Sample Size Calculations - bebac.at

1 1 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeHelmut Sch tzBEBACH elmut Sch tzBEBACW ikimediaWikimediaCommons Commons 2007 2007 Sujit KumarSujit Kumar Creative Commons AttributionCreative Commons UnportedUnportedSample Size CalculationsSample Sample Size CalculationsSize CalculationsNamaste!Namaste!2 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeOverviewOverview Classical Sample size estimation in BE Patient s & producer s risk Power in study planning Uncertainties Variability Test/Reference-ratio Sensitivity analysis Recent developments Review of guidelines3 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC)

2 , Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma Edge --ErrorError All formal decisions are subjected to two typesof error: Error Type I ( -Error, Risk Type I) Error Type II ( -Error, Risk Type II)Example from the justice system:Error type IICorrectPresumption of innocence accepted(not guilty)CorrectError type I Presumption of innocence not accepted(guilty)Defendant guiltyDefendant innocentVerdict4 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma Edge --ErrorError Or in more statistical terms: In BE-testing the null hypothesis is bioinequivalence( 1 2)!

3 Error type IICorrect (H0)Failed to reject null hypothesisCorrect (Ha)Error type I Null hypothesis rejectedNull hypothesis falseNull hypothesis trueDecisionProducer s riskCorrect (not BE)Failed to reject null hypothesisCorrect (BE)Patients riskNull hypothesis rejectedNull hypothesis falseNull hypothesis trueDecision5 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma Edge95% one-sided CIparticular one-sided CIparticular two-sided CI= two 95% one-sidedpopulation of --ErrorError -Error: Patient s Riskto be treated with a bioinequivalentformulation (H0falsely rejected) BA of the test compared to reference in a particularpatient is risky eitherbelow 80% orabove 125%.

4 If we keep the risk of particular patientsat (5%), the risk of the entirepopulation of patients(<80% and>125%) is 2 (10%) expressed as:90% CI = 1 2 = 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma Edge --ErrorError -Error: Producer s Riskto get no approval fora bioequivalentformulation (H0falsely notrejected) Setin study planning to , wherepower = 1 = 80% If power is set to 80 %One out of five studies will fail just by chance!

5 A posteriori(post hoc) power does not make sense!Eithera study has demonstrated BE ornot. BEBE 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgePower CurvesPower CurvesPower to show BE with 12 36 subjects forCVintra20%n24 16:power T/ :power 2 Cross-over T/ RPower20% 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgePower Power SizeSample Size It is not possible to calculate the requiredsample size directly.

6 Power is calculated instead; the smallestsample size which fulfills the minimum target power is used. Example: , target power 80%( ), T/R , CVintra20% minimum Sample size 19 (power 81%),rounded upto the next even number ina 2 2 study (power 83%).n 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgePower Power SizeSample Size2 2 cross-over, T/R , AR 80 125%, target power 80%08162432405%10%15%20%25%30%CVintrasam ple size80%85%90%95%100%powersample sizepowerpower for n=1210 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC)

7 , Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeToolsTools Sample Size Tables (Phillips, Diletti, Hauschke, Chow, Julious, ..) Approximations (Diletti, Chow, Julious, ..) General purpose (SAS, S+, R, StaTable, ..) Specialized Software (nQuery Advisor, PASS, FARTSSIE, StudySize, ..) Exact method (Owen implemented in R-package PowerTOST)** Thanks to Detlew Labes!11 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeBackgroundBackground Reminder: Sample Size is not directlyobtained; only power Solution given by DB Owen (1965) as a difference of two bivariate noncentralt-distributions Definite integrals cannot be solved in closed form Exact methods rely on numerical methods (currently the most advanced is AS 243 of RV Lenth; implemented in R, FARTSSIE, EFG).

8 NQuery uses an earlier version (AS 184).12 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeBackgroundBackground Power Brute force methods (also called resampling or Monte Carlo ) converge asymptotically to the truepower; need a good random number generator ( , Mersenne Twister) and may be time-consuming Asymptotic methods use large Sample approximations Approximations provide algorithms which should converge to the desired power based on thet-distribution13 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeComparisonComparisonCV%original valuesMethodAlgorithm5 (2011)

9 ExactOwen s Q46881012121416162022 Patterson & Jones (2006)noncentr. tAS 2434578911121315161922 Diletti et al. (1991)noncentr. tOwen s Q457NA9NA12NA15NA19 NAnQuery Advisor 7 (2007)noncentr. tAS 18446881012121416162022 FARTSSIE (2008)noncentr. tAS 2434578911121315161922noncentr. tAS 2434578911121315161922brute force ElMaestro4578911121315161922 StudySize (2006)central t?NA578911121315161922 Hauschke et al. (1992)approx. tNA NA881012121416162022 Chow & Wang (2001)approx. tNA668810121214161822 Kieser & Hauschke (1999)approx. t2NA68NA101214NA162024 EFG (2009)CV%original valuesMethodAlgorithm (2011)exactOwen s Q242628303434404450546066 Patterson & Jones (2006)noncentr. tAS 243232628303334394449546066 Diletti et al. (1991)noncentr. tOwen s Q23NA28NA33NA39NA NA NA NA NAnQuery Advisor 7 (2007)noncentr.

10 TAS 184242628303434404450546066 FARTSSIE (2008)noncentr. tAS 243232628303334394449546066noncentr. tAS 243232628303334394449546066brute force ElMaestro232628303334394449546066 StudySize (2006)central t?232628303334394449546066 Hauschke et al. (1992)approx. t242628303436404650566470 Chow & Wang (2001)approx. t242628303434384450566268 Kieser & Hauschke (1999)approx. tNA283032NA38424854606674 EFG (2009)14 57 Sample Sample Size CalculationsSize CalculationsIn vitro in vivoIn vitro in vivoCorrelation (IVIVC), Biowaivers & Statistical Aspects of BioequCorrelation (IVIVC), Biowaivers & Statistical Aspects of Bioequivalenceivalencein Drug product Developmentin Drug product Development| | MumbaiMumbai, , 27 27 January January 20122012 Pharma EdgeSample Size (Limits) Sample Size (Limits) Minimum 12: WHO, EU, CAN, NZ, AUS, AR, MZ, ASEAN States,RSA 12: USA A pilot study that documents BE can beappropriate, provided its design and execution aresuitable and a sufficient number of subjects ( ,12) have completed the study.