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Tang, N, Yu, B. Simultaneous confidence interval for assessing non‐inferiority with assay sensitivity in a three‐arm trial with binary endpoints. Pharmaceutical Statistics. 2020; 1– 14. https://doi.org/10.1002/pst.2010
Non-inferiority (NI) trials are often conducted to demonstrate that the efficacy of a new experiment treatment is not worse than that of the reference treatment by more than a prespecified small amount. Many methods have been developed to make inference on two-arm trials. But two-arm NI trials have often some problems with interpretation, for example, the selection of the non-inferiority margin and the assessment of assay sensitivity, defined as the ability to distinguish an effective treatment from a less effective or ineffective treatment. To this end, if ethically acceptable and practically feasible, a three-arm NI trial including an experimental treatment, an active reference treatment and a placebo is often implemented to simultaneously establish NI and assay sensitivity. When endpoints are binary, various hypothesis-test-based approaches via a fraction or prespecified margin have been proposed to assess NI with assay sensitivity in a three-arm trial. But existing NI testing approaches are developed for sufficiently large sample sizes and they behave poor for small sample sizes or sparse data structure. To address these issues, this paper considers the problem of simultaneous confidence interval construction for assessing both NI and assay sensitivity in a three-arm trial with small sample sizes, due to the duality of hypothesis testing and interval estimation. Several hybrid approaches are developed. For comparison, we present normal-approximation-based and bootstrap-resampling-based simultaneous confidence intervals. Simulation studies show that the hybrid approach with the Wilson score statistic performs better than other approaches in terms of empirical coverage probability and mesial-noncoverage probability. This method can be extended to non-inferiority trials with multiple new treatments or several active controls.