A Bayesian Non-Inferiority Approach to Evaluation of Bridging Studies Chin-Fu Hsiao, Jen-Pei Liu

1. A Bayesian Non-Inferiority Approach to Evaluation of Bridging Studies Chin-Fu Hsiao, Jen-Pei Liu Division of Biostatistics and Bioinformatics National Health Research Institites Huey-Miin Hsueh Department of Statistics National Cheng-Chi University The views expressed in this paper are professional opinions of the presenter and may not necessarily represent the position of the National Health Research Institutes, Taiwan

2. Outline • Introduction • Bridging Study • A Bayesian Non-Inferiority Approach • Discussion

3. Introduction ICH (International Conference on Harmonisation) E5 Ethnic Factors in the Acceptability of Foreign Clinical Data The purpose of this guidance is to facilitate the registration of medicines among ICH regions by recommending a framework for evaluating the impact of ethnic factors upon a medicine’s effect, i.e., its efficacy and safety at a particular dosage and dose regimen.

4. Objectives of ICH E5 • To describe the characteristics of foreign clinical data that • will facilitate their extrapolation to different population and support their acceptance as a basis for registration on a medicine in a new region • To describe regulatory strategies that minimize duplication of clinical data and facilitate acceptance of foreign clinical data in the new region • To describe the use of bridging studies, when necessary, to allow extrapolation of foreign clinical data to a new region • To describe development strategies capable of characterizing ethnic factor influences on safety, efficacy, dosage, and dose regimen

5. Bridging Study A bridging study is defined as a study performed in the new region to provide pharmacodynamic or clinical data on efficacy, safety, dosage, and dose regimen in the new region that will allow extrapolation of the foreign clinical data to the population in the new region

6. Extrapolation and Similarity • If the bridging study shows that dose response, safety and efficacy in the new region are similar, then the study is readily interpreted as capable of “bridging” the foreign data • If a bridging study, properly executed, indicates that a different dose in the new region results in a safety and efficacy profile that is not substantially different from that derived in the original region, it will often be possible to extrapolate the foreign data to the new region, with appropriate dose adjustment, if this can be adequately justified (e.g., by pharmacokinetic and/or pharmacodynamic data).

7. Bridging Studies • ICH E5 • Only after the medicine is approved in the original region • Performed in the new region

8. Bayesian Approach For bridging studies • Small sample size • No power • Information on dose response, efficacy and safety of the original region can not be concurrently obtained from the local bridging studies but are available in the trials conducted in the original region • Need to borrow “strength” from CCDP of the original region • Information on dose response, efficacy and safety of the original region can and should be incorporated in a statistically sound manner to evaluate bridging evidence by local bridging studies.

9. Bayesian Non-Inferiority Approach Step 1: From the complete clinical data package, use the technique of meta-analysis to integrate the results from the original region to formulate the mean and variability of the prior distribution for test product and placebo Step 2: Use the data from the bridging study in the new region and prior distribution to obtain the mean and variability of the posterior distribution for the difference of test products between new and original regions Step 3: Evaluate the posterior probability that difference is greater or equal to some clinically acceptable limit Step 4: If the posterior probability is sufficiently large, say 80%, then conclude the similarity between the new and original regions.

10. Assumption and Notation • Assess similarity of efficacy for comparing a test productand a placebo control • Since the test product has been already approved in the original region due to its proven efficacy against placebo control, the concept of non-inferiority is referred to as the similarity between the treatment effects from both regions • Pindicates the common placebo effect for both new and original regions • NT(OT) represents the treatment mean for the new (original) region

11. Similarity Given the data from the bridging study and prior information on (P, NT, OT) formulated from the CCDP, we claim similarity on efficacy for the new region in terms of non-inferiority concept if the posterior probability PSI = P{NT- OT >-δ | bridging data and prior } > 1- for some pre-specified δ> 0 and > 0

12. The Equivalence Limit The equivalence limit δ can be expressed as a proportion of the relative efficacy of the test product against placebo δ=f(OT- P) where f is a fixed pre-specified constant and 0<f<1.

13. Example • We hypothesize an example based on our experience from literature review • We select four randomized studies of the effect of a test drug (versus placebo) in reducing the sitting diastolic blood pressure • The results of three studies are treated as the data from the original region, while the other one study is treated as the data from the new region • The alternative hypothesis of interest is that the difference of reduction from baseline in sitting diastolic blood pressure between the test drug and placebo is less than 0

15. Example • By letting f=0.5, we obtain that PSI=0.9999 • We therefore conclude that the efficacy observed in the bridging study of the new region is similar to the efficacy from the original region by the concept of non-inferiority

16. Discussion • From our example, it can be seen that all the results from the original region are very significant, while the results from the new region are not significant at all • Even so, the Bayesian non-inferiority approach still conclude the similarity of efficacy between both regions

17. Discussion • One way to resolve issue is to use weights other than sample size to combine the data from both regions • Another approach is to use different prior. For the data given above and under the non-informative prior, the posterior probability of non-inferiority, PSI is 0.3228