Bayesian considerations for noninferiority clinical trials with case example

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1 Bayesian considerations for noninferiority clinical trials with case example Fanni Natanegara, PhD Eli Lilly and Company Duke Industry-Statistics Symposium October 23, 2015

2 Acknowledgement Pengfei Li (Eli Lilly) Margaret Gamalo-Siebers (FDA), Aijun Gao (Inventiv Health Clinical), Mani Lakshminarayanan (Pfizer), Guanghan Liu (Merck), Fanni Natanegara (Eli Lilly), Radha Railkar (Merck), Heinz Schmidli (Novartis), Guochen Song (Quintile) Bayesian Methods for the Design and Analysis of Non- Inferiority. JBS, /27/2015 Company Confidential 2015 Eli Lilly and Company 2

3 Motivations Compare efficacy in one ethnic group to another group for an approved drug Compare a new formulation (SC) to an existing one (IV) Compare a drug in development to standard of care 10/27/2015 Company Confidential 2015 Eli Lilly and Company 3

4 Non-inferiority (NI) Trial What NI trials seek to show is that any difference between the two treatments is small enough to allow a conclusion that the new drug (T) has at least some effect or, in many cases, an effect that is not too much smaller than the active control (C). Source: FDA2010 draft guidance for NI trials, lines /27/2015 Company Confidential 2015 Eli Lilly and Company 4

5 ABC of NI trial (Julious 2011) Assay sensitivity: C had its expected effect in the NI study Bias: to be minimized by ensuring that patient population and endpoint are similar between past placebo-controlled and current NI studies Constancy assumption of effect: similarity of C effect vs P in studies Placebo creep Shift in patient population 10/27/2015 Company Confidential 2015 Eli Lilly and Company 5

6 Practical consideration: NI Margin FDA CDER and CBER 2010 NI draft guidance: single greatest challenge in the design, conduct and interpretation of NI trials M 1 margin: entire effect of C relative to Placebo (P) in the NI study An assumed value since P is not observed Show that T had effect > 0 or superior to P M 2 margin: largest clinically relevant difference of T vs C smaller than M 1 (20-50% of M 1 ) HESDE: Historical Evidence of Sensitivity to Drug Effect (ICH E-10) Past trials showing a consistent estimate of a drug s treatment effect compared to P 10/27/2015 Company Confidential 2015 Eli Lilly and Company 6

7 NI Study Interpretations 1. NI and superiority of T 2. NI only 3. NI but C is superior to T 4. NI not demonstrated 0 M T C Negative direction: smaller is better C T Positive direction: bigger is better

8 NI Study Interpretations 1. NI not demonstrated 2. NI but C is superior to T 3. NI only 4. NI and superiority of T M 0 T C Positive direction C T Negative direction

9 Practical consideration: Fixed margin method Pre-specified M from past studies then uses CI to reject the H 0 of inferiority by M Hypothesis testing H 0 : T C < M vs H 1 : T C M where T and C are treatment response for T and C, respectively Fixed margin M = f*( C P ) = f* CP where P is treatment response of P, CP is treatment effect of C over P, and f is between 0 and 1 Conservative estimate of CP is to use lower bound of CI H 0 is rejected if 10/27/2015 Company Confidential 2015 Eli Lilly and Company 9

10 Practical consideration: Synthesis method Combines estimate of T vs C in NI study with estimates of C from past placebo controlled studies Use variability from current and past studies to yield a CI for testing NI hypothesis that the treatment effect rules out a loss of pre-specified fixed fraction of the C effect Hypothesis testing H 0 : TC < f* CP vs H 1 : TC f* CP H 0 is rejected if The synthesis approach is always more efficient than the fixed margin test. Fixed margin method controls a Type I error rate within the NI study for a prespecied M Synthesis method controls an unconditional error rate for H 0 provided that data from the historical studies for C were treated similarly as in the current NI study. 10/27/2015 Company Confidential 2015 Eli Lilly and Company 10

11 Bayesian motivation to NI trials NI trials provides 2 comparisons, Direct comparison of T vs C Indirect comparison of T vs P Existing past trials on C vs P and the essential need to incorporate those data frequentist s methods are not well suited for such situation Hypotheses of interests can be based on posterior distribution, which in turn can provide direct probability statements Increase in power and reduction in sample size, with appropriate assumptions 10/27/2015 Company Confidential 2015 Eli Lilly and Company 11

12 Bayesian approach: Meta-analytic-predictive Indirect comparison to P using historical data Note that T P = ( T C ) + ( C P ) current NI trial historical trial(s) Strict constancy assumption: C P = ( 1 C 1 P) = = ( m C m P) = CP Likelihood: X j ~ N( j, 2 j) where j (T, C) Prior: Meta-analysis of historical trials, X H, can provide posterior distribution P( CP X H ), which can be used for prior on C P Posterior distribution on P( T P X T, X C, X H ) Alternative model: allow between trial variability ( C P ), ( 1 C 1 P),, ( m C m P) ~ N( CP, 2 ) 10/27/2015 Company Confidential 2015 Eli Lilly and Company 12

13 Bayesian approach: Hierarchical priors Likelihood: X ij ~ N( j, 2 j) where j (T, C) Information on active control(s) incorporated into model as informative priors T and C have informative priors obtained from historical data e.g. meta-analysis Posterior distribution on T C Decision rule for concluding NI where p is pre-specified and can be used to control Type I error rate How much borrowing is needed from the historical trials? Power prior (Ibrahim and Chen, 2000) Review paper of historical borrowing (Viele, 2014) 10/27/2015 Company Confidential 2015 Eli Lilly and Company 13

14 Case example: background We consider a mock diabetes NI trial, comparing T and C in their effects in lowering the HbA1c of Type 1 diabetes patients In diabetes NI trial, a fixed margin of 0.3% or 0.4% is usually used % is a unit in the measurement of HbA1c 10/27/2015 Company Confidential 2015 Eli Lilly and Company 14

15 Case example: model and decision rule We assume a simple Normal-based ANCOVA model for the observed changed from baseline in HbA1c in i th subject and j th treatment group Y ij ~ N ( ij, ) ij = α 0 *baseline ij + α T * I[T] i + α C * (1 I[T] i ), α T and α C are changes in HbA1c for T and C, respectively, and I[T] is an indicator variable for T Decision rule: upper bound of 95% Credible Interval of ( T C ) < 0.4% 10/27/2015 Company Confidential 2015 Eli Lilly and Company 15

16 Case example: Bayesian hierarchical prior model Likelihood Current trial : two arms (T and C), N=150 per arm Sample size assumption: no treatment difference, common sd=1.2%, NI margin=0.4%, 80% of power Prior information Historical studies for the C group Historical study N Baseline (sd) Change (sd) S (1.6) (1) S (0.74) 0.06 (0.56) S (0.86) 0.9 (0.56) 10/27/2015 Company Confidential 2015 Eli Lilly and Company 16

17 Case example: Bayesian hierarchical prior model Prior information Prior 1: non-informative prior on regression coefficients ie α ~ N(0, sd=100), ~ U(0,100) Prior 2: informative prior on effects on C and baseline based on 3 historical studies in a hierarchical fashion Power prior (Chen, 2000) was used to generate the priors for the current trial by controlling the amount of historical data used via power parameter a (0=no borrowing, 1=full borrowing) Prior 2A: full borrowing of historical data a=1 Prior 2B: S1 used a=1; S2 and S3 used a=0.5 10/27/2015 Company Confidential 2015 Eli Lilly and Company 17

18 Case example: Bayesian hierarchical prior model Frequentist analyses on the current trial was conducted in SAS PROC MIXED; 95% CI for the LSM difference of (T C) will be used for making NI conclusion Bayesian inference was conducted in SAS PROC MCMC with 5K burn-in, 50K posterior samples and thin=5. Posterior mean for T and C was reported. Upper tail of 95% posterior equaltail intervals for T C was used for making NI conclusion. 10/27/2015 Company Confidential 2015 Eli Lilly and Company 18

19 Case example: analyses results Methods Estimate for coefficient of Baseline Estimate C (adj mean) Estimate T (adj mean) Estimate T-C (95% interval) NI conclusion (margin 0.4) Frequentist (0.0677) (0.0731) ( , ) NI met Non-informative prior (0.0688) (0.0714) ( , ) NI met Informative prior S1(1), S2(1), S3 (1) (0.1566) (0.0706) ( , ) NI met Informative prior S1(1), S2(0.5), S3 (0.5) (0.1004) (0.0728) ( , ) NI met 10/27/2015 Company Confidential 2015 Eli Lilly and Company 19

20 Conclusions Fixed margin approach is well utilized in recent literature whether Bayesian or not Bayesian approach to NI trials provides advantages straightforward probabilistic statements takes into account uncertainty utilizes all relevant data to inform future studies Simulation work to understand sensitivity around inclusion of historical data and operating characteristics of NI study design

21 Questions?

22 Abstract The gold standard for evaluating treatment efficacy of a pharmaceutical product is a placebo controlled study. However, when a placebo controlled study is considered to be unethical or impractical to conduct, a viable alternative is a non-inferiority (NI) study in which an experimental treatment is compared to an active control treatment. The objective of such study is to determine whether the experimental treatment is not inferior to the active control by a pre-specified NI margin. The availability of historical studies in designing and analyzing NI study makes these types of studies conducive to the use of the Bayesian approach. In this presentation, we will highlight case examples for utilizing Bayesian methods in NI study and provide recommendations. 10/27/2015 Company Confidential 2015 Eli Lilly and Company 22