A Hypothesis Test Perspective on Content Uniformity Test. Lanju Zhang Data and Statistical Sciences AbbVie Inc

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1 A Hypothesis Test Perspective on Content Uniformity Test Lanju Zhang Data and Statistical Sciences AbbVie Inc

2 Disclosure Lanju Zhang is an employee of Abbvie Inc. The presentation was sponsored by AbbVie. AbbVie contributed to the design, research, and interpretation of data, writing, reviewing, and approving the publication. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 2

3 Outline Introduction to CU Current Methods A Controlled Test Performance Evaluation Summary Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 3

4 Introduction Assess unit dosage form attribute and process performance Target a label claim Adequate and consistent content for all dosage units Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 4

5 Introduction Uniformity Test Must on individual dose units Destructive tests May use the same or different methods as assay Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 5

6 Statistical Methods USP <905> Test CuDAL (Bergum and Li, 2007) PTIT (Lostrito, 2012) PT-TOST (FDA, 2005) Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 6

7 Statistical Methods USP <905> Test Stage 1: Sample 10 units 98. 5, ii X < M= X, if < X < , if X > k 1 =2.4; k 2 =2.0 M-X +k 1 s<15 All inside (.75M, 1.25M)??? No Stage 2: Sample 20 more units Yes M-X +k 2 s<15 All inside (.75M, 1.25M)??? No Fail. Pass. Yes Pass. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 7

8 Statistical Methods USP <905> Test Indifference zone (98.5, 101.5) tolerates off-target products Requirement on individual values in (.75M, 1.25M) Fixed sample size; fixed k factors No confidence statement? k s can have confidence component Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 8

9 Statistical Methods USP <905> Test, if Ignoring the indifference zone, ie, let M=100% Removing the individual requirement It is essentially checking cpk M-X +ks<15 min X 88 3s, 111 X 3s >k/3 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 9

10 Statistical Methods PTIT/PT-TOST Stage 1: Sample n 1 units k 1 aaa k 2 are determined based on n 1 aaa n 2, L, U, type I error rate, content level L < X k 1 s < X + k 1 s < U??? Yes No Stage 2: Sample n 2 more units L < X k 2 s < X + k 2 s < U??? No Fail. Pass. Yes Pass. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 10

11 Statistical Methods PTIT Stage 1: Sample n 1 =10 units k 1 aaa k 2 are determined based on n 1 aaa n 2, L, U, type I error rates α 1 = , α 2 = , content level p=.875 L < X k 1 s < X + k 1 s < U k 1 =3.119, L=85, U=115??? Yes No Stage 2: Sample n 2 =20 more units L < X k 2 s < X + k 2 s < U k 1 =2.155, L=85, U=115??? No Fail. Pass. Yes Pass. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 11

12 Statistical Methods PT-TOST Stage 1: Sample n 1 =10 units k 1 aaa k 2 are determined based on n 1 aaa n 2, L, U, type I error rates α 1 = , α 2 = , content level p=.875 L < X k 1 s < X + k 1 s < U k 1 =3.052, L=85, U=115??? Yes No Stage 2: Sample n 2 = 22 more units L < X k 2 s < X + k 2 s < U k 1 =2.155, L=85, U=115??? No Fail. Pass. Yes Pass. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 12

13 Statistical Methods PTIT or PT-TOST No indifference zone No requirement on individual values Based on tolerance interval Flexible sample size, content level, confidence level Admits a confidence statement Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 13

14 Statistical Methods: composite null hypothesis PTIT Φ U μ σ Φ L μ σ P PT-TOST μ Z p σ L or μ + Z p σ U Equivalently H 0 : µ T + Z p σ B T: target value, (U+L)/2, usually 100% LC Z p : percentile of content, say 93.75% B: A boundary, say (U-L)/2 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 14

15 Statistical Methods : composite null hypothesis A weighted sum of bias and variability H 0 : µ T + Z p σ B Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 15

16 Question Is the test unbiased? Or, is the type I error rate control right? H 0 : µ T + Z p σ B Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 16

17 Question Is the test unbiased? Or, is the type I error rate control right? Simulation: PT-TOST Take µ between 85.5 and For each µ calculate σ such that with p= , B=15, T=100 For each pair (µ, σ ), simulate n1=10 data points, check tier 1, if pass, stop; otherwise, simulate n2=20 more data points, check tier2 and record pass or not. Repeat this process 5000 times. µ T + Z p σ = B, Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 17

18 Simulation results: PT-TOST Type I error rate is well controlled at the end but too conservative in the middle <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 18

19 Simulation results: PT-TOST Type I error rate is well controlled at the end but too conservative in the middle Type I error rate is well controlled at the end but not the middle <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 19

20 Question Can we do better? PT-TOST is limited to the format of X ± ks Can we use MLE: X T + Z p s Take µ between 85.5 and For each µ Calculate σ such that with p= , B=15, T=100 µ T + Z p σ = B, For each pair (µ, σ ), simulate samples of size n1=10, calculate X T + Z p s for each sample, determine the lower percentile (C1); do the same with sample size n2=30, but determine the lower.034 percentile (C2) (only tier 1 failed ). simulate n1=10 data points, check X T + Z p s<c1, if pass, stop; otherwise, simulate n2=20 more data points, check X T + Z p s<c2 and record pass or not. Repeat this process 5000 times. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 20

21 Simulation results: MLE Type I error rate is less conservative in the middle but too conservative at the end <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 21

22 Simulation results: MLE Type I error rate is less conservative in the middle but too conservative at the end <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 22

23 Simulation results: USP Is the test unbiased? Or, is the type I error rate control right? <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 23

24 Simulation results: USP Type I error rate is not well controlled at the end or the middle <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 24

25 Simulation results Type I error rate is well controlled at the end but not the middle <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 25

26 Simulation results Type I error rate is well controlled at the end but not the middle <=0.05 >0.05 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 26

27 Statistical Methods : composite hypothesis Powering the design, what is the alternative? H 0 : µ T + Z p σ B 0 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 27

28 Statistical Methods : composite hypothesis Where do we want to control more? Off target? H 0 : µ T + Z p σ B 0 or µ T 10 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 28

29 Statistical Methods How to conduct the test H 0 : µ T + Z p σ B 0 or µ T 10 Test: X T + k s < B aaa 10 < X st α,n 1 / n T < X + st α,n 1 / n - T<10 k is determined based on one sided tolerance limit Here the correlation is ignored Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 29

30 Statistical Methods : composite hypothesis Where do we want to control more? Variability? H 0 : µ T + Z p σ B or σ 6 Test: X T + k s < B aaa s < 6χ 2 α,n 1 n 1 Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 30

31 Summary Content Uniformity test It is a test of composite null hypothesis Null hypothesis defined based on coverage is a weighted sum of bias (off target) and variability (standard deviation) USP test doesn t control type I error rate well PT-TOST/PTIT controls type I error rate conservatively, and more conservative at the middle of the spec range MLE based method controls type I error rate conservatively, less conservative at the middle but more conservative at the end Less conservative tests are more powerful with equal sample size. Which part is most interesting in terms of type I error control? End, middle? If middle, can we design a test that has right type I error rate control in the middle? Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 31

32 Acknowledge Thanks to Hannah Yang and Yuanyuan Duan for many stimulating discussions and help. Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 32

33 References USP <905> Yi Tsong presenation 2010 NCB, Lyon France. Steve Novick et al, 2009, AAPS PharSciTech, 10: Bergum J and Li H, PharTech. Lostritto R., Advisory Committee for Pharmaceutical Science Meeting Content Uniformity Test Midwest Biopharmaceutical Statistics Workshop May 19, 2015 Copyright 2013 AbbVie 33