292 97 2MB
English Pages 260 Year 2003
Microbiological Assay for Pharmaceutical Analysis A Rational Approach
Microbiological Assay for Pharmaceutical Analysis A Rational Approach
William Hewitt Interpharm /CRC Boca Raton London New York Washington, D.C.
This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”
/LEUDU\RI&RQJUHVV&DWDORJLQJLQ3XEOLFDWLRQ'DWD +HZLWW:LOOLDP² 0LFURELRORJLFDODVVD\IRUSKDUPDFHXWLFDODQDO\VLVDUDWLRQDODSSURDFK:LOOLDP+HZLWW SFP ,QFOXGHVELEOLRJUDSKLFDOUHIHUHQFHVDQGLQGH[ ,6%1 0LFURELRORJLFDODVVD\0LFURELRORJLFDODVVD\0DWKHPDWLFV,7LWOH >'1/0%LRORJLFDODVVD\PHWKRGV'DWD,QWHUSUHWDWLRQ6WDWLVWLFDO'RVDJH )RUPVVWDQGDUGV'UXJ6WDELOLW\0LFURELRORJLFDO7HFKQLTXHV3KDUPDFHXWLFDO 3UHSDUDWLRQVDQDO\VLV49+PD@ 450+ v³GF 7KLVERRNFRQWDLQVLQIRUPDWLRQREWDLQHGIURPDXWKHQWLFDQGKLJKO\UHJDUGHGVRXUFHV5HSULQWHGPDWHULDO LVTXRWHGZLWKSHUPLVVLRQDQGVRXUFHVDUHLQGLFDWHG$ZLGHYDULHW\RIUHIHUHQFHVDUHOLVWHG5HDVRQDEOH HIIRUWVKDYHEHHQPDGHWRSXEOLVKUHOLDEOHGDWDDQGLQIRUPDWLRQEXWWKHDXWKRUDQGWKHSXEOLVKHUFDQQRW DVVXPHUHVSRQVLELOLW\IRUWKHYDOLGLW\RIDOOPDWHULDOVRUIRUWKHFRQVHTXHQFHVRIWKHLUXVH 1HLWKHUWKLVERRNQRUDQ\SDUWPD\EHUHSURGXFHGRUWUDQVPLWWHGLQDQ\IRUPRUE\DQ\PHDQVHOHFWURQLF RUPHFKDQLFDOLQFOXGLQJSKRWRFRS\LQJPLFURÀOPLQJDQGUHFRUGLQJRUE\DQ\LQIRUPDWLRQVWRUDJHRU UHWULHYDOV\VWHPZLWKRXWSULRUSHUPLVVLRQLQZULWLQJIURPWKHSXEOLVKHU 7KHFRQVHQWRI&5&3UHVV//&GRHVQRWH[WHQGWRFRS\LQJIRUJHQHUDOGLVWULEXWLRQIRUSURPRWLRQIRU FUHDWLQJQHZZRUNVRUIRUUHVDOH6SHFLÀFSHUPLVVLRQPXVWEHREWDLQHGLQZULWLQJIURP&5&3UHVV//& IRUVXFKFRS\LQJ 'LUHFWDOOLQTXLULHVWR&5&3UHVV//&1:&RUSRUDWH%OYG%RFD5DWRQ)ORULGD 7UDGHPDUN1RWLFH 3URGXFWRUFRUSRUDWHQDPHVPD\EHWUDGHPDUNVRUUHJLVWHUHGWUDGHPDUNVDQGDUH XVHGRQO\IRULGHQWLÀFDWLRQDQGH[SODQDWLRQZLWKRXWLQWHQWWRLQIULQJH
9LVLWWKH&5&3UHVV:HEVLWHDWZZZFUFSUHVVFRP E\&5&3UHVV//& ,QWHUSKDUPLVDQLPSULQWRI&5&3UHVV//& 1RFODLPWRRULJLQDO86*RYHUQPHQWZRUNV ,QWHUQDWLRQDO6WDQGDUG%RRN1XPEHU /LEUDU\RI&RQJUHVV&DUG1XPEHU ISBN 0-203-50397-X Master e-book ISBN
ISBN 0-203-58859-2 (Adobe eReader Format)
Preface 2QHPXVWKDYHUHDVRQVIRUZULWLQJDERRN³WKHSUHIDFHSURYLGHVDQRSSRUWXQLW\ WRH[SODLQWKRVHUHDVRQV 0\EDFNJURXQGLVWKDWRIDQDQDO\WLFDOFKHPLVW%\FKDQFH,EHFDPHLQYROYHG LQPLFURELRORJLFDODVVD\VRPHGHFDGHVDJRDQGDOVREHFDPHLQWULJXHGE\WKHVHHP LQJO\XQXVXDOFDOFXODWLRQVWKDWZHUHXVHGWRDUULYHDWHVWLPDWHGSRWHQF\DQGFRQÀ GHQFH OLPLWV IRU WKH HVWLPDWH , ZDV IRUWXQDWH LQ KDYLQJ H[FHOOHQW WXWRUV ³ LQ SDUWLFXODU 3HWHU 7RRWLOO ZKR KDG EHHQ SURPLQHQW LQ SURPRWLQJ WKH XVH RI JRRG H[SHULPHQWDOGHVLJQVLQWKHVDQGV 6RPH\HDUVODWHU,HPEDUNHGRQDQRYHUVHDVFDUHHUDVDQDGYLVRURQDQDO\WLFDO FKHPLVWU\LQ(XURSH,QHYLWDEO\P\DWWHQWLRQZDVGUDZQWRWKHODFNRIXQGHUVWDQGLQJ RI WKH EDVLF PDWKHPDWLFDO SULQFLSOHV RI PLFURELRORJLFDO DVVD\ WKH DJDU GLIIXVLRQ DVVD\IRUDQWLELRWLFV ,VHWRXWWREULQJHQOLJKWHQPHQWLQWKLVÀHOG7KLVZDVÀUVWE\ VRPHSULQWHGQRWHVIRUORFDOXVH/DWHUUHFRJQL]LQJWKHZLGHUSRWHQWLDODSSOLFDWLRQ RI WKHVH QRWHV , ZDV DEOH WR H[SDQG RQ WKHP YHU\ VXEVWDQWLDOO\ DQG SXEOLVKHG 0LFURELRORJLFDO$VVD\$Q,QWURGXFWLRQWR4XDQWLWDWLYH3ULQFLSOHVDQG(YDOXDWLRQ LQ ERRN 1R ,W LV IDVFLQDWLQJ WR FRQWHPSODWH WKDW WKLV ERRN ZLWK LWV LQQXPHUDEOHFDOFXODWLRQVZDVDVVHPEOHGZLWKWKHDLGRIDPHFKDQLFDOW\SHZULWHUD ORWRIFRUUHFWLRQÁXLGDQGDSRFNHWFDOFXODWRU 6RPH \HDUV ODWHU VWLOO ZRUNLQJ DV DQ RYHUVHDV DGYLVRU DQG VWLOO YHU\ PXFK DQ DQDO\WLFDOFKHPLVW ,EHFDPHHYHQPRUHLPSUHVVHGE\WKHODFNRIDSSUHFLDWLRQRIWKH EDVLF SUDFWLFDO DZDUHQHVV QHHGHG WR DFKLHYH VXFFHVV LQ WKH ÀHOG RI PLFURELRORJLFDO DVVD\ 0DQDJHUV ZHUH VRPHWLPHV PLFURELRORJLVWV ³ PXFK PRUH FRPSHWHQW WKDQ P\VHOI LQ PLFURELRORJ\ EXW QRW VXIÀFLHQWO\ DZDUH WKDW WKH PLFURELRORJLFDO DVVD\ RI DQWLELRWLFV QHHGHG WR EH WUHDWHG DV D EUDQFK RI DQDO\WLFDO FKHPLVWU\ , UHFDOO RQH ODERUDWRU\LQZKLFK,IRXQGQRIDXOWZLWKWKHPLFURELRORJLFDODVSHFWRIWKHZRUNEXW LQZKLFKWKHRSWLFDOFRPSRQHQWVRIWKH]RQHPHDVXULQJGHYLFHZHUHFRDWHGZLWKWKH À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·VZRUN IRUDQH[SHULHQFHGSHUVRQ VXFKFDOFXODWLRQVZHUHUHJDUGHGDVVRPHWKLQJQRWWREH
DSSOLHGWRHDFKDVVD\EXWDVDGHPRQVWUDWLRQRIWKHSUHFLVLRQWKDWFRXOGEHH[SHFWHG RIDQDVVD\ 1RZDGD\VRQFHWKHSURJUDPKDVEHHQVHWXSRQWKHFRPSXWHUWKHFDOFXODWLRQ LVHIIRUWOHVV7KLVPLJKWVHHPWRLPSO\WKDWWKHDQDO\VWQHHGQRWFRQFHUQKLPVHOIRU KHUVHOIZLWKWKHFDOFXODWLRQEHLQJVDWLVÀHGWKDWLWKDVEHHQVHWXSE\DFRPSHWHQW VWDWLVWLFLDQDQGYDOLGDWHG+RZHYHU(XURSHDQSKDUPDFRSRHLDJXLGDQFHLVRWKHUZLVH 5HIHUULQJWRFRPSXWHUSURJUDPVWKHSKDUPDFRSRHLDGLUHFWVWKDW WKHÀQDOGHFLVLRQ WRDFFHSWUHMHFWRUPRGLI\WKHREVHUYHGGDWDPXVWEHWDNHQE\WKHDQDO\VWLQWKH OLJKWRIWKHGHWDLOHGUHVXOWVJLYHQE\WKHFRPSXWHU,QUHDFKLQJDGHFLVLRQWKHDQDO\VW VKRXOGEHDULQPLQGWKDW´VWDWLVWLFDOVLJQLÀFDQFHµLVQRWV\QRQ\PRXVZLWK´SUDFWLFDO LPSRUWDQFHµ³DIDFWWKDWLVZHOOLOOXVWUDWHGLQWKLVERRN :KLOHWKHDQDO\VWZLOOSUREDEO\DFFHSWWKHSULQFLSOHVRIWKHVWDWLVWLFDOHYDOXDWLRQ ZLWKRXWKDYLQJDWKRURXJKXQGHUVWDQGLQJRIVWDWLVWLFDOWKHRU\WKHUHLVFOHDUO\DQHHG IRUWKHDQDO\VWWRXQGHUVWDQGKRZWKHFDOFXODWLRQVZRUN,QWKHDQDO\VLVRIYDULDQFH LW LV QHFHVVDU\ WR EH DEOH WR LGHQWLI\ ZK\ YDULDWLRQ DWWULEXWDEOH WR DQ\ VRXUFH LV VWDWLVWLFDOO\VLJQLÀFDQW³WKHQWRDVVHVVZKHWKHUWKDWVLJQLÀFDQFHLVUHDOO\JRLQJWR MHRSDUGL]HWKHUHOLDELOLW\RIWKHDVVD\$PDMRUREMHFWLYHRIWKLVERRNLVWRSURYLGH DQLQVLJKWLQWRKRZWKHFDOFXODWLRQVZRUNDQGWRKHOSDQDO\VWVPDNHMXGJPHQWVRQ YDOLGLW\ 2QWKHSUDFWLFDOVLGHWKHREMHFWLYHVRIWKHERRNDUHPRUHOLPLWHG7KHUHH[LVWV H[FHOOHQWGHWDLOHGJXLGDQFHRQSUDFWLFDODVSHFWVRIWKHVXEMHFWLQ6WHSKHQ9LQFHQW·V FRQWULEXWLRQWRERRN7KLVLVQRWRXWGDWHG7KHJXLGDQFHJLYHQKHUHGUDZVDWWHQWLRQ WRWKHPLFURELRORJLFDODVSHFWVZKLFKPD\QRWEHVRREYLRXVWRWKHFKHPLFDODQDO\VW DQG WR DQDO\WLFDO DVSHFWV WKDW PD\ QRW EH VR REYLRXV WR WKH PLFURELRORJLVW $Q LPSRUWDQWIHDWXUHFRQFHUQVWKHQHHGIRUVWHULOHHTXLSPHQWDQGDVHSWLFWHFKQLTXHV )HZ ERRNV KDYH EHHQ ZULWWHQ SUHVHQWLQJ DQ RYHUDOO YLHZ RI PLFURELRORJLFDO DVVD\ 7KH YHU\ FRPSUHKHQVLYH $QDO\WLFDO 0LFURELRORJ\ HGLWHG E\ )UHGHULFN .DYDQDJK³YROXPHLQDQGYROXPHLQ³UHPDLQVRIJUHDWYDOXHWR WKRVHSUDFWLFLQJPLFURELRORJLFDODVVD\WRGD\,WLVKRSHGWKDW0LFURELRORJLFDO$VVD\ IRU3KDUPDFHXWLFDO$QDO\VLV$5DWLRQDO$SSURDFKZLOOVHUYHLWVLQWHQGHGSXUSRVH LQSURYLGLQJDQXSGDWHRQHDUOLHUSXEOLFDWLRQV
Author Biography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
Acknowledgments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³&KDSWHULQFOXGHVDGDSWDWLRQVIURP WKH ZRUN RI *DUUHWW DQG 0LOOHU 7KHVH DGDSWDWLRQV DUH PDGH ZLWK WKH NLQG SHUPLVVLRQRI:LOH\/LVV,QFDVXEVLGLDU\RI-RKQ:LOH\ 6RQV,QF 7KH8QLWHG6WDWHV3KDUPDFRSRHLDO&RQYHQWLRQ³&KDSWHUPDNHVUHIHUHQFHWR 863 WHVWV IRU RXWOLHUV DQG &KDSWHU LQWURGXFHV WKH FKLVTXDUHG WHVW7KH FRUUH VSRQGLQJWDEOHVRIDQQH[HVDQGDUHUHSULQWHGZLWKSHUPLVVLRQ7KH8QLWHG6WDWHV 3KDUPDFRSRHLDO&RQYHQWLRQ,QF$OOULJKWVUHVHUYHG 7KH (XURSHDQ 3KDUPDFRSRHLD &RPPLVVLRQ ³ ([WUDFWV IURP WKH FKDSWHUV RQ VWDWLVWLFDODQDO\VLVRIIRXUHGLWLRQVRIWKH(3DUHTXRWHGRUUHSURGXFHGZLWKWKHNLQG SHUPLVVLRQRIWKH(XURSHDQ3KDUPDFRSRHLD&RPPLVVLRQ,Q&KDSWHUWKHUHLVRQH TXRWDWLRQLQ&KDSWHUWKURXJK&KDSWHUWKHUHDUHIRXUTXRWDWLRQV(GLWLRQDQG SDJHUHIHUHQFHVDUHJLYHQLQWKHUHIHUHQFHOLVWDWWKHHQGRIHDFKFKDSWHU 7KH:RUOG +HDOWK 2UJDQL]DWLRQ ³ ,Q &KDSWHU UHIHUHQFH LV PDGH WR WKH:+2 SXEOLFDWLRQ´$FFHOHUDWHG6WDELOLW\6WXGLHVRI:LGHO\8VHG3KDUPDFHXWLFDO6XEVWDQFHV
XQGHU6LPXODWHG7URSLFDO&RQGLWLRQVµ 7DEOHDQG7DEOHDUHEDVHGRQ LQIRUPDWLRQ DEVWUDFWHG IURP WKLV SXEOLFDWLRQ ZLWK WKH NLQG SHUPLVVLRQ RI WKH:RUOG +HDOWK2UJDQL]DWLRQ,Q&KDSWHUUHIHUHQFHLVPDGHWRDSXEOLFDWLRQLQWKH-RXUQDO RI%LRORJLFDO6WDQGDUGL]DWLRQ$QQH[LVWDNHQIURPWKDWSXEOLFDWLRQDQGLVUHSURGXFHG YHUEDWLPZLWKWKHNLQGSHUPLVVLRQRIWKH:RUOG+HDOWK2UJDQL]DWLRQ 7KH6RFLHW\IRU*HQHUDO0LFURELRORJ\IRUJUDQWLQJSHUPLVVLRQWRUHSURGXFHÀ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ÀQGLQJV 6WHSKHQ9LQFHQW IRUPHUO\ RI *OD[R /DERUDWRULHV 8. IRU UHYLHZLQJ &KDSWHU DQGPDNLQJYDOXDEOHVXJJHVWLRQV
Table of Contents &KDSWHU
0LFURELRORJLFDO$VVD\LQ3HUVSHFWLYH
%LRORJLFDO$VVD\VLQ*HQHUDO 7KH'LIIHUHQW6RUWVRI0LFURELRORJLFDO$VVD\ 7KH$JDU'LIIXVLRQ$VVD\ 7KH7XEHRU)ODVN$VVD\IRU*URZWK3URPRWLQJ6XEVWDQFHV 7KH7XEH$VVD\IRU*URZWK,QKLELWLQJ6XEVWDQFHV 7KH%DVLVRI&DOFXODWLRQRI3RWHQF\(VWLPDWHV 3DUDOOHO/LQH$VVD\V 6ORSH5DWLR$VVD\V :KLFK0DWKHPDWLFDO0RGHO" 5HIHUHQFHV &KDSWHU
7KH$JDU'LIIXVLRQ$VVD\³,WV4XDQWLWDWLYH%DVLV
+LVWRULFDO,QWURGXFWLRQ 7KH7KHRU\RI=RQH)RUPDWLRQ :KDW+DSSHQVLQ3UDFWLFH 3ULQFLSOHRI&DOFXODWLRQRI3RWHQF\(VWLPDWH 5HIHUHQFHV &KDSWHU
7KH7KHRU\DQG3UDFWLFHRI7XEH$VVD\VIRU*URZWK3URPRWLQJ 6XEVWDQFHV
,QWURGXFWLRQ 7KH0RGHRI$FWLRQRI*URZWK3URPRWLQJ6XEVWDQFHV *URZWK/LPLWHGE\$PLQR$FLGV *URZWK/LPLWHGE\9LWDPLQV 3URGXFWLRQRI$FLGE\/DFWREDFLOOL &ULWLFDO)DFWRUVLQWKH$VVD\RI*URZWK3URPRWLQJ6XEVWDQFHV 2WKHU6RXUFHVRI(UURU 5HIHUHQFHV &KDSWHU
7KH7KHRU\DQG3UDFWLFHRI7XEH$VVD\VIRU*URZWK,QKLELWLQJ 6XEVWDQFHV
+LVWRULFDO,QWURGXFWLRQ 0HDVXUHPHQWRI5HVSRQVH
7KH)RUPRIWKH5HVSRQVH/LQH +LVWRULFDO'HYHORSPHQWRIWKH7XUELGLPHWULF0HWKRG /LQHDUL]DWLRQRI6LJPRLG&XUYHV 7KH4XDQWLWDWLYH7KHRU\RI0LFURELDO*URZWKDQG,QKLELWLRQ $3UDFWLFDOO\'HWHUPLQHG/RJ'RVH5HVSRQVH&XUYH )DFWRUV$IIHFWLQJ)LQDO&HOO&RXQW 7KH,QÁXHQFHRI7HPSHUDWXUH 7KH,QÁXHQFHRI7LPH 6XPPDU\DQG&RQFOXVLRQV 5HIHUHQFHV &KDSWHU
:KDW'R:H:DQWRIDQ$VVD\"+RZ'R:H$WWDLQ2XU*RDO"
,QWURGXFWLRQ 3KDUPDFRSRHLDO,QWHQWLRQ &RQWURORI$QWLELRWLF%XON0DWHULDOV &RQWUROLQ5RXWLQH0DQXIDFWXUH 5HVHDUFKDQG'HYHORSPHQW ² @==
Parallel-Line Assays — Some Designs and Their Evaluation
119
7KHUH DUH WZR FRQWUDVWV RYHU WZR GRVH LQWHUYDOV HDFK KDYLQJ D UHSOLFDWLRQ RI VL[ KHQFHWKHGHQRPLQDWRU 6WHS &DOFXODWH ) WKH PHDQ GLIIHUHQFH EHWZHHQ XQNQRZQ DQG VWDQGDUG UHVSRQVHV ) > ²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tatistical Evaluation 7KHDQDO\VLVRIYDULDQFHFRPSULVHVWZRSDUWV ,GHQWLÀFDWLRQRIYDULDQFHGXHWRWKHVL[GLIIHUHQWWUHDWPHQWV ,GHQWLÀFDWLRQRIYDULDQFHGXHWRGLIIHUHQWEORFNV³URZVDQGFROXPQVRQ WKHSODWHLQWKLVSDUWLFXODUDVVD\GHVLJQ 9DULDQFH GXH WR WKH GLIIHUHQW LQGLYLGXDO WUHDWPHQWV LV FDOFXODWHG XVLQJ RUWKRJRQDO SRO\QRPLDOFRHIÀFLHQWVDVVKRZQLQ7DEOH
120
Microbiological Assay for Pharmaceutical Analysis
TABLE 9.6 Factorial Coefficients for a Three-Dose Level Symmetrical Assay Applied to the Data of Example 9.2 as a Part of the Analysis of Variance Row D E DE T DT 7UHDWPHQW 7RWDOVA
S1
S2
S3
U1
U2
U3
² ² ²
² ²
² ² ²
² ²
² ²
ei
Ti
² ²
Ti2/(6 = ei)
9DOXHVIRUWKHUHPDLQLQJVRXUFHVRIYDULDWLRQDUHFDOFXODWHGWKXV 6WHS )URP WKH UDZ GDWD DV DSSHDULQJ RQ WKH SODWH FDOFXODWH WKH WRWDO GHYLDWLRQVTXDUHVDV
7 <
²
PHDQFRUUHFWLRQ 0&
6WHS)URPWKHURZWRWDOVDVDSSHDULQJRQWKHSODWHFDOFXODWH
< 0&
² 6WHS)URPWKHFROXPQWRWDOVDVDSSHDULQJRQWKHSODWHFDOFXODWH
< 0&
² 6WHS)URPWKHWUHDWPHQWWRWDOVFDOFXODWH
< 0&
²
121
Parallel-Line Assays — Some Designs and Their Evaluation
$VXPPDU\RIWKHDQDO\VLVRIYDULDQFHLVSUHVHQWHGLQ7DEOH Discussion of Assay Validity Based on the Analysis of Variance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ÀGHQFHOLPLWVIRUWKHSRWHQF\ HVWLPDWHPD\EHFDOFXODWHG
TABLE 9.7 Summary of Analysis of Variance, Example 9.2, a Three-Dose Level Assay Using a Large Plate and a 6 = 6 Latin Square Design Source of Variance
d.f.
Sums of Squares
Mean Squares
3UHSDUDWLRQV 5HJUHVVLRQ 3DUDOOHOLVP 4XDGUDWLFFXUYDWXUH 2SSRVHGFXUYDWXUH
6XEWRWDO
7UHDWPHQWV 5RZV &ROXPQV (UURUE\GLIIHUHQFH
7RWDO
Variance Ratio
Limiting Value
At Arbitrary Probability Level, P
!
Calculated Probability
1RWH/LPLWLQJYDOXHVLQFROXPQUHIHUWRWKHFRUUHVSRQGLQJDUELWUDU\SUREDELOLW\OHYHORIFROXPQ
122
Microbiological Assay for Pharmaceutical Analysis
6WHS&DOFXODWHWKHWHUP6[[WKHVXPRIWKHVTXDUHVRIGHYLDWLRQVRILQGL YLGXDOORJGRVHVIURPWKHPHDQORJGRVH7KHGRVHUDWLRLVVRWKHORJ GRVH LQWHUYDO LV 7KHUH DUH KLJK DQG ORZ GRVHV PLG GRVHV FRQWULEXWHQRWKLQJWRWKLVFDOFXODWLRQVRWKHYDOXHLVREWDLQHGDV 6[[ => ² @ 6WHS&DOFXODWHJWKHLQGH[RIVLJQLÀFDQFHRIWKHVORSHEDV J
V = W E = 6[[
VRWKDWLQWKLVDVVD\ J
= =
ZKHUHVEDQG6[[KDYHWKHYDOXHVDOUHDG\FDOFXODWHGDQGWLV6WXGHQW·VWREWDLQHG IURPWDEOHVIRU3 DQGGHJUHHVRIIUHHGRPDV$EULHIIRUPRIWKLV WDEOHLVJLYHQLQ$SSHQGL[ $VJLVOHVVWKDQFDOFXODWHFRQÀGHQFHOLPLWVRIWKHSRWHQF\HVWLPDWHVE\WKHVR FDOOHGDSSUR[LPDWHPHWKRG 6WHS&DOFXODWH90v WKHYDULDQFHRIWKHORJDULWKPRIWKHSRWHQF\HVWLPDWH RIWKHXQNQRZQE\VXEVWLWXWLQJWKHNQRZQYDOXHVLQWKHHTXDWLRQ
90
V E
0
³ µ 1 V 17 6[[
90
³
µ
6WHS2EWDLQVP WKHVWDQGDUGHUURURIWKHORJDULWKPRIWKHSRWHQF\HVWLPDWH DV VP >90 @ ZKHUHYDOXHVDUH VP
Parallel-Line Assays — Some Designs and Their Evaluation
123
6WHS/RJSHUFHQWFRQÀGHQFHOLPLWVDUHJLYHQE\ W=VP
ZKHUHYDOXHVDUH = DQG 7KHFRUUHVSRQGLQJSHUFHQWDJHOLPLWVDUHDQG3 $OWHUQDWLYHO\H[SUHVVHGLQWHUPVRIWKHVWDQGDUGSRWHQF\WKHHVWLPDWHGSRWHQF\LV ZLWKOLPLWVWR3
A TWO-DOSE LEVEL ASSAY FOR FOUR PREPARATIONS (THREE UNKNOWNS) USING A LARGE PLATE AND AN 8 = 8 LATIN SQUARE DESIGN 7KLVDVVD\XVLQJDQ=/DWLQVTXDUHGHVLJQSURYLGHVIRUWKHVLPXOWDQHRXVDVVD\ RI WKUHH XQNQRZQV DW WZR GRVH OHYHOV (DFK WUHDWPHQW KDV D UHSOLFDWLRQ RI HLJKW FRUUHVSRQGLQJWRREVHUYDWLRQVSHUSUHSDUDWLRQ7KLVGHVLJQPD\EHXVHIXOLQURXWLQH TXDOLW\ FRQWURO LQ WKH SKDUPDFHXWLFDO LQGXVWU\ ZKHQ OHYHOV RI ´DVVLJQHG SRWHQF\µ EHIRUHDVVD\ PD\EHJLYHQZLWKUHDVRQDEOHFRQÀGHQFH7KHGRVHUDWLRHPSOR\HGLV IUHTXHQWO\ RU ,Q WKLV FDVH WKH UDWLR FKRVHQ ZDV QR GRXEW EHFDXVH WKH JHQHUDOO\SRRUVORSHRIQHRP\FLQDVVD\VSHUPLWVDZLGHUUDQJHWREHXVHG (;$03/($1$66$ ² @ 6WHS)URPWKHKLJKDQGORZGRVHWRWDOVIRULQGLYLGXDOSUHSDUDWLRQVFDO FXODWHSDUDOOHOLVPVTXDUHVDV
! < < #
² UHJUHVVLRQVTXDUHV
²
6WHS&DOFXODWHZHLJKLQJVZLWKLQSUHSDUDWLRQVDV
!6$
+
6$/ < 6%+ 6%/
# !8$
+
! < #
! < #
8$/ < 8%+ 8%/
#
138
Microbiological Assay for Pharmaceutical Analysis
6WHS&DOFXODWHUHJUHVVLRQ=ZHLJKLQJVDV ,W LV FRQYHQLHQW WR H[SUHVV WKLV OHQJWK\ FDOFXODWLRQ DV UHJUHVVLRQ = ZHLJKLQJV $²%²& ZKHUH $ >6$+²6$/ @>6%+²6%/ @>8$+²8$/ @>8%+² 8%/ @ % UHJUHVVLRQVTXDUHVIRUVWDQGDUG ^>6$+6%+ ²6$/6%/ @` & UHJUHVVLRQVTXDUHVIRUXQNQRZQ ^>8$+8%+ ²8$/8%/ @` VRWKDW
$ >² @>² @`>² @ >² @` % ^> ² @` & ^> ² @`
DQGUHJUHVVLRQ=ZHLJKLQJV ²² TABLE 9.13A Summary of the Analysis of Variance for Example 9.4a, a Two-Dose Level Assay Comparing One Unknown With the Reference Standard Using a Large Plate and an 8 = 8 Latin Square Design, with Duplicate Weighings of Each of the Two Preparations Sum of Mean d.f. Squares Squares
Variance Ratio
Limiting Value
At Arbitrary Probability Level, P
Calculated Probability
3UHSDUDWLRQV 5HJUHVVLRQ 3DUDOOHOLVP >GHYLDWLRQVIURP@ :HLJKLQJVZLWKLQ SUHSDUDWLRQV 5HJUHVVLRQ= ZHLJKLQJV
!
Source of Variance
6XEWRWDO
7UHDWPHQWV 5RZV &ROXPQV (UURUE\GLIIHUHQFH
7RWDO
1RWH/LPLWLQJYDOXHVLQFROXPQUHIHUWRWKHFRUUHVSRQGLQJDUELWUDU\SUREDELOLW\OHYHORIFROXPQ
Parallel-Line Assays — Some Designs and Their Evaluation
139
Discussion of Assay Validity Based on the Analysis of Variance ,QWKLVWZRGRVHOHYHODVVD\WKHSKDUPDFRSRHLDOUHTXLUHPHQWVFRQFHUQLQJYDULDQFH UDWLRVDSSO\WRUHJUHVVLRQDQGSDUDOOHOLVPRQO\7KHYDULDQFHUDWLRIRUUHJUHVVLRQDW RYHUJUHDWO\H[FHHGVWKHOLPLWLQJYDOXHRI7KHYDULDQFHUDWLRIRUSDUDO OHOLVPDWLVZHOOEHORZWKHOLPLWLQJYDOXHRI 7KHYDOXHIRUSUHSDUDWLRQVDWH[FHHGVWKHZDUQLQJOHYHORI7KLVLV FRQVLVWHQWZLWKWKHHVWLPDWHGSRWHQF\RIWKHXQNQRZQEHLQJSHUFHQWRIWKDW RI WKH VWDQGDUG )RU WKH VDPH UHDVRQV DV JLYHQ LQ ([DPSOH LW LV FRQVLGHUHG WKDWWKHUHPD\EHDVOLJKWELDVLQWKHSRWHQF\HVWLPDWHEXWQRWHQRXJKWRLQYDOLGDWH WKH DVVD\ 7KH YDOXHV IRU YDULDQFH UDWLRV IRU ZHLJKLQJV ZLWKLQ SUHSDUDWLRQV DQG UHJUHVVLRQ=ZHLJKLQJVDUHOHVVWKDQWKHDUELWUDU\OLPLWVRWKHVHVHHPVDWLVIDFWRU\ +RZHYHU D GLIIHUHQW FRQFOXVLRQ LV UHDFKHG IURP WKH PRUH FULWLFDO UHYLHZ LQ ([DPSOHE $V WKH DVVHVVPHQW RI WKH DQDO\VLV RI YDULDQFH VHHPV VDWLVIDFWRU\ FRQÀGHQFH OLPLWVIRUWKHSRWHQF\HVWLPDWHPD\EHFDOFXODWHG 6WHS &DOFXODWH WKH WHUP 6[[ WKH VXP RI WKH VTXDUHV RI GHYLDWLRQV RI LQGLYLGXDOORJGRVHVIURPWKHPHDQORJGRVH7KHGRVHUDWLRLVVRWKH ORJGRVHLQWHUYDOLV7KHUHDUHKLJKDQGORZGRVHVVRWKH YDOXHLVREWDLQHGDV > ² @ 6WHS&DOFXODWHJWKHLQGH[RIVLJQLÀFDQFHRIWKHVORSHEXVLQJ(TXDWLRQ DV J
= =
7KHYDOXHRIJLVZHOOEHORZWKHOLPLWRIDQGVRWKHYDULDQFHRI0DQGFRQÀGHQFH OLPLWVPD\EHFDOFXODWHGE\WKHDSSUR[LPDWHPHWKRG 6WHS&DOFXODWHWKHYDULDQFHRI0E\(TXDWLRQ DV 90
³ µ
6WHS&DOFXODWHV0E\(TXDWLRQ DV V0
140
Microbiological Assay for Pharmaceutical Analysis
6WHS/RJSHUFHQWFRQÀGHQFHOLPLWVDUH = WR FRUUHVSRQGLQJWRFRQÀGHQFHOLPLWVRIWR
EXAMPLE 9.4B A MORE CRITICAL EXAMINATION DUPLICATE WEIGHINGS
OF AN
ASSAY
WITH
7KHUDZGDWDRI([DPSOHDUHH[DPLQHGKHUHLQ([DPSOHELQPRUHGHWDLOWR JDLQ DQ LQVLJKW LQWR WKH PHDQLQJV RI WKH FRPSRQHQWV RI YDULDWLRQ DWWULEXWHG WR GLIIHUHQFHV LQ WKH WZR ZHLJKLQJV RI VWDQGDUG DQG XQNQRZQ$ VLPSOH FRPSDULVRQ RI VWDQGDUG % ZLWK VWDQGDUG $ DQG VLPLODUO\ D FRPSDULVRQ RI XQNQRZQ % ZLWK XQNQRZQ$ZLOOJLYHÀJXUHVWKDWDUHLPPHGLDWHO\PHDQLQJIXOWRWKHDQDO\VW8VLQJ WKHYDOXHRIEREWDLQHGIURPDFRQVLGHUDWLRQRIDOOUHVSRQVHV FDOFXODWH WKHSRWHQF\RIVWDQGDUG%LQWHUPVRIVWDQGDUG$ ) < ² 0 ) E ² ² 5 DQWLORJ ² 6LPLODUO\FDOFXODWHWKHSRWHQF\RIXQNQRZQ%LQWHUPVRIXQNQRZQ$ ) < 0 ) E 5 DQWLORJ ,Q URXQG ÀJXUHV WKH GLVFUHSDQFLHV EHWZHHQ ZHLJKLQJV % DQG ZHLJKLQJV $ DUH ² LQ WKH FDVH RI WKH VWDQGDUGV DQG LQ WKH FDVH RI WKH XQNQRZQV 7KLV LV FOHDUO\ QRW JRRG HQRXJK LQ DQ DVVD\ LQWHQGHG WR EH RI TXLWH KLJK DFFXUDF\ DQG SUHFLVLRQ= ²²= @= 6WHS&DOFXODWH)WKHPHDQGLIIHUHQFHLQXQFRUUHFWHG UHVSRQVHVEHWZHHQ WKHXQNQRZQDQGWKHUHIHUHQFHIRUWKHÀQDOJURXSRIWKUHHSODWHV
163
Parallel-Line Assays — Some Designs and Their Evaluation
0HDQ=RQH'LDPHWHUPP
'RVH,8PORQORJDULWKPLFVFDOH REVHUYHGYDOXHVVWDQGDUGVDQGUHIHUHQFHSRLQW FDOFXODWHGLGHDOYDOXHVIRUORZDQGKLJKGRVHV
REVHUYHGYDOXHXQNQRZQ
FIGURE 9.6 $ JUDSKLFDO UHSUHVHQWDWLRQ RI WKH GDWD RI H[DPSOH ,W LV EDVHG RQ WKH FRUUHFWHGPHDQ]RQHVL]HVRI7DEOH7KHVWUDLJKWOLQHLVGUDZQWRMRLQWKHYDOXHVRI / DQG+WKDWZHUHFDOFXODWHGXVLQJ(TXDWLRQ DQG(TXDWLRQ UHVSHFWLYHO\
) ² ² 6WHS&DOFXODWHEWKHPHDQGLIIHUHQFHLQUHVSRQVHIRUDWHQIROGLQFUHDVHLQ GRVH E (, ORJ 6WHS&DOFXODWHWKHYDOXHRI0WKHORJDULWKPRIWKHUDWLRRIWKHSRWHQF\RI XQNQRZQWRWKDWRIWKHVWDQGDUG 0 )E ² ² 6WHS &DOFXODWH SRWHQF\ HVWLPDWH RI WKH XQNQRZQ WHVW VROXWLRQ UHODWLYH WR WKDWRIWKHUHIHUHQFHWHVWVROXWLRQ DQWLORJ0 &RPSDUHWKLVZLWKREWDLQHGJUDSKLFDOO\ 6WHS&DOFXODWHSRWHQF\HVWLPDWHRIWKHVDPSOH$FWXDOSRWHQF\HVWLPDWHRI WKHXQNQRZQWHVWVROXWLRQLV == ,8PO
164
Microbiological Assay for Pharmaceutical Analysis
7KHFRQFHQWUDWLRQRIWKHWHVWVROXWLRQLV+JPORUPJPO VRWKDW HVWLPDWHGSRWHQF\LV ,8PJ 7KHUHIRUH D YLDO KDYLQJ DQ DYHUDJH ZHLJKW RI FRQWHQWV RI J LV HVWLPDWHG WR FRQWDLQ = PJRINDQDP\FLQEDVH Statistical Evaluation 6WHS )URP WKH FRUUHFWHG GDWD RI7DEOH FDOFXODWH WKH WRWDO GHYLDWLRQ VTXDUHVDV
7 <
<
PHDQFRUUHFWLRQ 0&
6WHS)URPWKHWUHDWPHQWWRWDOVFDOFXODWH
< 0&
< 6WHS)URPWKHSUHSDUDWLRQWRWDOVFDOFXODWH
< 0&
< 6WHS8VLQJRUWKRJRQDOSRO\QRPLDOFRHIÀFLHQWVFDOFXODWHVTXDUHVIRUUHJUHV VLRQDQGGHYLDWLRQVIURPUHJUHVVLRQVTXDUHVDVVKRZQLQ7DEOH 6WHS ,QVHUW WKH NQRZQ GHYLDWLRQ VTXDUHV LQ 7DEOH WKH VXPPDU\ RI DQDO\VLVRIYDULDQFHDQGFDOFXODWHWKHUHVLGXDOHUURUVTXDUHVE\GLIIHUHQFH Discussion of Assay Validity Based on the Analysis of Variance )LUVW D FRPPHQW RQ WKH QXPEHU RI GHJUHHV RI IUHHGRP LV DSSURSULDWH )RU WKH FDOFXODWLRQV XVLQJ RUWKRJRQDO SRO\QRPLDO FRHIÀFLHQWV WKH YDOXH RI WKH UHIHUHQFH
165
Parallel-Line Assays — Some Designs and Their Evaluation
TABLE 9.21 Factorial Coefficients for a Five-Dose Level Standard Curve Applied to the Data of Example 9.10
E T U V
S1
S2
S3
S4
S5
ei
² ²
² ² ²
²
² ² ²
7UHDWPHQWWRWDOVA
Ti
Ti2/(9 = ei)
² ²
TABLE 9.22 Summary of Analysis of Variance for Example 9.6, an Assay Using Small Plates and the USP Five-Dose Level Standard Curve Procedure
Source of Variance d.f.
Sum of Squares
Mean Squares
Variance Limiting Ratio Value
3UHSDUDWLRQV 5HJUHVVLRQ 4XDGUDWLFFXUYDWXUH &XELFFXUYDWXUH 4XDUWLFFXUYDWXUH
6XEWRWDO
7UHDWPHQWV (UURUE\GLIIHUHQFH
7RWDO
!
At Arbitrary Probability Level, P
Calculated Probability
1RWH/LPLWLQJYDOXHVLQFROXPQUHIHUWRWKHFRUUHVSRQGLQJDUELWUDU\SUREDELOLW\OHYHORIFROXPQ 1RWH$GMDFHQW GRVH OHYHOV RI VWDQGDUG ZHUH LQ WKH UDWLR 7KHUH ZDV D VLQJOH OHYHO RI WKH XQNQRZQ SUHSDUDWLRQ
SRLQWZDVXVHGHIIHFWLYHO\QLQHWLPHVVRWKDWWKHQXPEHURIUHVSRQVHVXVHGLQWKH FDOFXODWLRQZDVZKLFKZRXOGQRUPDOO\OHDGWRDWRWDORIGHJUHHVRIIUHHGRP +RZHYHUWKHUHZHUHQRWQLQHLQGHSHQGHQWUHIHUHQFHSRLQWVDQGVRHIIHFWLYHO\WKHUH ZHUHRQO\LQGHSHQGHQWUHVSRQVHVOHDGLQJWRDWRWDORIGHJUHHVRIIUHHGRP ,QWKLVDVVD\WKHSKDUPDFRSRHLDOUHTXLUHPHQWVFRQFHUQLQJYDULDQFHUDWLRVDSSO\ WRUHVSRQVHVWRWKHÀYHVWDQGDUGWUHDWPHQWVRQO\WKDWLVWRUHJUHVVLRQDQGGHYLDWLRQV IURPOLQHDULW\7KHODWWHULVEURNHQGRZQLQWRLWVFRPSRQHQWSDUWVTXDGUDWLFFXELF DQGTXDUWLFFXUYDWXUH9DULDQFHUDWLRVIRUWKHWKUHHGHYLDWLRQVIURPOLQHDUUHJUHVVLRQ ZHUHDOOZHOOZLWKLQWKHOLPLWDQGQRWVWDWLVWLFDOO\VLJQLÀFDQW+RZHYHUWKHUHOLDELOLW\
166
Microbiological Assay for Pharmaceutical Analysis
RIWKHVHÀJXUHVLVTXHVWLRQDEOH7KHSUHOLPLQDU\LQVSHFWLRQRIGDWDVKRZHGWKDWWKH UDQJHVRIUHVSRQVHVWRDGMDFHQWWUHDWPHQWOHYHOVRYHUODSSHGLQWZRFDVHV7KLVRYHUODS VXJJHVWHG WKHUHIRUH WKDW WKH ÀJXUHV IRU FXELF DQG TXDUWLF FXUYDWXUH PD\ ZHOO EH GXHWRUDQGRPHUURU$OWKRXJKTXDGUDWLFFXUYDWXUHPLJKWEHH[SHFWHGRQWKHRUHWLFDO JURXQGVWKLVDVVD\ZLWKDQRYHUDOOVKRUWGRVHUDQJHPD\EHLQVXIÀFLHQWO\VHQVLWLYH WRGHWHFWWUXHFXUYDWXUH:KDWLVVHHQPD\EHGXHWRUDQGRPHUURU ,WPD\EHDSSURSULDWHWRFDOFXODWHDSRROHGHUURUWHUPFRPSULVLQJWKHUHVLGXDO HUURUSOXVDOOGHYLDWLRQVIURPOLQHDUUHJUHVVLRQ7KLVSRVVLELOLW\ZLOOEHH[SORUHGLQ WKH´$OWHUQDWLYH&DOFXODWLRQµ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²SHUFHQWPD\EHH[SHFWHG7KLV WRSLFLVGLVFXVVHGLQ&KDSWHU 7KH DVVHVVPHQW RI WKH DQDO\VLV RI YDULDQFH LV VDWLVIDFWRU\ DQG VR FRQÀGHQFH OLPLWVIRUWKHSRWHQF\HVWLPDWHPD\EHFDOFXODWHG&DOFXODWHWKHWHUP6[[WKHVXP RI WKH VTXDUHV RI GHYLDWLRQV RI LQGLYLGXDO ORJ GRVHV IURP WKH PHDQ ORJ GRVH7KH GRVHUDWLRLVVRWKHORJGRVHLQWHUYDOLV7KHGHYLDWLRQVIURPWKHPHDQ ORJGRVHDUHRQHORJGRVHLQWHUYDOGRVHOHYHOVDQG DQGWZRORJGRVHLQWHUYDOV GRVHOHYHOVDQG WKHUHSOLFDWLRQLVVRWKDW6[[LVREWDLQHGDV
= EV=6[V\@>EX=6[X\@ 6TXDUHVIRUGHYLDWLRQVIURPUHJUHVVLRQDUHREWDLQHGDVWKHGLIIHUHQFH SUHSDUDWLRQVTXDUHV²UHJUHVVLRQVTXDUHV 6TXDUHVIRUUHVLGXDOHUURUDUHREWDLQHGDVWKHGLIIHUHQFH WRWDOVTXDUHV²SUHSDUDWLRQVTXDUHV
174
Microbiological Assay for Pharmaceutical Analysis
6WHS&DOFXODWHJWKHLQGH[RIVLJQLÀFDQFHRIWKHVORSHXVLQJWKHH[SUHVVLRQ J
V = W = 6[X [X
EV 6[ V [ V 6[X [X < 6[ V [X
6WHS:KHQJLVOHVVWKDQDVLWLQYDULDEO\LVLQDQ\DVVD\WKDWLVRIDQ\ YDOXH FDOFXODWHWKHYDULDQFHRIWKHSRWHQF\UDWLR95 XVLQJWKHVLPSOLÀHG H[SUHVVLRQ V 6[ [ 56[ V [X 5 6[X [X µ 9 5 ³ µ = ³ V V EV ³ 6[ V [ V 6[X [X < 6[ V [X µ
6WHS2EWDLQWKHVWDQGDUGHUURURIWKHSRWHQF\UDWLRV5DV V5 >95 @
6WHS3URFHHGWRWKHFDOFXODWLRQRIFRQÀGHQFHOLPLWVDV 5W=V5
EVALUATION OF A TWO-DOSE LEVEL ASSAY USING THE BLISS PROCEDURE $ QLDFLQ DVVD\ FDUULHG RXW LQ ZLOO EH XVHG WR LOOXVWUDWH WKLV FDOFXODWLRQ 7KH UDZGDWDDUHSUHVHQWHGLQ7DEOH (;$03/( 7KHDVVD\RIQLDFLQXVLQJDÀYHSRLQWFRPPRQ]HURDVVD\GHVLJQ 7HVWRUJDQLVP/DFWREDFLOOXVDUDELQRVXV1&,% 6WDQGDUGGRVHOHYHOVDQG+JPO 6DPSOHGRVHOHYHOVQRPLQDOO\DQG+JPO
$V PHQWLRQHG LQ WKH VHFWLRQ RQ SUHOLPLQDU\ HYDOXDWLRQ RIWHQ LQ VORSH UDWLR DVVD\VUHVSRQVHVWR]HURGRVHDUHQRWFROOLQHDUZLWKUHVSRQVHVWRGRVHVRIVWDQGDUG DQGRIXQNQRZQ&RPSDULVRQRIWKHVORSHVLQ7DEOHVKRZVWKDWVXFKLVWKHFDVH LQWKLVH[DPSOH7KHH[WHQWRIGHYLDWLRQIURPFROOLQHDULW\LVLOOXVWUDWHGYLVXDOO\LQ
175
Slope Ratio Assays — Some Designs and Their Evaluation
TABLE 10.1 The Raw Data from Example 10.1, a Turbidimetric Assay of Niacin Using a Five-Point Common-Zero Design Standard Doses A
Zero
Low
High
Unknown Low
High
7UHDWPHQWWRWDOVA
7UHDWPHQWPHDQVA
6ORSHVEDVHGRQPHDQUHVSRQVHV VWDQGDUGORZ²]HUR
VWDQGDUGKLJK²VWDQGDUGORZ
XQNQRZQORZ²]HUR
XQNQRZQKLJK²XQNQRZQORZ
1RWH5HFRUGHGREVHUYDWLRQVDUH=RSWLFDODEVRUEDQFHDWQP
)LJXUH DQG )LJXUH ,Q )LJXUH OLQHV RI EHVW ÀW DUH SORWWHG EDVHG RQ DOO PHDQ UHVSRQVHV LQ )LJXUH OLQHV RI EHVW ÀW DUH SORWWHG H[FOXGLQJ PHDQ UHVSRQVHWR]HURGRVH,WDSSHDUHGIURPWKHJUDSKVWKDWGHYLDWLRQZDVQRWVHULRXV ,QFDVHVZKHUHWKHPHDQ]HURGRVHUHVSRQVHGHYLDWHVVLJQLÀFDQWO\IURPFROOLQHDULW\ LWLVSHUPLVVLEOHWRRPLWLWIURPWKHFDOFXODWLRQ ,WZDVVKRZQLQWKHVWDWLVWLFDOHYDOXDWLRQWKDWIROORZVWKDWWKHGHYLDWLRQZDVQRW VLJQLÀFDQWDQGVRUHWHQWLRQRI]HURGRVHUHVSRQVHVZDVMXVWLÀHG 6WHS8VLQJFRGHGGRVHVDQGIRUORZDQGKLJKGRVHOHYHOVUHVSHF WLYHO\ FDOFXODWH WKH EDVLF IXQFWLRQV RI GRVH E\ XVLQJ (TXDWLRQ DQG (TXDWLRQDV 6[ V 6[X
176
5HVSRQVH[2SWLFDO$EVRUEDQFHDWQP
Microbiological Assay for Pharmaceutical Analysis
'RVH1LDFLQ+JP( UHIHUHQFHVWDQGDUG
XQNQRZQ
]HURGRVH
5HVSRQVH[2SWLFDO$EVRUEDQFHDWQP
FIGURE 10.1 $JUDSKLFDOUHSUHVHQWDWLRQRIDOOPHDQUHVSRQVHVLQ([DPSOH5HVSRQVHV WR]HURGRVHGHYLDWHVOLJKWO\IURPEHLQJFROOLQHDUZLWKWKRVHWRGRVHOHYHOVDQG7KHVOLJKW FXUYDWXUH RI WKH UHVSRQVH OLQHV LV MXVW GHWHFWDEOH RQ FDUHIXO LQVSHFWLRQ +RZHYHU FRPSDUH ZLWK)LJXUH
'RVH1LDFLQ+JP( UHIHUHQFHVWDQGDUG
XQNQRZQ
]HURGRVH
FIGURE 10.2 $ JUDSKLFDO UHSUHVHQWDWLRQ RI WKH PHDQ UHVSRQVHV WR GRVH OHYHOV DQG RI UHIHUHQFHVWDQGDUGDQGXQNQRZQLQ([DPSOH7KHWZRUHVSRQVHOLQHVFRLQFLGHZLWKWKH \ D[LV ]HUR GRVH DW D YDOXH RI ZKHUHDV WKH REVHUYHG PHDQ UHVSRQVH WR WKH ]HURGRVH FRQWUROVZDV7KLVGRHVQRWDSSHDUWREHDVHULRXVGLVFUHSDQF\EXWVHUYHVWRLOOXVWUDWHWKH SULQFLSOHVRQZKLFKLWPLJKWEHDSSURSULDWHWRRPLWIURPWKHFDOFXODWLRQVWKHDFWXDOUHVSRQVHV WR]HURGRVH
177
Slope Ratio Assays — Some Designs and Their Evaluation
6WHS &DOFXODWH WKH YDOXHV RI WKH WKUHH IXQFWLRQV RI GRVH XVLQJ (TXDWLRQ WR(TXDWLRQ
6[ V [ V S < 6[X [X T < 6[ V [X U < =