Accurate p-values for adaptive designs with binary endpoints.

Adaptive designs encompass all trials allowing various types of design modifications over the course of the trial. A key requirement for confirmatory adaptive designs to be accepted by regulators is the strong control of the family-wise error rate. This can be achieved by combining the p-values for each arm and stage to account for adaptations (including but not limited to treatment selection), sample size adaptation and multiple stages. While the theory for this is novel and well-established, in practice, these methods can perform poorly, especially for unbalanced designs and for small to moderate sample sizes. The problem is that standard stagewise tests have inflated type I error rate, especially but not only when the baseline success rate is close to the boundary and this is carried over to the adaptive tests, seriously inflating the family-wise error rate. We propose to fix this problem by feeding the adaptive test with second-order accurate p-values, in particular bootstrap p-values. Secondly, an adjusted version of the Simes procedure for testing intersection hypotheses that reduces the built-in conservatism is suggested. Numerical work and simulations show that unlike their standard counterparts the new approach preserves the overall error rate, at or below the nominal level across the board, irrespective of the baseline rate, stagewise sample sizes or allocation ratio. Copyright © 2017 John Wiley & Sons, Ltd.