Antunes Paes

14.1 Introduction Infant deaths represent a serious public health problem in the world, especially in less developed regions, which led the United Nations (UN) to include as a priority goal in the Sustainable Development Goals (SDGs), by 2030, the reduction of neonatal mortality to 12.0 per 1000 live births (p/1000 lb) and an end to deaths from preventable causes ONU (UN, 2015). Neonatal deaths constituted about 43.3% of the total deaths of children under 5 years old in the world, at the year of 2016. This relation was observed even in countries with high levels of development (Naghavi et al., 2017). Positioning Brazil among the ten countries in the world with the highest Gini Indexes (0.53 in 2019) (The World Bank Group, 2022) internally, different regional realities coexist, which impose different living conditions on the population. In the last 27 years, Infant Mortality Rates (IMR) have experienced a significant drop in Brazil, ranging from 47.1 p/1000 lb. in 1990 to 13.4 in 2017 p/1000 lb. It is estimated that in Brazil one in four infant deaths occurred in the first 24 h of the newborn’s life, in the other words, in the early neonatal period (0–7 days) (Uchoa et al., 2017). Although current levels of neonatal mortality in Brazil have decreased dramatically, there is still room for reduction, especially in less developed regions such as the North and Northeast of the Brazilian country (Brasil, 2015). In the Brazilian Northeast, the state of Paraíba is located with a population around 4.0 million inhabitants in 2018 and it had an HDI of 0.709 in 2017, occupying the 20th position in development among the 27 states in the country. The public health sector – the

T. D. de Farias Coutinho · N. A. Paes () Health and Decision Modelling Postgraduate Course, Federal University of Paraíba, João Pessoa, Brazil e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_14

175

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SUS – provides universal access to health care, which is the sole provider of health care coverage for at least 75% of the population (IBGE, 2017). IMR decreased from 81.9 in 1990 to 15.4 p/1000 lb. in 2017. In that same year, 764 infant deaths were recorded, of which about 70% occurred in the early neonatal period and 530 were classified as preventable, i.e., 69% (Brasil, 2021). There is a complex network of direct and indirect factors such as biological, socioeconomic, behavioral, demographic and health system factors that affect neonatal mortality (Sardinha, 2014). Factors such as low birth weight, prematurity, type of delivery and some sociocultural characteristics of mothers constitute important risks (Lucas et al., 2016). The preventable basic causes are also evident, which are the factor responsible for more than 40% of all neonatal deaths, especially those in the group that can be reduced by adequate care for the newborn, followed by the group that provides adequate care for women during pregnancy (Moreira et al., 2017). Thus, the main causes of death are linked to prematurity, congenital malformation, and infections. As for early neonatal deaths, respiratory distress in the newborn, followed by extreme immaturity, stands out as the underlying cause (Gaiva et al., 2015). Thus, the main objective was to associate the set of preventable neonatal death causes with maternal and child risk factors for the state of Paraíba in Brazil in the period from 2009 to 2017.

14.2 Materials and Methods This is a longitudinal ecological study of the causes of neonatal infant deaths (0–7 days) covering the 223 municipalities in the state of Paraíba/Brazil, which uses information on the variables present in the Death Certificate (DC) and in the Live birth declaration (DN from 2009 to 2017. The municipalities were organized separately and grouped into their respective typologies: adjacent rural, adjacent intermediate and urban. Data from the 2009 to 2017 time series were aggregated into three-year periods (2009–2011; 2012–2014; 2015–2017). For analysis purposes, the underlying causes of death were grouped according to the preventability criteria for children under 5 years of age according to the Tenth Revision of the International Classification of Diseases (ICD-10) and the Brazilian Preventability List (LBE) (Lisboa et al., 2016) in the following groups, with the respective codes: E1 – Reduced by immunization actions; E2 – Reducible by adequate assistance to women during pregnancy; E3 – Reducible by adequate assistance to women during childbirth; E4 – Reducible by adequate assistance to the newborn; E5 – Reducible by diagnostic actions and adequate treatment; E6 – Reducible by health promotion actions linked to attention actions; NE – Not Avoidable. MD – Ill define causes.

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For the panel data modeling, the proportion of neonatal deaths from preventable causes was considered as the response variable (Pevt ), which was calculated according to the equation: Pevt =

.

NDeit TNDeit

Where: NDeit is the number of preventable neonatal deaths in region i in year t; TNDeit is the number of total neonatal deaths in region i in year t. The maternal-infant variables used as explanatory variables in the panel data model were: weighted average of mother’s education (mother’s education), mother’s average age (mother’s age), proportion of non-white race (non-white race), proportion of preterm infants (prematurity), proportion of singleton pregnancy (pregnancy), proportion of cesarean section deliveries (cesarean section deliveries), average proportion of living children (living children), average proportion of dead children (dead children) and average birth weight (birth weight). These variables were extracted from the Death Certificate and the Live Birth Certificate (DN). Before proceeding with the modeling, the Kolmogorov-Smirnov test was used at the level of significance (α = 0.05) to verify the normality of the variables. In the case where the data distribution of the variables is not normal, the Spearman’s Correlation Coefficient was used (Siegel, 1981). To verify the hypothesis of independence between the predictor variables, the Chi-square test of independence was applied (α = 0.05 and Confidence Level of 95%). The verification and measurement of multicollinearity was calculated using the Variance Inflation Factor (VIF). Once the correlations between the maternal-infant explanatory variables and the response variable proportion of preventable neonatal deaths were investigated, it was applied regression to panel data, which allows modeling data with information in which the observation units are arranged in a time series or cross-sections. Another advantage is that the data tend to have greater variability, less collinearity between variables and more degrees of freedom (Gujarati & Basic, 2011). Therefore, the following generic specification for a panel data model was considered: Yit = αi + β1it x + β2it x + · · · + βkit x + uit x ↔ yit = αi + xit βit + uit

.

Where βit corresponds to the vector (k × 1) of unknown parameters relative to individual i at time t and xit to the matrix (k × 1) of explanatory variables, whose first column, in the case of the the model, the independent term will be fully constituted by 1’s. Note that the model is descriptive, insofar it says only that individual i has a given specific reaction function at each moment in time, in addition to being nonestimable in this way, since it has more coefficients than observations. As a methodological path for the modeling, two stages were carried out: in the first stage, the Model Specification Tests were performed to choose between the Pooled OLS Model (Ordinary Least Square); Fixed Effects Models or Random Effects Models designated as: Chow F Test, Breusch-Pagan LM Test and Hausman Test Machado (2016); Wooldridge (2005).

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Eliminated in the initial tests, the Pooled OLS Model, in the second stage the estimations of panel data models were accomplished through different methods and linkage functions: Fixed models (negative binomial models, poisson models, fixed effects models; Arellano effects; logistic model); Random models (generalized least squares (GLS); weighted least squares model (WLS)). The estimation of the models was evaluated according to the goodness of fit, through the criteria: adjusted R2 ; the Akaike information criterion (AIC); the Bayesian Information Criterion (BIC) (Schwarz, 1978). Finally, the adequacy of the model was verified through residual analysis: residuals eij follow a normal distribution with mean zero and variance σ 2 ; the errors are independent of each other, that is, there is no serial autocorrelation present; the residues are homoscedastic; no strong or perfect multicollinearity is present.

14.3 Results and Discussion In the state of Paraíba, 7241 deaths of children under one year old were recorded from 2009 to 2017. It was 71.1% of these which occurred in the neonatal period, that is, 5149 deaths, the proportion of which remained practically stable over the years in the period. The registered neonatal deaths correspond to about 81% of the total neonatal deaths in the state, since the complementary portion was underreported. Thus, the hypothesis was that the 5149 neonatal deaths reflect the pattern of general characteristics of the approximately 19% of deaths not recorded in the period. The survey of neonatal death records revealed that, among the causes of death reported in the DCs, 358 different types of underlying causes were observed, of which 220 (61.5%) were classified as belonging to the group of non-preventable causes, being the complement of the group of preventable causes. A breakdown of the percentage of the most reported underlying causes in the region (Table 14.1) indicates that, among the 15 causes of death with the highest frequency among neonatal deaths in Paraíba, 11 of them were of the preventable type. Among the causes belonging to the preventability group, the three leading causes in descending order were: unspecified bacterial septicemia of the newborn (14.6%), respiratory distress syndrome of the newborn (12.7%) and congenital pneumonia unspecified (3.3%). The first is part of the causes of death attributed to group E4 (Reducible by adequate assistance to the newborn), and the last two to group E3 (Reducible by adequate assistance to women during childbirth). Added together, they accounted for 30.6% of all neonatal deaths. The literature points out that these three leading causes are part of a major health bottleneck in other developing countries as reported by the UN (2015; ONU, 2017). The other types of causes accounted for 41.0% of deaths (this percentage includes preventable, not clearly preventable and ill-defined causes). In view of this, comparisons between different countries carried out by RAD (Rad et al., 2013), credit as the main factor to minimize preventable causes, effective government

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Table 14.1 Number and percentage of the leading reported underlying causes of neonatal deaths in Paraíba/Brazil, 2009 to 2017 Type of preventability E4 E3 E3 E3 E3 NE NE E3 E3 E3 NE E3 NE E3 E2 – Total

Cause of death Unspecified bacterial septicemia of the newborn Newborn respiratory distress syndrome Unspecified congenital pneumonia Intrauterine hypoxia diagnosed during labor delivery & delivery Extreme immaturity Anencephaly Other specified congenital malformations of the heart Unspecified intrauterine hypoxia Other preterm newborns Unspecified congenital malformations Unspecified asphyxia at birth Unspecified perinatal infection Unspecified malformation of the heart Unspecified respiratory distress of the newborn Fetus and newborn affected by other forms of placental abruption and hemorrhage Other causes (not clearly avoidable) –

N 750 656 172 164

% 14.6 12.7 3.3 3.2

161 149 138 118 116 115 112 109 106 97 87

3.1 2.9 2.7 2.3 2.3 2.2 2.2 2.1 2.1 1.9 1.7

2099 5149

41.0 100.0

Source: Mortality Information System (SIM) E1 – Reduced by immunization actions; E2 – Reducible by adequate assistance to women during pregnancy; E3 – Reducible by adequate assistance to women during childbirth; E4 – Reducible by adequate assistance to the newborn; E5 – Reducible by diagnostic actions and adequate treatment; E6 – Reducible by health promotion actions linked to attention actions; NE – Not Avoidable

actions by highlighting social and economic impact management on neonatal mortality, especially among countries with lower per capita incomes. Actions aimed at newborns and family support are effective alternatives to qualify newborn care Gaiva et al., (2015). Table 14.2 shows an overview of maternal and child variables and the underlying cause of death by municipal characterization, in which the average values for the period from 2009 to 2017 were observed to be above or below the average reference value for the state of Paraíba. From this perspective, it is observed that no variable was above average in all groups of municipalities at the same time. The difference between urban and rural is clear in this table, since only in the variable age of the mother the two groups were above average. The fact that the mother’s age is above average also refers to late fertility, which also had an impact on rural municipalities. In the adjacent intermediate municipalities, only three variables (non-white race, dead children and weight) had averages above the state average. The proportion of preventable deaths, the proportion of the average education level, the proportion of premature babies and the proportion of cesarean sections deliveries were above average only in urban municipalities. The proportion of singleton pregnancies

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Table 14.2 Overview of maternal and child variables and underlying cause of death for regionalized spaces classified as above or below the state average, Paraíba, 2009–2017 Variables Preventable cause Mother’s education Mother’s age Non-white race Prematurity Single pregnancy Cesarean section delivery Living children Dead children Birth weight

Urban Above x x x

Below

x x x x x x x

Adjacent rural Above Below x x x x x x x x x x

Adjacent intermediate Above Below x x x x x x x x x x

Source: Mortality Information System – SIM/Information System on Live Births – SINASC Note: Reference Value is the State average of Paraíba

and the average number of live children were higher only in the adjacent rural municipalities. In this sense, the numbers indicate that the magnitudes and trends of the variables for urban municipalities differ from the others, suggesting a generic cut in the maternal-infant profile of urban and non-urban neonatal deaths in Paraíba. This more general approach corroborates the evidence that, in these municipalities, access to and supply of health services are more available, which favors urban profiles of maternal and child variables of neonatal mortality that are differentiated from other municipalities. The association between neonatal deaths from preventable causes and maternal and child variables included in the Death Certificate was investigated using Spearman’s Correlation Coefficient (rs ) It was found that the proportion of preventable neonatal deaths correlated strongly (rs ≥ 0.5) with prematurity and moderately (0.4 ≤ rs < 0.5) with low birth weight and cesarean sections delivery. In these cases, the signs of Spearman’s statistics indicated a direct relationship between these variables. Thus, the increase in prematurity, low birth weight and the number of cesarean sections deliveries was related to the increase in neonatal deaths from preventable causes in the state of Paraíba. Spearman’s coefficients indicated a weak correlation (rs ≤ 0.4) with mother’s education, mother’s age, pregnancy, live child and dead child. The correlation coefficient indicated very low correlation (rs ≤ 0.01) with the variable race. The result of the Chi-square test of independence between the maternal and child variables (mother’s education, mother’s age, non-white race, single pregnancy, live children, dead children) that were used as independent variables in the modeling, and the percentage of deaths preventable variables that make up the dependent variable, did not obtain significant p-values (p > 0.05). However, the variables

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prematurity and cesarean sections showed a significant relationship. In this case, the hypothesis of independence could not be rejected. Then, a test to verify the existence of multicollinearity between the variables was applied, finding the values of the Variance Inflation Factors (VIF), which were between 1 and 10. Therefore, there was no statistical evidence of multicollinearity between the variables, except for the birth weight variable. However, this variable will remain in the model, as the literature points to a strong relationship between birth weight and infant mortality and, consequently, with neonatal mortality (Gaiva et al., 2015; Gonzaga et al., 2016; Lima et al., 2012). The Breusch and Pagan Suitability Test and the Hausman Test were performed in order to decide which type of panel data model best fits the data set. Therefore, the hypothesis of the existence of a correlation not observed in the model was initially verified. In this sense, the Breusch and Pagan Test was applied, which resulted in a pvalue = 0.995. Therefore, it is concluded that the effects were not correlated with the explanatory variables, indicating that the random models would fit better. However, the Hausman Test was applied to corroborate this finding, since it tests whether the effects are random or fixed under the null hypothesis that the model estimators have consistent and efficient random effects, obtaining the p-value = 0.451, that is, the hypothesis that the random model better fit the data was not rejected. Although the specification tests carried out here indicate the suitability of random effects models, there are many studies that use fixed models as adequate (Silva & Paes, 2019; Rasella et al., 2018). Therefore, regression models were estimated for panel data with maternal-infant variables as explanatory variables, considering both the random model and the fixed model. It was observed that the values of the coefficients of determination of the models (R2 ) reached similar levels, all above 72.4% and below 75.2%. In this sense, in almost all models tested, the education variable was significant, pointing to the importance of this variable in neonatal mortality. From the observed intra-variable correlations, between schooling and the other variables, it can be noted that this one had a significant correlation with the others. Literature has argued for infant mortality that when maternal education increases, the probability of infant death is reduced. As a summary of this previous analysis, only random effects models were considered as final models. The first model with GLS estimation, that is, through generalized least squares, it was not possible to calculate the R2 , presenting an adjustment measured by the Akaike AIC and Bayesian BIC criteria of −85.400 and − 75.034, respectively. In this case, it was observed that the education, prematurity and delivery variables were significant to explain the behavior of neonatal deaths from preventable causes. The second case of random models was the WLS, which was generated through weighted least squares and which obtained an R2 fit of 72.35% and statistics of AIC = 95.6617 and BIC = 108.6201. In this model, it is observed that the adjustments were satisfactory with AIC and BIC with the highest values among the models tested. In addition, the statistically significant variables to explain the

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Table 14.3 Final model of normalized weighted least squares panel data, Paraíba/Brazil, 2009– 2017 Final model Independent variable Mother’s education1 Prematurity3 Cesarean section delivery3 Living children2 R2 AIC BIC F statistic p-value (F)

Coefficient −18.561 15.472 8.827 −2.751

Standard error 8.473 4.737 3.479 1.145

Statistic t −2.190 3.266 2.537 −2.401

p-value 0.043a 0.005a 0.021a 0.028a 72.353 95.662 108.620 4.943 0.002

Source: Mortality Information System (SIM) SIM/Information System on Live Births – SINASC Note: a Significant p ≤ α =0.05. 1 Weighted average of the categories; 2 Average of values; 3 Percentage of category

behavior of preventable neonatal deaths were the mother’s education, prematurity, type of delivery and living children. In the Random Effects Model (WLS), the error variances were estimated per unit, thus circumventing the problem of heteroscedasticity. And, it proved to be the best model. Thereby, seeking the best fit of the data to the panel data model, we proceeded to normalize the dependent variable (Percentage of preventable deaths). This model is shown in Table 14.3 as the final model for the proportion of infant deaths from preventable causes in the state of Paraíba between 2009 and 2017. In this direction, the normality of the residuals of the final model was tested by the Chi-Square test, concluding that the data do not follow the normal distribution with p-value = 0.237, which is greater than the significance level (0.05). However, the fact that the estimated coefficients do not have autocorrelation and the Wald test for heteroscedasticity indicates that the null hypothesis is rejected, this final model was maintained. In summary, the final model was estimated using a panel data model with weighted least squares random effects after normalization of the response variable. In this model, whose statistics are shown in Table 14.3, the relationships between the significant variables for the model (mother’s education, prematurity, delivery and live children) and the response variable (preventable neonatal deaths) showed a β with objective and parsimonious interpretations. In this model, it was observed that the relationship between preventable neonatal deaths and the mother’s education was inverse, indicating that the higher the mother’s education, the lower the number of preventable neonatal deaths. It is also noteworthy that this relationship exerts an important burden on neonatal mortality from preventable causes, that is, when the average proportion of mother’s education decreases by one degree there is an increase of 18.56% in the proportion of newborns who die from preventable causes. This behavior was expected, since a

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strong correlation between infant mortality and the mother’s education are also pointed out in other modelss (Fernandes, 2019; Santos et al., 2016; Carvalho, 2012). The estimated model showed that a one-unit increase in prematurity proportion contributes to a 15.47% increase in the proportion of preventable neonatal deaths in Paraíba during the study period. Therefore, deaths in newborns with less than 37 weeks of gestation are intrinsically related to low birth weight, since they occur in children weighing less than 2500 grams, who were born extremely premature (between the 22nd and 27th week of pregnancy) (Lucas et al., 2016). Considering, then, the percentages presented in Table 14.1 on notifications of underlying causes, the prevalence of causes related to the respiratory system was observed. Therefore, the study by Teixeira (2019), which associated infant mortality to prematurity, can be extended to causes of preventable death, which involves causes of the respiratory system. Among the factors influencing child mortality, Carvalho (2012) highlighted the importance of prematurity in this scenario. The study by Lisboa (2016), warns about the impact of prematurity on the occurrence of infant deaths. However, he points out that this factor may be related to the occurrence of cesarean sections without indication. According to the final model, when the type of delivery is cesarean section, there is a direct influence of 8.82% of the proportion of preventable neonatal deaths, as shown by the coefficient in Table 14.3. From this perspective, the study carried out by Soares (2019) argues that cesarean sections are risk factors for neonatal mortality. This inverse relationship was the object of study for Sleutjes (2018), when they argued that the lower the average number of living children, the higher the neonatal mortality, suggesting that the maternal history of previous pregnancies is important for the follow-up of adequating prenatal assistance, which may contribute to lower neonatal deaths. Based on the associations pointed out in this work by the final model, attention is drawn to the work by Teixeira (2019). Observing the causes of death in eight Brazilian federation units between 2010 and 2015, the authors found that from the 20 main causes of death, 70% are preventable and are related to prematurity, mothers without education and low birth weight. Thus, it is observed that the second preventable cause with the highest incidence in Paraíba in the period from 2009 to 2017, belongs to the group of avoidable causes by adequate assistance for women during pregnancy, making the relevance of prenatal assistance clear. Regarding the educational actions carried out in the prenatal consultations that took place in the Family Health Strategy (free primary care program for the Brazilian population), professionals guide pregnant women on how to lead a healthy pregnancy. However, many do not follow-up fully (The World Bank Group, 2022). It is noticed that the respiratory distress syndrome of the newborn, unspecified congenital pneumonia, intrauterine hypoxia diagnosed during labor and extreme immaturity, accounted for 22.3% of the underlying causes reported in the state of Paraíba. These causes are classified as reducible by adequate assistance for women during childbirth. So, it is reinforced that the quality of women’s access to the health system interferes with the reduction of neonatal mortality (Sanders et al., 2017).

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At the international comparative level, Chinese government interventions between 2014 and 2018 through neonatal referral centers and newborn transfer programs quickly and positively influenced the reduction of mortality rates in the country (Liu et al., 2021). Results of the study carried out by Kiross et al. (2020) with panel data grouped from 2000 to 2015 for 46 countries, indicated that investment in public and private health expenditures reduced infant mortality. On the other hand, public and external health expenditures showed a significant inverse association with neonatal mortality. In another example, the actions carried out in sub-Saharan Africa are highlighted, whose increase in monetary spending on health infrastructure has contributed to progress in reducing infant and neonatal mortality (Kiross et al., 2020). In Brazil, some actions such as: the network of maternal, neonatal and child assistance, called Rede Cegonha, implemented in 2011; the creation of National Guidelines on Cesarean Sections and Normal Birth in 2015 and 2017; the Mais Médicos Program and the immunization and breastfeeding promotion program contributed to the decline in infant deaths in the country in 2013. However, the neonatal mortality indicator is still high in relation to the developed world (Leal et al., 2018). Primary health assistance actions that take place in family health units directly reflect the improvement of child health, especially in regions with less economic power, such as rural areas in the North and Northeast (Santos et al., 2012). Linked to these interventions are income transfer programs, such as the Bolsa Família Program, which has been minimizing the population’s poverty and reducing infant mortality rates (Silva & Paes, 2019). Actions by the Chinese government, for example, which has an expressive part of the rural population, focuses efforts on improving the accessibility of medical services for women and children in rural areas, while in urban areas, actions are aimed at preventing premature deaths with less than 32 weeks of gestation (Liu et al., 2021). With this, the generated model, for having random effects, exposes that there are significant differences between the urban, adjacent intermediate and adjacent rural municipalities in Paraíba. Therefore, it is necessary that actions to combat neonatal mortality are carried out differently in the municipalities.

14.4 Conclusion The investigation on the association between neonatal deaths from preventable causes, maternal and infant factors in the state of Paraíba/Brazil, from 2009 to 2017, was quite enlightening through the application of regression models of panel data with ordinary random effects. This application used data from the 223 municipalities that are part of the state according to the regional typology in three categories. Two points are highlighted from this modeling. First, a clear association between preventable neonatal death and maternal and child factors was evidenced: mother’s education, prematurity, type of delivery and living children. Second, this association was quite different between urban and rural areas.

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Since regionalization is an important political-geographical aspect in the North and Northeast regions of Brazil, as well as in several countries around the world, the results found in this work can serve as an indicative for studies in developing countries with similar purposes. It is hoped that this work can contribute to the formulation, planning and direction of public policies to promote maternal and child health in the sense of reducing neonatal mortality from preventable causes. In this way, being able to achieve the goal set by the United Nations when it was included as a priority in the Sustainable Development Goals (SDGs), by 2030, the reduction of neonatal mortality to 12.0 per 1.000 living births and an end to preventable deaths.

References Brasil. (2015). Ministério da Saúde. Portal Brasil. UN: Brazil meets target to reduce infant mortality. Available in: http://www.brasil.gov.br/cidadania-ejustica/2015/09/onu-brasil-cumpre-metade-reducao-damortalidade-infantil. Accessed 12 June 2018. Brasil. (2021). Ministério da Saúde. Secretaria de Vigilância em Saúde. Infant mortality in Brazil. Boletim epidemiológico, 52, 1–15. Carvalho, S. R. D. E. (2012). Determinants and predictors of infant deaths, in the state of Goiás. Use of linkage of SUS health information systems databases, 2017. Fernandes, M. M. C. E. (2019). Application of panel data to treat infant mortality information. (Master Degree) UFPB/CCEN 63f f. Gaiva, M. A. M., Fujimori, E., & Sato, A. P. S. (2015). Neonatal mortality: Analysis of preventable causes. Revista de Enfermagem, 23(2), 247–253. Gonzaga, I. C. A., et al. (2016). Prenatal care and risk factors associated with prematurity and low birth weight in a capital city in northeastern Brazil. Ciência & Saúde Coletiva, 21(6). Gujarati, D., & Basic, N. (2011). Econometrics. Markon Books. IBGE. (2017). Classification and characterization of rural and urban spaces in Brazil: A first approach. [S.l: s.n.]. Available in: http://biblioteca.ibge.gov.br/ http://www.ibge.gov.br/home/geociencias/geografia/ visualizacao/livros/liv100643.pdf. espacos_rurais_e_urbanos/default.shtm. Accessed 12 June 2018. Kiross, G. T., et al. (2020). The effects of health expenditure on infant mortality in sub-Saharan Africa: Evidence from panel data analysis. Health Economics Review, 10(1), 1–9. Leal, M. D. C., et al. (2018). Reproductive, maternal, neonatal and child health in the 30 years since the creation of the Unified Health System (SUS). Ciência e Saude Coletiva, 23(6), 1915–1928. Lima, E. F. A., et al. (2012). Risk factors for neonatal mortality in the municipality of Serra, Espírito Santo. Revista Brasileira Enfermagem. Brasília, 65(4), 578–585. Lisboa, L., et al. (2016). Infant mortality: Main preventable causes in the central region of Minas Gerais, 1999–2011. Epidemiologia e Serviços de Saúde, 24(4), 711–720. Liu, Y., et al. (2021). Neonatal mortality and leading causes of deaths: A descriptive study in China, 2014–2018. BMJ Open, 11(2), e042654. Lucas, E. S., Pedrosa, R. L., & Gerais, M. (2016). Profile of neonatal mortality in the city of Ubá/MG. Brasil, 18(3), 24–31. Machado, M. A. V. (2016). Asset growth, profitability and shareholder return: Empirical evidences of the Brazilian market. 54f. (Bachelor’s Degree in Statistics) – Federal University of Paraíba. Moreira, K. F. A., et al. (2017). Profile and avoidance of neonatal death in a municipality of the legal Amazon. Cogitare Enfermagem, 22(2), 22.

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Naghavi, M., et al. (2017). Global, regional and national age-sex specific mortality for 264 causes of death, 1980–2016: A systematic analysis for the global burden of disease study 2016. The Lancet, 390(10100), 1151–1210. ONU. (2017). Level E trends in child mortality. Org Colin Mathers, Daniel Hogan, Jessica Ho, Wahyu Retno Mahanani. Rad, E. H., et al. (2013). Comparison of the effects of public and private health expenditures on the health status: A panel data analysis in eastern Mediterranean countries. International Journal of Health Policy and Management, 1(2), 163. Rasella, D., et al. (2018). Child morbidity and mortality associated with alternative policy responses to the economic crisis in Brazil: A nationwide microsimulation study. PLoS Medicine, 15(5), 5. Sanders, L. S. D. E. C., et al. (2017). Infant mortality: Analysis of associated factors in a capital city in the Brazilian Northeast. Cadernos Saúde Coletiva, 25(1), 83–89. Santos, A. M. A., Jacinto, P. A., & Tejada, C. A. O. (2012). Causality between income and health: An analysis through the panel data approach with the states of Brazil. Estudos Econômicos (São Paulo). Santos, S., et al. (2016). Factors associated with infant mortality in a northeastern Brazilian capital. Revista Brasileira de Ginecologia e Obstetrícia/RBGO Gynecology and Obstetrics, 38(10). Sardinha, L. M. V. Infant mortality and factors associated with health care: A case-control study in the Federal District (2007–2010). 2014. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. http://www.jstor.org/stable/2958889. Accessed 15 May 2022 Siegel, S. (1981). Non-parametric statistics. Editora McGraw Hill do Brasil. Silva, E. S. A., & Paes, N. A. (2019). Bolsa familia programme and the reduction of child mortality in the municipalities of the Brazilian semiarid region. Ciência e Saúde Coletiva, 24(2), 623– 630. Sleutjes, F. C. M., et al. (2018). Risk factors for neonatal death in the interior region of São Paulo. Brazil. Ciência & Saúde Coletiva, 23(8), 2713–2720. Soares, R. A. S. (2019). Spatial decision-making model for the reduction of infant mortality: A discussion in the context of rurality in Paraíba. (Ph.D Thesis). 185 f. PPGMDS, Federal University of Paraíba. Teixeira, J. A. M., et al. (2019). Mortality on the first day of life: Trends, causes of death and preventability in eight Brazilian federation units, between 2010 and 2015. Epidemiologia e Serviços de Saúde, 28(1), 1–11. The World Bank Group. (2022). Available in: https://data.worldbank.org/indicator/ SI.POV.GINI?locations=BR. Accessed 12 June 2022. Uchoa, M., et al. (2017). Neonatal deaths in the municipality of São Luís: Basic causes and factors associated with early neonatal death. Revista de Pesquisa em Saúde, 1(8), 1–18. UN. (2015). Transforming our world: The 2030 agenda for sustainable development. Available in: https://sustainabledevelopment.un.org/post2015/transformingourworld. Accessed 12 June 2018. Wooldridge, J., & Introductory, M. (2005). Econometrics, a modern approach (3rd ed.). SouthWestern College Pub.

Chapter 15

Comparing the Mortality Regimes in 39 Populations Konstantinos N. Zafeiris

15.1 Introduction Mortality transition, part of the demographic transition (denoting the transformation of a traditional society into a modern one; see Lee & Reher, 2011; Frejka, 2017), is a well-studied phenomenon. It is related to the epidemiological transition (Omran, 1971, 1998) or the health transition (see Caldwell, 1993). It is broadly recognised that mortality transition has different origins, timetables and paces among the human population worldwide (see Zafeiris & Skiadas, 2022). A striking example is the ex-socialist countries which diverged significantly from the rest of Europe by the time of the cardiovascular revolution. Some of them started to converge with the rest of Europe in the 1990s. Others remain distant even today (see Meslé & Vallin, 2011). Thus, the existing mortality diversity is expected to be significant worldwide. Many other factors contribute to this diversity. For example, the economic crisis of 2008 affected the existing mortality regimes and increased heterogeneity (see, for instance, Alicandro et al., 2019; Ballester et al., 2019). Additionally, one must not forget the nature of the social determinants of health inequalities which are either structural or intermediary. The structural factors are delimited socioeconomically and politically and act through intermediate determinants operating on the individual level and producing health outcomes. Such determinants are psychosocial circumstances, behavioural and biological factors, health system and community contextual factors and others (Solar & Irwin, 2010). Thus, many elements control mortality levels and -also- gender disparities (see Lindahl-Jacobsen

K. N. Zafeiris () Department of History and Ethnology, Laboratory of Physical Anthropology, Democritus University of Thrace, Komotini, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 C. H. Skiadas, C. Skiadas (eds.), Quantitative Demography and Health Estimates, The Springer Series on Demographic Methods and Population Analysis 55, https://doi.org/10.1007/978-3-031-28697-1_15

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et al., 2013; Clark & Perk, 2012; Sundberg et al., 2018), all of them adding to the existing heterogeneity by acting differentially in the two genders within a population of each of the genders among different populations. Within this diversity, the question is, how can you identify homogeneous population groups in regard to their overall mortality regimes? And what are the results of this segmentation? In this paper, Human Mortality Database served as a data provider to answer these questions. Thus, we selected the life tables of 39 populations scattered in Europe, Asia, Oceania and America. Based on these data, several measures were calculated to describe the mortality regime in each of them by gender. Because of multicollinearity problems, the original variables were transformed into unrelated components with Principal Component Analysis. The uncorrelated data were used in Cluster Analysis to identify the segmentation of the populations. The details of this approach are discussed in the Data and Methods section of this paper, and the Clustering Solutions in the Results Section later.

15.2 Data and Methods Data come from The Human Mortality Database (https://www.mortality.org/) in the form of full life tables closing at the age of 110+. Data refer to the year 2019, the last one before the emergence of the COVID19 pandemic, which altered the mortality regimes in the human populations tremendously. 36 countries were included in the analysis. For one of them, the UK, the three distinct populations of Scotland, England and Wales, and Northern Ireland were analysed. Thus a total of 39 populations was included in the analysis. The variables used include mean duration of life (e0), lifespan diversity, age separating early and late deaths and the location and length of the old age heap, all of them being the major characteristics of a mortality regime in a population. Many other variables could have been added to the analysis, but it was found that their use did not solely affect the results while adding more “noise” to them. Note that the three diversity measures used in this paper (Gini Coefficient, e-dagger and interquartile range) are calculated in a totally different way having at the same time different analytical abilities and thus contributing solely to a more detailed description of a mortality regime. Thus, the following variables were included in the analysis: 1. Life expectancy at birth (e0), represents a measure of the mean duration of life. 2. e† (e-dagger) dates back to the Keyfitz (1977) era and the life table entropy. It measures the diversity and inequalities in people’s life spans. According to Vaupel and Canudas-Romo (2003), e† represents the average number of person-years lost due to deaths in a life table. The following formula serves for the calculation of e† (Shkolnikov et al., 2003; Shkolnikov & Andreev, 2010):

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 lω 1   dx ey+1 − ay + ∗ eω lx y=x 2λx ω−1

ex† =

.

Thus, e† quantifies the age-at-death diversity as the weighted average of individual differences. It can serve to study the variation in life expectancy losses between populations either longitudinally, over time, or cross-sectionally. Vaupel et al. (2011) found a negative relationship between e0 and e† : an increase in e0 is usually accompanied by a decrease in e† . Additionally, Keyfitz (1977) entropy is: ex† Hx ∼ = ex

.

where x and ω, are the ages, e is the life expectancy or the life losses, l the survivors at the beginning of each age (or ω), and αx , is the proportion of person-years spent in an age class. Entropy is a measure of a system’s disorder in Physics. In life table analysis, it describes the changes in the average lifespan associated with changes in the agespecific mortality pattern (see Fernadez & Beltrán-Sánchez, 2015). Considering the above two equations, the entropy Hx of a life table is the proportional expression of e† to life expectancy. Entropy will be used for the calculation of α † (see below). 3. α † (α-dagger) is the age separating early and late deaths according to the characteristics of the age-specific mortality pattern. It is an assessment of how changes on either side of this value cause changes in e† , giving at the same time valuable information about the health system and, ultimately, social cohesion in a country. α† calculation relates to e† and Hx (see Fernadez & Beltrán-Sánchez, 2015; Zhang & Vaupel, 2009). If the life table’s entropy is less than 1, the following equation holds: e† (α) = e(a) ∗ (1 − H (a))

.

α† corresponds to the age at which the difference between the two terms of the equation above becomes zero. This age is calculated by linear interpolation between two known ages of a life table. It is clear that deaths are characterised as late or early exclusively according to a population’s mortality pattern, not forgetting, of course, that, as Keyfitz (1977) said, every death is, in reality, premature. The separation of early from late deaths based on this method is essential in mortality analysis because reducing early deaths reduces lifespan diversity (Vaupel et al., 2011). When the same occurs in late deaths, it increases it. At the same time, α† tends to increase in the more effective health and social cohesion systems. The opposite happens in

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the less advanced ones. Because of this discriminating ability, α† will be critical in describing mortality regimes among populations and between genders. 4. Interquartile range (IQR), corresponds to: I QR = Q25 − Q75

.

The Q25 and Q75 quartiles correspond to the ages where 25 and 75% of people have survived, as seen from a life table’s survival curve. Unlike e† , the interquartile range does not consider the changes that occur between quartiles, which limits its discriminating power (Shkolnikov et al., 2003). It is another measure of diversity in a life table. It serves at the same time for the estimation of the degree of death concentration at the old age heap. 5. Gini Coefficient. It is an index of diversity or inequality related to the Lorenz curve (Lorenz, 1905; see also Sitthiyot & Holasut, 2021). When applied to life table analysis, the Gini Coefficient measures the inter-individual variability in the age at death (see, for example, Le Grand, 1987; Wilmoth & Horiuchi, 1999) as the mean of the absolute differences of the individuals’ length of life to the average length of life in a population (Shkolnikov et al., 2003). It is zero if all individuals die at the same age and one if all people die during infancy, except one who dies at an infinitely old age (Shkolnikov et al., 2003). Globally, it seems that as e0 increases, the Gini coefficient tends to decrease, i.e. the deaths tend to concentrate more tightly around the modal age at death; consequently, the Gini Coefficient is a measure of rectagularisation of the survival curves (Cheung et al., 2005). Calculations for the three variables of diversity are according to Shkolnikov et al. (2003). 6. Modal age at death (M). It corresponds to the age at which most deaths occur in the old age heap (Canudas-Romo, 2008, 2010). M is a better indicator of mortality longevity in the modern era, as determined only by old-age mortality in an environment where the infant, child, juvenile, and early maturity mortality are very low. At the same time, the extension of human longevity in low-mortality countries results from improvements in old-age survival (see Horiuchi et al., 2013). 7. Length of the old age heap. Because of the concentration of mortality at older ages in the modern era in developed countries (Canudas-Romo, 2008), the length of the old age heap is of great importance in evaluating the processes that occur in the survival curves of human populations. If verticalisation (see Cheung et al., 2005, 2009) relates to the concentration of deaths around the old age heap, i.e. with the width of the old age heap, the shorter the latter is, the more rectangular the survival curves tend to be. A dynamic procedure for the necessary calculations used in this paper is described in the following paragraphs (see also Zafeiris, 2023).

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15.3 The Procedure of Calculating Modal Age at Death and the Width of the Old Age Heap • Step 1. Smoothing of mortality curves with a method of non-linear regression analysis. According to this method, a death density function g(x) is fitted to the data (see: Jansen & Skiadas, 1995; Skiadas & Skiadas, 2010, 2013, 2014), having the form:   −3/2 − (l−(bx)c )2  c 2x x .g(x) = k l + (c − 1) (bx) e where x is the age and c, b, l, and k are the fit parameters. • Step 2. Calculation of Modal age at death (M) (see above). • Calculation of the right and left inflexion points of the death density distribution. The first derivative of the g(x) function is called “speed of the death distribution”. The second derivative is “acceleration of the death distribution”. In the left inflexion point (LIP), the speed of the death distribution becomes maximum, and the acceleration is 0. In the right inflexion point (RIP), the “speed of the death distribution” becomes minimum and the acceleration is 0. The age distance between the right and left inflexion points (RIP-LIP) estimates the length of the mortality curve at the old age heap (also see Zafeiris & Skiadas, 2017). After estimating the seven variables included in the analysis, The emerging question is how to explore any population segmentations. Bivariate correlations and the Variance Inflation Factor (see Allison, 1999) demonstrated the problem of multicollinearity, which must be addressed in the analysis, if some clustering technique is applied to the data (see Ketchen & Shook, 1996). Zafeiris (2022) and Zafeiris and Tsoni (2021) discuss this problem giving some solutions. According to their approach, further reducing the parameters in this paper did not solve the problem. Thus a Principal Component Analysis (PCA; see Jolliffe & Cadima, 2016) was performed to reduce the original set of variables to a smaller one while keeping most of the information but producing new uncorrelated variables. Thus, the problem of multicollinearity was solved (for this ability of PCA, see Liu et al., 2003; Field, 2013, pp. 665–719), especially after applying the orthogonal Varimax rotation method. The statistical tests for performing the PCA analysis (Table 15.1) revealed its validity. The rotated component matrices of PCA are in Table 15.2, and the component plots of the factors are in Fig. 15.1. Because the scope of the analysis here is not to study a particular phenomenon after developing meaningful factors, but to produce uncorrelated variables, the subsequent analysis included three components. The reason is that we tried to maximise the total Variance explained, i.e., to retain as much information as possible, aiming to avoid the distortion of the subsequent cluster analysis. Thus, after selecting three components, the Variance

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Table 15.1 Statistical test for PCA Test Keiser-Meyer-Olkin measure of sampling adequacy Bartlett’s test of sphericity

Males 0.741 942.2, p < 0.001

Females 0.588 628.47, p < 0.001

Table 15.2 Rotated component matrix of PCA Males Rotated component matrixa Component 1 Life expectancy at birth 0.797 e-dagger −0.439 Gini coefficient −0.505 Interquartile range −0.533 Age seperating early and late deaths 0.872 Modal age at death 0.894 Length of the old age heap −0.723 Extraction method: Principal component analysis Rotation method: Varimax with Kaiser normalizationa Females Rotated component matrixa Component 1 Life expectancy at birth −0.451 e-dagger 0.932 Gini Coefficient 0.864 Interquartile Range 0.878 Age seperating early and late deaths −0.353 Modal age at death −0.254 Length of the old age heap 0.716 Extraction method: Principal component analysis Rotation method: Varimax with Kaiser normalizationa a Rotation

2 −0.598 0.893 0.861 0.819 −0.463 −0.447 0.645

3 0.065 0.053 −0.048 0.173 −0.128 −0.007 0.244

2 0.887 −0.275 −0.481 −0.343 0.840 0.958 −0.333

3 −0.056 0.150 0.085 0.286 −0.397 −0.122 0.612

converged in 4 iterations

explained in males and females was maximised, as seen in Table 15.3, being almost perfect. Based on the regression scores of the PCA, a cluster analysis followed. Because the produced variables were uncorrelated, we applied several clustering procedures: complete linkage, flexible linkage, single linkage, unweighted pair group average and weighted pair group average. The same happened with the distances serving to compute the distance between each pair of observations during the analysis. After producing numerous dendrograms, those with the best cophenetic correlation coefficient were selected for presentation for males and females (for the whole procedure, see Sokal & Rohlf, 1962; Sokal & Michener, 1958). The best dendrograms were

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Fig. 15.1 Component plot of factors of PCA

produced for both genders with the unweighted pair group average method and Euclidean distance. The cophenetic coefficient for these solutions was 0.84 in males and 0.82 in females. Thus, an almost excellent representation of the actual distances was attained.

15.4 Results The analysis revealed that male populations form two large clusters (Fig. 15.2). The most diversified are those of the ex-socialist countries (9 countries). The rest of the populations, collectively called here “western”, belong to a rather heterogeneous group subdivided into two major clusters, A (13 populations) and B (17) in Fig. 15.2. Slovenia is an exception of ex-socialist countries, clustering more tightly and distantly in cluster B. Except for three Asiatic countries (Hong Kong, Japan and Korea), cluster B includes European populations only. Cluster A pertains to the remaining populations scattered around the world. Note that Scotland, Northern Ireland, and England and Wales belong to this group but in different, smaller clusters, all forming the United Kingdom. This fact indicates the differentiation of mortality regimes among the country’s major populations, even if the differences are not that large. (For the situation in females, see Fig. 15.3). Actually, subclusters A and B can be divided into smaller and smaller entities, representing the progressive strengthening of the segmentation of the mortality regimes. A paradigm of this situation is that of New Zealand and France. They belong to the larger Cluster (A and B), to subcluster A, to the smaller numbered as one and so on.

Males Total variance explained Initial eigenvalues Component Total % of variance Cumulative % 6.468 92.399 92.399 1 2 0.414 5.911 98.310 3 0.080 1.150 99.459 4 0.035 0.494 99.953 0.003 0.036 99.989 5 0.001 0.009 99.998 6 0.000 0.002 100.000 7 Extraction method: Principal component analysis Females Total variance explained Component Initial eigenvalues Total % of variance Cumulative % 5.674 81.062 81.062 1 0.971 13.873 94.935 2 0.254 3.632 98.567 3 0.068 0.966 99.533 4 0.024 0.350 99.883 5 6 0.007 0.105 99.988 0.001 0.012 100.000 7 Extraction method: Principal component analysis

Table 15.3 Total variance explained by the PCAs

Rotation sums of squared loadings Total % of variance Cumulative % 3.451 49.295 49.295 3.396 48.519 97.814 0.115 1.645 99.459

Rotation sums of squared loadings Total % of variance Cumulative % 3.292 47.027 47.027 2.946 42.087 89.114 0.662 9.454 98.567

Extraction sums of squared loadings Total % of variance Cumulative % 6.468 92.399 92.399 0.414 5.911 98.310 0.080 1.150 99.459

Extraction sums of squared loadings Total % of variance Cumulative % 5.674 81.062 81.062 0.971 13.873 94.935 0.254 3.632 98.567

194 K. N. Zafeiris

15 Comparing the Mortality Regimes in 39 Populations

195

Males New Zealand France Northern Ireland Canada Finland Australia Portugal Luxembourg England & Wales Chile Scotland Taiwan USA Greece Slovenia Hong Kong Japan Denmark Spain Germany Switzerland Ireland Italy Sweden Netherlands Belgium Norway Iceland Korea Austria Estonia Hungary Czechia Poland Bulgaria Latvia Croatia Slovakia Lithuania

1 A 2

3

B

4

5

0

0.5

1

C

1.5 Dissimilarity

2

2.5

3

Fig. 15.2 Dendrogram of Cluster analysis. Males

Any analysis of the characteristics of these clusters and subclusters relies on the clustering level chosen for this purpose. In this paper, the results for subclusters A, B, and C will be cited (Table 15.4); however, one could select to present the sub-clusters of a different level, like the third one, including sub-clusters 1–6.

196

K. N. Zafeiris

Females Belgium Germany France Austria Netherlands Canada New Zealand Chile Spain Switzerland Australia Finland Japan Greece Norway Iceland Luxembourg Sweden Hong Kong Portugal Italy Korea Slovenia Denmark Estonia Ireland Czechia Croatia England & Wales Scotland Bulgaria Taiwan Poland Slovakia Hungary USA Lithuania Northern Ireland Latvia

1 A 2

3

B

4

C 5

6

0

0.5

D

1

1.5

2

2.5

Dissimilarity

Fig. 15.3 Dendrogram of Cluster analysis. Females

Before further discussion, note that according to World Bank data (https://data. world-bank.org/indicator/SP.DYN.LE00.MA.IN), in 2020, life expectancy at birth ranged between 62 years in low-income countries to 78 years in high-income ones in males. Thus, the populations studied lie at the upper part of e0 global distribution,

15 Comparing the Mortality Regimes in 39 Populations

197

i.e. they are in a more or less advanced stage of mortality transition in both genders. Consequently, their following classification refers only to this stage. The three clusters (A, B, and C) have the following characteristics (note that the differences between the clusters are always statistically significant): • Cluster B: More advanced mortality transition. The mean duration of life (e0) is higher than the other clusters. At the same time, the variables describing life inequalities are lower. The same happens with age separating early and late deaths. It seems then that social cohesion and health systems are more effective in these populations and have reduced the existing inequalities between people. At the same time, the modal age at death is higher and the length of the old age heap shorter; therefore, the survival curves in these populations tend to be more rectangular than the others. • Cluster A: Moderate mortality transition. This cluster lies in an intermediate position between the other two; however, it has more affinities with cluster A. • Cluster C: Less advanced mortality transition. All the variables used in the analysis are in a worse position than the other clusters. It seems then that the ex-socialist countries follow the others with a time lag, hypothesising that the mortality transition is an ongoing process simultaneously. The situation is somewhat different in females, in which mortality transition has moved considerably ahead. As discussed in the introductory section of this paper, mortality transition began in different periods amongst the human populations with differential paces, timetables and general characteristics. All these specialise differentially in the two genders, which adds more complexity to the phenomenon. This differentiation may have biological or social origins (see Zafeiris, 2020) and produced the cluster solution of Fig. 15.3, according to which the female populations have different segmentation than the male ones. Furthermore, this segmentation is not as clear as it is in males. Second, dividing populations into two large groups seen is still valid, but this segmentation has different characteristics. Except for Slovenia, the ex-socialist countries still hold a distant position, but many other “western” populations group with them. The third most striking difference is that females form four sub-clusters, compared with the 3 in males. Of course, many other subclusters can be seen in Fig. 15.3, but in this paper, as happened in males, the characteristics of the four subclusters will be discussed (Table 15.5; all the differences are statistically significant). Therefore, the clusters formed in the female populations have the following characteristics. 1. More advanced mortality transition • Cluster B. It has similar qualitative characteristics with the analogous cluster in males, but all the indicators used in this paper suggest a considerably more advanced mortality transition. This cluster consists of 7 European populations and 2 Asian. • Cluster A. It has many similarities with cluster B, but life expectancy at birth is lower. On the contrary, e-dagger, Gini coefficient, and IQR have slightly larger

Total

C

B

Class A

Males

Mean N Std. Deviation Mean N Std. Deviation Mean N Std. Deviation Mean N Std. Deviation F P

Life expectancy at birth 78.97 13 1.429 80.44 17 1.118 73.5 9 1.869 78.35 39 3.092 72.27