Simultaneous confidence interval for assessing non-inferiority with assay sensitivity in a three-arm trial with binary endpoints

A three-arm trial including an experimental treatment, an active reference treatment and a placebo is often used to assess the non-inferiority (NI) with assay sensitivity of an experimental treatment. Various hypothesis-test-based approaches via a fraction or pre-specified margin have been proposed to assess the NI with assay sensitivity in a three-arm trial. There is little work done on confidence interval in a three-arm trial. This paper develops a hybrid approach to construct simultaneous confidence interval for assessing NI and assay sensitivity in a three-arm trial. For comparison, we present normal-approximation-based and bootstrap-resampling-based simultaneous confidence intervals. Simulation studies evidence that the hybrid approach with the Wilson score statistic performs better than other approaches in terms of empirical coverage probability and mesial-non-coverage probability. An example is used to illustrate the proposed approaches.