Adaptive group-sequential design with population enrichment in phase 3 randomized controlled trials with two binary co-primary endpoints.

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The use of co-primary endpoints in drug development allows investigators to capture an experimental intervention's multidimensional effect more comprehensively than a single primary endpoint. We propose the theoretical basis and development of an adaptive population enrichment design with co-primary endpoints, provide stage-wise boundary values for futility and efficacy, and discuss power under different efficacy configurations, subgroup prevalence, and analysis times using a pre-specified decision criterion. We considered a two-arm, two-stage, parallel group design where population enrichment occurs at the interim analysis by dropping any non-responsive subgroups. A test for efficacy is conducted only in the enriched population. Two binary endpoints are evaluated as co-primary endpoints. Our trial objective is to determine whether the experimental intervention is superior to the control intervention, with superiority required in both endpoints. We define the stopping boundary using alpha spending functions. Using a 0.025 significance level for each endpoint, we obtain the stage I threshold boundary values for futility and efficacy as -0.1040 and 2.2761, respectively, and the stage II boundary value for futility and efficacy is 2.2419. We show that in the presence of substantial heterogeneity of treatment effect, we gain more power to observe an effect in the subgroup where the benefits are greater. By allowing the dropping of non-responsive subgroups at an early stage, our design reduces the likelihood of obtaining false-negative results due to inclusion of the heterogeneous treatment effects of both subgroups, which would dilute the responsive subgroup's results.