Part II - BEBAC • Consultancy Services for Bioequivalence

6/6 | Statistical Design and Analysis IIIMaximum Sample SizeNew Zealand ‘If the calculated number of subjects appears to be higher thanis ethically justifiable, it may be necessary to accept astatistical power which is less than desirable. Normally it is notpractical to use more than about 40 subjects in abioavailability study.’All others Not specified in Guidelines (judged by IEC/IRB or localAuthorities); ICH E9, Section 3.5 applies: ‘The number ofsubjects in a clinical trial should always be large enough toprovide a reliable answer to the questions addressed.’informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 20103 • 68

6/6 | Statistical Design and Analysis IIIEUNfG on the Investigation of BA/BE (2001)The number of subjects required is determined by the error variance associated with the primarycharacteristic to be studied as estimated from a pilot experiment, previous studies, or published data, the significance level desired, the expected deviation (∆) from the reference productcompatible with BE and, the required power.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 20104 • 68

6/6 | Statistical Design and Analysis IIIEUNfG on the Investigation of BA/BE (2001)Problems/solutions… the error variance associated with theprimary characteristic to be studied … Since BE must be shown both for AUC and C max , and, if you plan your sample size only for the ‘primary characteristic’(e.g., AUC), in many cases you will fail for thesecondary parameter (e.g., C max ), which most likely showshigher variability – your study will be ‘underpowered’. Based on the assumption, that CV is identical for test andreference (what if only the reference formulation has highvariability, e.g., some formulations of PPIs?).informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 20105 • 68

6/6 | Statistical Design and Analysis IIIEUNfG on the Investigation of BA/BE (2001)Problems/solutions … as estimated from a pilot experiment, previous studies, or published data, The correct order should read:1. previous studies → 2. pilot study → 3. published data Only in the first case you ‘know’ all constraints resultingin variability Pilot studies are often too small to get reliable estimatesof variability Advisable only if you have data from a couple of studiesinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 20106 • 68

6/6 | Statistical Design and Analysis IIIEUNfG on the Investigation of BA/BE (2001)Problems/solutions … the significance level desired … Throughout the NfG the significance level(α, error type I: patient’s risk to be treated with abioinequivalent drug) is fixed to 5% (correspondingto a 90% confidence interval) You may desire a higher significance level, but sucha procedure is not considered acceptable In special cases (e.g., dose proportionality testing),a correction for multiplicity may be necessary In some legislations (e.g., Brazil’s ANVISA), α must betightened to 2.5% for NTIDs (95% confidence interval)informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 20107 • 68

6/6 | Statistical Design and Analysis IIIEUEMA BE Guideline (2010)The number of subjects to be included in the studyshould be based on anappropriateCookbook?sample size calculation.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201010 • 68

6/6 | Statistical Design and Analysis IIIHintsLiterature search for CV%Preferably other BE studies (the bigger, the better!)PK interaction studies (Cave: mainly in steadystate! Generally lower CV than after SD)Food studies (CV higher/lower than fasted!)If CV intra is not given (quite often), a little algebrahelps. All you need is the 90% geometricconfidence interval and the sample size. Point estimate (PE) from the CIPE = CL ⋅CLlohiinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201011 • 68

6/6 | Statistical Design and Analysis IIIAlgebra…Calculation of CV intra from CI Estimate the number of subjects / sequence (example2×2 cross-over) If total sample size (N) is an even number, assume (!)n 1 = n 2 = ½N If N is an odd number, assume (!)n 1 = ½N + ½, n 2 = ½N – ½ (not n 1 = n 2 = ½N!) Difference between one CL and the PE in log-scale; usethe CL which is given with more significant digits∆ = ln PE − ln CL or ∆ = ln CL − ln PECL lo CL hiinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201012 • 68

6/6 | Statistical Design and Analysis IIIAlgebra…Calculation of CV intra from CI Calculate the Mean Square Error (MSE)MSE⎛⎞⎜⎟⎜ ∆CL⎟= 2 ⎜ ⎟⎜ ⎛ 1 1 ⎞+ ⋅t⎟1−2 ⋅ α , n1 + n2−2⎜ ⎜n1 n⎟ ⎟⎝ ⎝ 2 ⎠ ⎠ CV intra from MSE as usual% 100 MSECV1intra= ⋅ e −2informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201013 • 68

6/6 | Statistical Design and Analysis IIIAlgebra…Calculation of CV intra from CI Example: 90% CI [0.91 – 1.15], N 21 (n 1 = 11, n 2 = 10)PE = 0.91⋅ 1.15 = 1.023∆ = ln1.15 − ln1.023 = 0.11702CLMSECV⎛⎞⎜⎟0.11702= 2⎜⎟ = 0.04798⎜ ⎛ 1 1 ⎞ ⎟⎜ ⎜ + ⎟ × 1.729 ⎟⎝ ⎝11 10 ⎠ ⎠0.04798intra% = 100 × e − 1 = 22.2%2informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201014 • 68

6/6 | Statistical Design and Analysis IIIAlgebra…Proof: CI from calculated values Example: 90% CI [0.91 – 1.15], N 21 (n 1 = 11, n 2 = 10)ln PE = ln CL ⋅ CL = ln 0.91× 1.15 = 0.02274SE∆lohi2 ⋅ MSE 2 × 0.04798= = = 0.067598N 21CI = e ∆ = eCICIln PE± t⋅ SE 0.02274± 1.729×0.0675980.02274− 1.729×0.067598lo= e= 0.910.02274+ 1.729×0.067598hi= e= 1.15informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201015 • 68

6/6 | Statistical Design and Analysis IIISensitivity to ImbalanceIf the study was more imbalanced that youassumed, the estimated CV is conservative Example: 90% CI [0.89 – 1.15], N 24 (n 1 = 16, n 2 = 8, butnot reported as such); CV 24.74% in the studyn 11213141516n 212111098CV%26.2926.2025.9125.4324.74informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201016 • 68

6/6 | Statistical Design and Analysis IIILiterature data12108frequency642total0101 520C V s253 02 00 m g100 m gstudiesinformalife sciencesDoxicycline (37 studies from Blume/Mutschler, Bioäquivalenz: Qualitätsbewertung wirkstoffgleicherFertigarzneimittel, GOVI-Verlag, Frankfurt am Main/Eschborn, 1989-1996)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201017 • 68

6/6 | Statistical Design and Analysis IIIPooling of CV%Intra-subject CV from different studies can bepooledDo not use the arithmetic mean (or the geometricmean either) of CVsIn the parametric model of log-transformed data,additivity of variances (not of CVs!) applyBefore pooling variances must be weightedacccording to the sample sizeCalculate the variance from CVσ = ln( CV + 1)2 2Wintrainformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201018 • 68

6/6 | Statistical Design and Analysis IIIPooling of CV%Intra-subject CV from different studiesCalculate the total variance weighted by degreesof freedom∑σ 2df WCalculate the pooled CV from total variance2CV e σ Wdf df=∑ ∑−1Optionally calculate an upper (1-α) % confidencelimit on the pooled CV (recommended α=0.20)CLCV∑ σ χ − ∑2 2Wdf1 α , df1= e −informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201019 • 68

6/6 | Statistical Design and Analysis IIIPooling of CV%Example 1: n 1 =n 2 ;CV Study1 < CV Study2studies N df (total) α 1-α total CV pooled CV mean2 24 20 0.2 0.8 1.2540 0.254 0.245χ² (1-α,df) 14.578 0.300 +17.8%CV intra n seq. df (mj) σ W σ² W σ² W × dfCV intra /pooled>CL upper0.200 12 2 10 0.198 0.0392 0.3922 78.6% no0.300 12 2 10 0.294 0.0862 0.8618 117.9% yesinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201020 • 68

6/6 | Statistical Design and Analysis IIIPooling of CV%Example 2: n 1 CL upper0.200 12 2 10 0.198 0.0392 0.3922 73.5% no0.300 24 2 22 0.294 0.0862 1.8959 110.2% noinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201021 • 68

6/6 | Statistical Design and Analysis IIIPooling of CV%Example 3: n 1 >n 2 ;CV Study1 < CV Study2studies N df (total) α 1-α total CV pooled CV mean2 36 32 0.2 0.8 1.7246 0.235 0.245χ² (1-α,df) 25.148 0.266 +13.2%CV intra n seq. df (mj) σ W σ² W σ² W × dfCV intra /pooled>CL upper0.200 24 2 22 0.198 0.0392 0.8629 85.0% no0.300 12 2 10 0.294 0.0862 0.8618 127.5% yesinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201022 • 68

6/6 | Statistical Design and Analysis IIIα- vs. β-Errorinformalife sciencesα-Error (aka error type I): patient’s risk to betreated with a bioinequivalent formulationReminder: BA in a particular patient can be eitherbelow 80% or above 125%.If we keep the risk of particular patients at 0.05 (5%),the risk of entire the population of patients (125%) is 2×α (10%)That’s where the 90% confidence intervalcomes from (CI = 1 – 2×α = 0.90)Although α is generally set to 0.05, sometimes

6/6 | Statistical Design and Analysis IIIα- vs. β-Errorinformalife sciencesβ-Error (aka error type II): producer’s risk to getno approval for a bioequivalent formulationGenerally set in study planning to ≤0.2, wherepower = 1 - β = ≥80%No guidelines about power (‘appropriate’), but70% only in exceptional cases>90% may raise questions from the Ethics Committee(suspection of ‘forced bioequivalence’)There is no a posteriori (aka post hoc) power!Either a study has shown BE or not.Phoenix’/WinNonlin’s output is statistical nonsense!Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201024 • 68

6/6 | Statistical Design and Analysis IIIPower vs. Sample Sizeinformalife sciencesIt is not possible to directly calculate theneeded sample size.Power is calculated instead, and the lowestsample size which fulfills the minimum targetpower is used.Example: α 0.05, target power 80%(β=0.2), T/R 0.95, CV intra 20% →minimum sample size 19 (power 81%),rounded up to the next even number ina 2×2 study (power 83%).Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 2010n power16 73.54%17 76.51%18 79.12%19 81.43%20 83.47%25 • 68

6/6 | Statistical Design and Analysis IIIToolsSpecialized Software (nQuery Advisor, PASS,FARTSSIE, StudySize, …)General purpose (SAS, R, S+, StaTable, …)Sample Size Tables (Phillips, Diletti, Hauschke,Chow, Julious, …)Approximations (Diletti, Chow, Julious, …)informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201026 • 68

6/6 | Statistical Design and Analysis IIIBackgroundReminder: Sample Size is not directlyobtained; only powerSolution given by DB Owen (1965) as adifference of two bivariate noncentral t-distributionsDefinite integrals cannot be solved in closed form‘Exact’ methods rely on numerical methods (currentlythe most advanced is AS 243 of RV Lenth;implemented in R, FARTSSIE, EFG). nQuery uses anearlier version (AS 184).informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201027 • 68

6/6 | Statistical Design and Analysis IIIBackgroundPower calculations…‘Brute force’ methods (also called ‘resampling’ or‘Monte Carlo’) converge asymptotically to the truepower; need a good random number generator (e.g.,Mersenne Twister) and may be time-consuming‘Asymptotic’ methods use large sampleapproximationsApproximations provide algorithms which shouldconverge to the desired power based on thet-distributioninformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201028 • 68

6/6 | Statistical Design and Analysis IIIComparisoninformalife sciencesCV%original values Method Algorithm 5. 7.5 10. 12. 12.5 14. 15. 16. 17.5 18. 20. 22.Patterson & Jones (2006) exact AS 243 4 5 7 8 9 11 12 13 15 16 19 22Diletti et al. (1991) exact ? 4 5 7 9 12 15 19nQuery Advisor 7 (2007) exact AS 184 4 6 8 8 10 12 12 14 16 16 20 22FARTSSIE 1.6 (2008) exact AS 243 4 5 7 8 9 11 12 13 15 16 19 22EFG 1.01 (2009)exact AS 243 4 5 7 8 9 11 12 13 15 16 19 22brute force ElMaestro 4 5 7 8 9 11 12 13 15 16 19 22StudySize 2.0.1 (2006) asympt. ? 5 7 8 9 11 12 13 15 16 19 22Hauschke et al. (1992) approx. 8 8 10 12 12 14 16 16 20 22Chow & Wang (2001) approx. 6 6 8 8 10 12 12 14 16 18 22Kieser & Hauschke (1999) approx. 2 6 8 10 12 14 16 20 24CV%original values Method Algorithm 22.5 24. 25. 26. 27.5 28. 30. 32. 34. 36. 38. 40.Patterson & Jones (2006) exact AS 243 23 26 28 30 33 34 39 44 49 54 60 66Diletti et al. (1991) exact ? 23 28 33 39nQuery Advisor 7 (2007) exact AS 184 24 26 28 30 34 34 40 44 50 54 60 66FARTSSIE 1.6 (2008) exact AS 243 23 26 28 30 33 34 39 44 49 54 60 66EFG 1.01 (2009)exact AS 243 23 26 28 30 33 34 39 44 49 54 60 66brute force ElMaestro 23 26 28 30 33 34 39 44 49 54 60 66StudySize 2.0.1 (2006) asympt. ? 23 26 28 30 33 34 39 44 49 54 60 66Hauschke et al. (1992) approx. 24 26 28 30 34 36 40 46 50 56 64 70Chow & Wang (2001) approx. 24 26 28 30 34 34 38 44 50 56 62 68Kieser & Hauschke (1999) approx. 28 30 32 38 42 48 54 60 66 74Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201029 • 68

6/6 | Statistical Design and Analysis IIIApproximationsinformalife sciencesHauschke D, Steinijans VW, Diletti E, and M BurkeSample Size Determination for BioequivalenceAssessment Using a Multiplicative ModelJ Pharmacokin Biopharm 20/5, 557-561 561 (1992)Patient’s risk α 0.05, Power 80% (Producer’s risk β0.2), AR [0.80 – 1.25], CV 0.2 (20%), T/R 0.951. ∆ = ln(0.8)-ln(T/R) ln(T/R) = -0.17192. Start with e.g. n=8/sequence1. df = n 2 – 1 = 8 × 2 - 1 = 142. t α,df= 1.76133. t β,df= 0.86814. new n = [(t α,df+ t β,df)²(CV/∆)])]² =(1.7613+0.8681)² × (-0.2/(0.2/0.1719)0.1719)² = 9.35803. Continue with n=9.3580/sequence (N=18.716 → 19)1. df = 16.716; roundup to the next integer 172. t α,df= 1.73963. t β,df= 0.86334. new n = [(t α,df+ t β,df)²(CV/∆)])]² =(1.7396+0.8633)² × (-0.2/(0.2/0.1719)0.1719)² = 9.17114. Continue with n=9.1711/sequence (N=18.3422 → 19)1. df = 17.342; roundup to the next integer 182. t α,df= 1.73413. t β,df= 0.86204. new n = [(t α,df+ t β,df)²(CV/∆)])]² =(1.7341+0.8620)² × (-0.2/(0.2/0.1719)0.1719)² = 9.12335. Convergence reached (N=18.2466 → 19):Use 10 subjects/sequence (20(total)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 2010S-C C Chow and H WangOn Sample Size Calculation in Bioequivalence TrialsJ Pharmacokin Pharmacodyn 28/2, 155-169 169 (2001)Patient’s risk α 0.05, Power 80% (Producer’s risk β0.2), AR [0.80 – 1.25], CV 0.2 (20%), T/R 0.951. ∆ = ln(T/R) – ln(1.25) = 0.17192. Start with e.g. n=8/sequence1. df = roundup(2n-2)2α2)2-2 2 = (2×8-2)×22)×2-2 2 = 262. df β= roundup(4n-2) = 4×8-2 = 303. t α,df= 1.70564. t β/2/2,df= 0.85385. new n = β²²[(tα,df+ t β/2/2,df)²/∆² =0.2² × (1.7056+0.8538)² / 0.1719² = 8.87233. Continue with n=8.8723/sequence (N=17.7446 → 18)1. df = roundup(2n-2)2α2)2-2=(2×8.87232=(2×8.8723-2)×22)×2-2 2 = 302. df β= roundup(4n-2) = 4×8.8723-2 2 = 343. t α,df= 1.69734. t β/2/2,df= 0.85235. new n = β²²[(tα,df+ t β/2/2,df)²/∆² =0.2² × (1.6973+0.8538)² / 0.1719² = 8.80454. Convergence reached (N=17.6090 → 18):Use 9 subjects/sequence (18(total)sample size 18 19 20power % 79.124 81.428 83.46830 • 68

6/6 | Statistical Design and Analysis IIIApproximations obsoleteinformalife sciencesExact sample size tables still useful inchecking the plausibility of software’s resultsApproximations obsolete,since exact methodavailable (FARTSSIE17)or …http://individual.utoronto.ca/ddubins/FARTSSIE17.xlsBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 2010alpha

6/6 | Statistical Design and Analysis IIIPower CurvesPower to show2×2 Cross-overBE with 12 – 36subjects forCV intra = 20%n 24 → 16:power 0.896→ 0.735Power10.90.80.70.60.50.40.30.23624161220% CVinformalife sciencesµ T /µ R 1.05 → 1.10:power 0.903→ 0.700Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 20100.100.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25µT/µR32 • 68

6/6 | Statistical Design and Analysis IIIEU GL on BE (2010)HVDs/HVDPsThe regulatory switching condition θ s is derivedfrom the regulatory standardized variation σ 0 .For CV WR = 30% we get2σ0= ln(0.3 + 1) = 0.2936andθ sln(1.25)= = 0.7601σ0informalife sciencesTothfalusi L, Endrenyi L and A Garcia ArietaEvaluation of Bioequivalence for Highly Variable Drugs with Scaled Average BioequivalenceClin Pharmacokinet 48/11, 725-743 (2009)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201033 • 68

6/6 | Statistical Design and Analysis IIIEU GL on BE (2010)HVDs/HVDPsAverage Bioequivalence (ABE) with ExpandingLimits (ABEL) If you have σ WR(the intra-subject standard deviationof the reference formulation) go to the next step;if not, calculate it from CV WR: Calculate the scaled acceptance range based on theregulatory constant k (0.7601):[ ]U L e σ2ln( CVWR1)σ = +WRk WR, =± ⋅informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201034 • 68

6/6 | Statistical Design and Analysis IIIEU GL on BE (2010)HVDs/HVDPsScaling allowed for C max only (not AUC!)based on CV WR >30% in the study.Limited to a maximum of CV WR 50% (i.e., higherCVs are treated as if CV = 50%).PE restricted with 80% – 125% in any case.No commercial software for sample size estimationcan handle the PE restriction.Expect a solution from thecommunity soon…informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201035 • 68

6/6 | Statistical Design and Analysis IIIHVDs/HVDPsEU GL on BE (2010)CV% L% U%30 80.00 125.0032 78.87 126.7934 77.77 128.5836 76.69 130.3938 75.64 132.2040 74.61 134.0242 73.61 135.8544 72.63 137.6846 71.68 139.5248 70.74 141.3650 69.83 143.20Acceptance limits [% Ref.]15014013012011010090807060EU SABE20 30 40 50 60informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 2010µT/µR36 • 68

6/6 | Statistical Design and Analysis IIIHVDs/HVDPsinformalife sciencesTotfalushi et al. (2009), Fig. 3Simulated (n=10000) three-period replicate design studies (TRT-RTR) in 36 subjects;GMR restriction 0.80–1.25. (a) CV=35%, (b) CV=45%, (c) CV=55%.ABE: Conventional Average Bioequivalence, SABE: Scaled Average Bioequivalence,0.76: EU criterion, 0.89: FDA criterion.Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201037 • 68

6/6 | Statistical Design and Analysis IIIHVDs/HVDPsinformalife sciencesReplicate designs4-period replicate designs:sample size = ½ of 2×2 study’s sample size3-period replicate designs:sample size = ¾ of 2×2 study’s sample sizeReminder: number of treatments (and biosamples)is identical to the concentional 2×2 cross-over.Allow for a safety margin – expect a higher numberof drop-outs due to the additional period(s).Consider increased blood loss (ethics!)Eventually bioanalytics has to be improved.Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201038 • 68

6/6 | Statistical Design and Analysis IIIExample ABELinformalife sciencesRTR–TRT Replicate Design, n=18Subj Seq Per Trt Cmax Subj Seq Per Trt Cmax Subj Seq Per Trt Cmax1 1 1 R 209.91 7 1 1 R 58.49 13 2 1 T 92.761 1 2 T 111.05 7 1 2 T 62.80 13 2 2 R 59.541 1 3 R 116.36 7 1 3 R 123.23 13 2 3 T 56.842 1 1 R 101.16 8 1 1 R 105.34 14 2 1 T 159.202 1 2 T 100.31 8 1 2 T 103.32 14 2 2 R 155.502 1 3 R 31.71 8 1 3 R 43.67 14 2 3 T 165.313 1 1 R 14.83 9 1 1 R 59.73 15 2 1 T 162.413 1 2 T 57.10 9 1 2 T 169.03 15 2 2 R 47.313 1 3 R 21.47 9 1 3 R 48.26 15 2 3 T 88.234 1 1 R 118.71 10 1 1 R 38.34 16 2 1 T 19.444 1 2 T 37.34 10 1 2 T 31.19 16 2 2 R 42.804 1 3 R 52.29 10 1 3 R 19.43 16 2 3 T 18.935 1 1 R 36.11 11 2 1 T 51.95 17 2 1 T 90.585 1 2 T 83.95 11 2 2 R 195.71 17 2 2 R 42.395 1 3 R 17.76 11 2 3 T 65.87 17 2 3 T 54.576 1 1 R 146.44 12 2 1 T 18.72 18 2 1 T 42.966 1 2 T 40.45 12 2 2 R 20.63 18 2 2 R 171.866 1 3 R 38.34 12 2 3 T 7.45 18 2 3 T 59.15Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201039 • 68

6/6 | Statistical Design and Analysis IIIExample ABEL σ WR(WinNonlin)informalife sciencesCalculate the scaled acceptance range based on theregulatory constant k (0.7601) and the limiting CV:[ ]U L e σk WR, =± ⋅σ WR 0.4628CV WR 0.4887L 0.7154U 1.3977CV2exp(WR1)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 2010WR= σ −30%

6/6 | Statistical Design and Analysis IIIExample ABELinformalife sciencesABEPE: 99.8990% CI:72.04, 138.52failed ABEfailed 75 – 13330

6/6 | Statistical Design and Analysis IIISensitivity AnalysisICH E9Section 3.5 Sample Size, paragraph 3 The method by which the sample size is calculatedshould be given in the protocol […]. The basis ofthese estimates should also be given. It is important to investigate the sensitivity of thesample size estimate to a variety of deviations fromthese assumptions and this may be facilitated byproviding a range of sample sizes appropriate for areasonable range of deviations from assumptions. In confirmatory trials, assumptions should normallybe based on published data or on the results ofearlier trials.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201042 • 68

6/6 | Statistical Design and Analysis IIISensitivity AnalysisExamplenQuery Advisor:σ = ln( CV + 1); ln(0.2 + 1) = 0.198042w2 2intrainformalife sciences20% CV:n=2625% CV:power 90% → 78%20% CV, 4 drop outs:power 90% → 87%25% CV, 4 drop outs:power 90% → 69%Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201020% CV, PE 90%:power 90% → 69%43 • 68

6/6 | Statistical Design and Analysis IIISensitivity Analysisinformalife sciencesMust be done before the study (a priori)A posteriori power:High values do not support the claim of alreadydemonstrated bioequivalenceLow values do not invalidate a bioequivalentformulationFurther reader:JM Hoenig and DM HeiseyThe Abuse of Power: The Pervasive Fallacy of Power Calculations for Data AnalysisThe American Statistician 55/1, 19–24 (2001)http://www.math.uiowa.edu/~rlenth/Power/2badHabits.pdfRV LenthTwo Sample-Size Practices that I don’t recommendJoint Statistical Meetings, Indianapolis (2000)http://www.math.uiowa.edu/~rlenth/Power/2badHabits.pdfBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201044 • 68

6/6 | Statistical Design and Analysis IIISample Size: Pilot StudiesPilot StudiesSmall pilot studies (sample size

6/6 | Statistical Design and Analysis IIIJustificationGood Scientific Practice!Every influental factor can be tested in a pilot study.Sampling schedule: matching C max, lag-time (firstpoint C maxproblem), reliable estimate of λ zBioanalytical method: LLOQ, ULOQ, linear range,metabolite interferences, ICSRFood, posture,…Variabilty of PK metricsLocation of PEinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201046 • 68

6/6 | Statistical Design and Analysis IIIJustificationBest description by FDA (2003)The study can be used to validate analytical methodology,assess variability, optimize sample collectiontime intervals, and provide other information.For example, for conventional immediate-releaseproducts, careful timing of initial samples may avoida subsequent finding in a full-scale study that thefirst sample collection occurs after the plasma concentrationpeak. For modified-release products, apilot study can help determine the samplingschedule to assess lag time and dose dumping.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201047 • 68

6/6 | Statistical Design and Analysis IIIApplicationMost common to assess CV and PE needed insample size estimation for a pivotal BE studyTo select between candidate test formulationscompared to one referenceTo find a suitable referenceIf design issues (clinical performance, bioanalytics)are already known, a two-stage sequential designwould be a better alternative!informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201048 • 68

6/6 | Statistical Design and Analysis IIIDrawbacksCV-estimates have a high degree ofuncertainty (in the pivotal study it is more likelythat you will be able to reproduce the PE, thanthe CV)The smaller the size of the pilot, the more uncertainthe outcome.The more formulations you have tested, lesserdegrees of freedom will result in worse estimates.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201049 • 68

6/6 | Statistical Design and Analysis IIISolutionsDo not use the pilot study’s CV, but calculatean upper confidence interval!Gould recommends a 75% CI (i.e., a producer’s riskof 25%).Unless you are under time pressure, a two-stagedesign will help in dealing with the uncertainestimate from the pilot.informalife sciencesLA GouldGroup Sequential Extension of a Standard Bioequivalence Testing ProcedureJ Pharmacokin Biopharm 23/1, 57-86 (1995)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201050 • 68

6/6 | Statistical Design and Analysis IIISample Size: Pilot StudiesPilot Studies (cont’d)Moderate sized pilot studies (sample size ~12–24)lead to more consistent results(both CV intra and PE). If you stated a procedure in your protocol, even BE may beclaimed in the pilot study, and no further study will benecessary. If you have some previous hints of high intra-subjectvariability (>30%), a pilot study size of at least 24 subjectsis reasonable.A Sequential Design may also avoid an unnecessary largepivotal study.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201051 • 68

6/6 | Statistical Design and Analysis IIITwo-Stage DesignEMA GL on BE (2010)Section 4.1.8Initial group of subjects treated and data analysed.If BE not been demonstrated an additional groupcan be recruited and the results from both groupscombined in a final analysis.Appropriate steps to preserve the overall type I error(patient’s risk).Stopping criteria should be defined a priori.‘Internal PilotStudy Design’First stage data should be treated as an interimanalysis.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201052 • 68

6/6 | Statistical Design and Analysis IIITwo-Stage DesignEMA GL on BE (2010)Section 4.1.8 (cont’d)Both analyses conducted at adjusted significancelevels (with the confidence intervals accordinglyusing an adjusted coverage probability which willbe higher than 90%). […] 94.12% confidenceintervals for both the analysis of stage 1 and thecombined data from stage 1 and stage 2 would beacceptable, but there are many acceptable alternativesand the choice of how much alpha to spendat the interim analysis is at the company’s discretion.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201053 • 68

6/6 | Statistical Design and Analysis IIITwo-Stage DesignEMA GL on BE (2010)Section 4.1.8 (cont’d)Plan to use a two-stage approach must be prespecifiedin the protocol along with the adjustedsignificance levels to be used for each of theanalyses.When analysing the combined data from the twostages, a term for stage should be included in theANOVA model.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201054 • 68

6/6 | Statistical Design and Analysis IIISequential DesignsHave a long and accepted tradition in laterphases of clinical research (mainly Phase III)Based on work by Armitage et al. (1969),McPherson (1974), Pocock (1977), O’Brien andFleming (1979) and othersFirst proposal by LA Gould (1995) in the area ofBE did not get regulatory acceptance in Europe, butStated in the current Canadian Draft Guidance(November 2009).informalife sciencesLA GouldGroup Sequential Extension of a Standard Bioequivalence Testing ProcedureJ Pharmacokin Biopharm 23/1, 57-86 (1995)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201055 • 68

6/6 | Statistical Design and Analysis IIISequential Designsinformalife sciencesCurrent work by D Potvin et al. (2007) seemspromisingWork backed by support form FDA, USP,Health Canada,…Likely to be implemented by US-FDAShould be acceptable as a Two-Stage Design inthe EUTwo of BEBAC’s protocols approved by BfArMand competent EC in May and December 2009Potvin D, Diliberti CE, Hauck WW, Parr AF, Schuirmann DJ, and RA SmithSequential design approaches for bioequivalence studies with crossover designsPharmaceut Statist (2007), DOI: 10.1002/pst.294http://www3.interscience.wiley.com/cgi-bin/abstract/115805765/ABSTRACTBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201056 • 68

6/6 | Statistical Design and Analysis IIIPotvin et al. (2007)Evaluate power at Stage 1Method ‘C’using α-level of 0.050If power ≥80%, evaluate BE atStage 1 (α = 0.050) and stopIF BE met,stopIf power

6/6 | Statistical Design and Analysis IIIPotvin et al. (2007)informalife sciencesTechnical AspectsOnly one Interim Analysis (after Stage 1)If possible, use software (too wide step sizes in Diletti’stables)Should be called ‘Power Analysis’ not ‘BioequivalenceAssessment’ in the protocolNo a-posteriori Power – only a validated method in thedecision treeNo adjustment for the PE observed in Stage 1No stop criterion for Stage 2! Must be clearly stated inthe protocol (may be unfamiliar to the IEC, becausestandard in Phase III)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201058 • 68

6/6 | Statistical Design and Analysis IIIPotvin et al. (2007)Technical Aspects (cont’d)Adjusted α of 0.0294 based on Pocock 1977In the pooled analysis (data from Stages 1 + 2),α 0.0294 is used (i.e., the 94.12% ConfidenceInterval is calculated)informalife sciencesOverall patient’s risk is ≤0.05Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201059 • 68

6/6 | Statistical Design and Analysis IIIPotvin et al. (2007)informalife sciencesTechnical Aspects (cont’d)If the study is stopped after Stage 1,the (conventional) statistical model is:fixed: treatment+period+sequencerandom: subject(sequence)If the study continues to Stage 2,the model for the combined analysis is:fixed: treatment+period+sequence+stage×treatmentrandom: subject(sequence×stage)No poolability criterion; combining is alwaysallowed – even for significant differencesbetween Stages.Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201060 • 68

6/6 | Statistical Design and Analysis IIIPotvin et al. (2007)informalife sciencesAdvantageCurrently the only validated procedure for BE!DrawbacksNot validated for a correction of effect size (PE)observed in Stage 1 (must continue with theone used in sample size planing).No stop criterion (EMA GL on BE?)Not validated for any other design than theconventional 2×2 crossover (no higher ordercrossovers, no replicate designs).Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201061 • 68

6/6 | Statistical Design and Analysis IIINuisance: group effectMore than one group of subjects‘If a crossover study is carried out in two or moregroups of subjects (e.g., if for logistical reasons onlya limited number of subjects can be studied at onetime), the statistical model should be modified toreflect the multigroup nature of the study. Inparticular, the model should reflect the fact that theperiods for the first group are different from theperiods for the second group.’informalife sciencesFDA, Center for Drug Evaluation and Research (CDER)Guidance for Industry: Statistical Approaches to Establishing Bioequivalence (2001)Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201062 • 68

6/6 | Statistical Design and Analysis IIINuisance: group effectMore than one group of subjectsCases where ‘… the study is carried out in two ormore groups and those groups are studied at differentclinical sites, or at the same site but greatlyseparated in time (months apart, for example) […]should be discussed with the appropriate CDERreview division.’EMEA BA/BE (2001), BE GL (2010)The study should be designed in such a way that theformulation effect can be distinguished from othereffects.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201063 • 68

6/6 | Statistical Design and Analysis IIINuisance: group effectIncreasing number of referrals (deficiencyletters) fromCanadaGulf States (Saudia Arabia, Emirates, Oman)Extended Statistical model (fixed effects inANOVA)GroupGroup × Treatment InteractionIf both terms are not significant (p>0.05), pooling ofgroups is justified.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201064 • 68

6/6 | Statistical Design and Analysis IIINuisance: group effectRecommendationsIf possible, multiple groups should be avoided.Keep the time interval between groups as short aspossible.Do not split the study into equally sized groups. Perform at least one group in the maximum capacityof the clinical site(e.g., 24+8 instead of 16+16 for a total of 32). If a significant group and/or group × treatmentinteraction is found (preventing a pooled analysis),it may still be possible to demonstrate BE in thelargest group only.informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201065 • 68

6/6 | Statistical Design and Analysis IIIAre we making progress?About 3 000 – 10 000 BE studies / year are conductedworldwide; only ∼ 1 – 5% of them are published.Although a standard for publishing data of BE studieswas already suggested in 1992, 1) a review in 2002 found only 17 complete data sets on AUCand 12 on C max . 2) Since no ‘real world’ data are available, proposed methods(e.g., reference-scaled ABE) rely entirely on simulations! Studies seen by regulators are ‘selection biased’.1) Sauter R, Steinijans VW, Diletti E, Böhm E and H-U SchulzInt J Clin Pharm Ther Toxicol 30/Suppl.1, S7-S30 (1992)2) Nakai K, Fujita M and M TomitaInt J Clin Pharmacol Ther 40, 431-438 (2002)informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201066 • 68

6/6 | Statistical Design and Analysis IIIBell curve (and beyond?)informalife sciences Abraham de Moivre (1667-1754),Pierre-Simon Laplace (1749-1827)Central limit theorem 1733, 1812 Carl F. Gauß (1777-1855)Normal distribution 1795 William S. Gosset, aka Student(1876-1937)t-distribution 1908 Frank Wilcoxon (1892-1965)Nonparametric tests 1945Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201067 • 68

6/6 | Statistical Design and Analysis IIICongratulations!Statistical Designand Analysis IIOpen Questions?(References in your Handouts)Helmut SchützBEBACConsultancy Services forBioequivalence and Bioavailability Studies1070 Vienna, Austriahelmut.schuetz@bebac.atinformalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201068 • 68

6/6 | Statistical Design and Analysis IIIQuote from RV Lenthinformalife sciencesThere is simple intuition behindresults like these: If my car madeit to the top of the hill, then it ispowerful enough to climb that hill;if it didn’t, then it obviously isn’tpowerful enough. Retrospectivepower is an obvious answer to arather uninteresting question. Amore meaningful question is toask whether the car is powerfulenough to climb a particular hillnever climbed before; or whethera different car can climb that newhill. Such questions areprospective, not retrospective.Bioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 2010The fact that retrospective poweradds no new information isharmless in its own right.However, in typical practice, it isused to exaggerate the validity ofa significant result (“not only is itsignificant, but the test is reallypowerful!”), or to make excusesfor a nonsignificant one (“well, Pis .38, but that’s only because thetest isn’t very powerful”). Thelatter case is like blaming themessenger.RV LenthTwo Sample-Size Practices that I don't recommendhttp://www.math.uiowa.edu/~rlenth/Power/2badHabits.pdf69 • 68

6/6 | Statistical Design and Analysis IIIReferencesCollection of links to global documentshttp://bebac.at/Guidelines.htmICH E3: Structure and Content of Clinical StudyReports (1995) E6: Good Clinical Practice (1996) E8: General Considerations for Clinical Trials(1997) E9: Statistical Principles for Clinical Trials (1998)WHO Guidelines for GCP for trials on pharmaceuticalproducts (WHO Technical Report Series No.850, Annex 3, 1995) Handbook for GCP (2005) WHO Expert Committee on Specifications forPharmaceutical Preparations, Fortieth Report(WHO Technical Report Series No. 937, Annex9: Additional guidance for organizations performingin vivo bioequivalence studies. 2006)US FDA 21CFR320: BA and BE Requirements (Revision 2008) Center for Drug Evaluation and Research (CDER)CDER’s Manual of Policies and Procedures Review of BE Study Protocols (2006) Review of BE Studies with Clinical Endpoints inANDAs (2006) Center for Drug Evaluation and Research (CDER) Statistical Approaches Establishing Bioequivalence(2001) Bioavailability and Bioequivalence Studies for OrallyAdministered Drug Products – General Considerations(Rev.1 2003) ANDA Checklist for Completeness and Acceptability(2006) Bioequivalence Recommendations for Specific Products(2007) ANDA Checklist for Completeness and Accept-ability(2006) Submission of Summary BE Data for ANDAs (2009)informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201070 • 68

6/6 | Statistical Design and Analysis IIIReferencesEudraLex – The Rules Governing MedicinalProducts in the European Unionhttp://ec.europa.eu/enterprise/pharmaceuticals/eudralex/Directive 2001/20/EC: Implementation of GCP in theConduct of Clinical Trials on Medicinal Products forHuman Use (2001)EMEA GCP Inspector’s GroupProcedure for Conducting GCP Inspections requested by theEMEA Annex I: Investigator Site (2007) Annex IV: Sponsor Site and/or Contract Research Organisations(CRO) (2007) Annex V: Bioanalytical part, Pharmacokinetic and Statisticalanalyses of Bioequivalence Trials (2008)EMEA/CPMP/CHMP NfG on the Investigation of BA/BE (2001) Points to Consider on Multiplicity Issues in Clinical Trials(2002) BA/BE for HVDs/HVDPs: Concept Paper (2006); removedform EMEA’s website in Oct 2007. Available athttp://bebac.at/downloads/14723106en.pdf Questions & Answers on the BA and BE Guideline (2006) Draft Guideline on the Investigation of BE (2008) Questions & Answers : Positions on specific questionsaddressed to the EWP therapeutic subgroup on Pharmacokinetics(2009) Guideline on the Investigation of BE (2010)informalife sciencesBioequivalence and Bioavailability, Pre-Conference Workshop | Ljubljana, 17 May 201071 • 68