A new partition testing strategy for multiple endpoints.

To evaluate efficacy in multiple endpoints in confirmatory clinical trials is a challenging problem in multiple hypotheses testing. The difficulty comes from the different importance of each endpoint and their underlying correlation. Current approaches to this problem, which test the efficacy in certain dose-endpoint combinations and collate the results, are based on closed testing or partition testing. Despite their different formulations, all current approaches test their dose-endpoint combinations as intersection hypotheses and apply various union-intersection tests. Likelihood ratio test is seldom used owing to the extensive computation and lack of consistent inferences. In this article, we first generalize the formulation of multiple endpoints problem to include the cases of alternative primary endpoints and co-primary endpoints. Then we propose a new partition testing approach that is based on consonance-adjusted likelihood ratio test. The new procedure provides consistent inferences, and yet, it is still conservative and does not rely on the estimation of endpoint correlation or independence assumptions that might be challenged by regulatory agencies.