Familywise error control in multi-armed response-adaptive trials

TL;DR

This paper introduces adaptive testing procedures that guarantee strong familywise error control in response-adaptive trials with normally distributed outcomes, addressing a key regulatory concern and improving upon naive methods.

Contribution

The authors develop iterative adaptive testing procedures based on the conditional invariance principle that ensure strong familywise error control in response-adaptive designs.

Findings

Naive z-tests can have inflated type I error rates.

The proposed methods maintain or increase power for Bayesian adaptive schemes.

Extreme allocation probabilities significantly reduce power for error control.

Abstract

Response-adaptive designs allow the randomization probabilities to change during the course of a trial based on cumulated response data, so that a greater proportion of patients can be allocated to the better performing treatments. A major concern over the use of response-adaptive designs in practice, particularly from a regulatory viewpoint, is controlling the type I error rate. In particular, we show that the naive z-test can have an inflated type I error rate even after applying a Bonferroni correction. Simulation studies have often been used to demonstrate error control, but do not provide a guarantee. In this paper, we present adaptive testing procedures for normally distributed outcomes that ensure strong familywise error control, by iteratively applying the conditional invariance principle. Our approach can be used for fully sequential and block randomized trials, and for a large class of adaptive randomization rules found in the literature. We show there is a high price to pay in terms of power to guarantee familywise error control for randomization schemes with extreme allocation probabilities. However, for proposed Bayesian adaptive randomization schemes in the literature, our adaptive tests maintain or increase the power of the trial compared to the z-test. We illustrate our method using a three-armed trial in primary hypercholesterolemia.