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1 1 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesHelmut Sch tzBEBACH elmut Sch tzBEBACB iostatisticsSample Size Estimationfor BE StudiesBiostatisticsBiostatisticsSample Size EstimationSample Size Estimationfor BE Studiesfor BE StudiesBine ai venit !Bine ai venit !WikimediaWikimediaCommons Commons 2011 2011 KorinnaKorinna Creative Commons AttributionCreative Commons UnportedUnported2 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesTo bear in bear in a theory appears to youWhenever a theory appears to youas the only possible one, take this asas the only possible one, take this asa sign that you have neither undera sign that you have neither under--stood the theory nor the problemstood the theory nor the problemwhich it was intended to it was intended to R.

2 PopperKarl R. PopperEven though it s Even though it s appliedappliedsciencesciencewe re dealin with, it still is we re dealin with, it still is science!science!Leslie Z. BenetLeslie Z. Benet3 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesOverviewOverviewz Classical sample size estimation in BE Patient s & producer s risk Power in study planningzUncertainties Variability Test/Reference-ratio Sensitivity analysiszRecent developments Review of guidelines4 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE Studies and and zAll formal decisions are subjectedto two typesof error: Probability of Error Type I (aka Risk Type I) Probability of Error Type II (aka Risk Type II)Example from the justicesystem.

3 Error typeIICorrectPresumptionofinnocenceaccep ted(not guilty)CorrectError typeI Presumptionofinnocence not accepted(guilty)Defendant guiltyDefendant innocentVerdict5 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE Studies and and zOr in more statistical terms:zIn BE-testing the null hypothesis is bioinequivalence( 1 2)!Error typeIICorrect (H0)Failedtorejectnull hypothesisCorrect (Ha)Error typeI Null hypothesis rejectedNull hypothesis falseNull hypothesis trueDecisionProducer s riskCorrect(notBE)Failedtorejectnull hypothesisCorrect(BE)Patient s riskNull hypothesis rejectedNull hypothesis falseNull hypothesis trueDecision6 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE Studies.

4 ZPatient s Riskto be treated withan inequivalentformulation (H0falsely rejected) BA of thetest comparedto referencein a particularpatient is risky eitherbelow80% orabove125%. If we keep the riskof particular patientsat (5%), the riskof the entirepopulationof patients(<80% and>125%) is2 (10%) expressed as:90% CI = 1 2 = one-sided CI5% patients < one-sided CI5% patients > 95% one-sided CIs 90% two-sided CIpatient population [ , ] 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE and .. and zProducer s Riskto getno approval ofan equivalentformulation (H0falsely not rejected) Setin study planningto (20%), wherepower = 1 = 80% If power is set to 80 %,oneout of fivestudieswill fail just by chance!

5 = 1/5 A posteriori(post hoc) power does not make sense!Eithera study has demonstrated BE 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesPower CurvesPower CurvesPower to showBE with 12 36 subjects forCVintra20%n24 16 T/ 2 Cross-over T/ RPower20% 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesPower Power SizeSample SizezIt is not possible to calculate the requiredsample size 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%).

6 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesPower 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=1211 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesBackgroundBackgroundzReminder: Sample Size is not directlyobtained; onlypowerzSolution given byDB Owen (1965) asa differenceof two bivariate noncentralt-distributions Definite integrals cannot be solvedin closedform Exact methods relyon numerical methods(currently the most advanced isAS 243 of RV Lenth; implementedin R, FARTSSIE, EFG).

7 NQuery usesan earlier version(AS 184).12 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesBackgroundBackgroundzPower Bruteforce methods(also called resampling or Monte Carlo ) converge asymptoticallyto the truepower; needa good random number generator( , Mersenne Twister) and may betime-consuming Asymptotic methods use large sample approximations Approximations provide algorithms which should convergeto the desiredpower basedon thet-distribution13 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesSample Size Sample Size (Guidelines)(Guidelines)zRecommended minimum 12 WHO, EU, CAN, NZ, AUS, AR, MZ, ASEANS tates,RSA, Russia (2011 Draft) 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.

8 18 Russia(2008) 20 RSA (MR formulations) 24 Saudia Arabia (12 to 24if statistically justifiable) 24 Brazil Sufficient number Japan14 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesSample Size Sample Size (Limits)(Limits)zMaximum NZ:If the calculated numberof subjects appearsto behigher than is ethically justifiable, it may benecessaryto accepta statisticalpower which isless than desirable. Normally it is not practicaltouse more than about40 subjectsin a bioavailabilitystudy. All others: Not specified (judged by IEC/IRB or localAuthorities).ICH E9, Section applies: The number of subjects in a clinical trial should always be largeenough to provide a reliable answer to thequestions addressed.

9 15 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesPower & Power & Sample SizeSample SizezReminder Generally power is set to at least 80% ( , error type II: producers srisk to get no approval for a bioequivalentformulation; power = 1 ).1 out of 5 studies will fail just by chance! If you plan for power of less than 70%, probably you will face problems with the ethics committee (ICH E9). If you plan for power of more than 90% (especially withlow variability drugs), problems with regulators arepossible ( forced bioequivalence ). Add subjects ( alternates ) according to the expecteddrop-out rate especially for studies with more than twoperiods or multiple-dose 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesUS FDA, US FDA, Canada Canada TPDTPDzStatistical Approaches toEstablishing Bioequivalence(2001) Based on maximum difference of 5%.

10 Sample size based on 80 90% GL(2010)* Consider potency differences. Sample size basedon 80 90% power. Do notinterpolate linear betweenCVs (as stated in the GL)!* All points removed in current (2012) 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesEUEUzEMEA NfGon BA/BE (2001) Detailed information (data sources, significance level, expected deviation, desired power).zEMA GL on BE (2010) Batches must not differ more than 5%. The number of subjects to be included in the study should be based on an appropriate sample size 59 Workshop | Bucarest, 19 March 2013 Sample Size Estimation for BE StudiesSample Size Estimation for BE StudiesHierarchy Hierarchy of Designsof DesignszThe more sophisticated adesign is, the more information can be extracted.