A two-stage Fisher exact test for multi-arm studies with binary outcome variables

TL;DR

This paper introduces a two-stage Fisher exact test for multi-arm binary outcome studies, offering a less conservative alternative to existing exact methods with controlled error rates and optimized design parameters.

Contribution

It develops a novel two-stage Fisher exact test for multi-arm studies, enabling early stopping and precise error control, improving efficiency over traditional methods.

Findings

Less conservative than existing exact binomial designs

Effective control of familywise error rate

Optimized design parameters for desirable operating characteristics

Abstract

In small sample studies with binary outcome data, use of a normal approximation for hypothesis testing can lead to substantial inflation of the type-I error-rate. Consequently, exact statistical methods are necessitated, and accordingly, much research has been conducted to facilitate this. Recently, this has included methodology for the design of two-stage multi-arm studies utilising exact binomial tests. These designs were demonstrated to carry substantial efficiency advantages over a fixed sample design, but generally suffered from strong conservatism. An alternative classical means of small sample inference with dichotomous data is Fisher's exact test. However, this method is limited to single-stage designs when there are multiple arms. Therefore, here, we propose a two-stage version of Fisher's exact test, with the potential to stop early to accept or reject null hypotheses, which is applicable to multi-arm studies. In particular, we provide precise formulae describing the requirements for achieving weak or strong control of the familywise error-rate with this design. Following this, we describe how the design parameters may be optimised to confer desirable operating characteristics. For a motivating example based on a phase II clinical trial, we demonstrate that on average our approach is less conservative than corresponding optimal designs based on exact binomial tests.