### Optimal multiple testing and design in clinical trials

Statistics Seminar

4th February 2022, 4:00 pm – 5:00 pm

Virtual Seminar, Zoom link: TBA

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal policies become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the policies. This leads us to formulate the optimal policy problem as an explicit optimization problem with an objective and constraints which describe its specific desiderata. We describe a complete solution for deriving optimal policies for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal policies that are identical to existing policies, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and in the APEX study of Cohen et al. (2016). We conclude by discussing extensions of interest: the case when more than two hypotheses testing problems are considered; and more complex designs with primary and secondary hypotheses.

This is joint work with Abba Krieger and Saharon Rosset.

*Organiser*: Juliette Unwin

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