Efficient determination of optimised multi-arm multi-stage experimental designs with control of generalised error-rates

TL;DR

This paper introduces an efficient method for designing multi-arm multi-stage experiments that control generalized error rates, optimizing for specific rejection criteria, with applications demonstrated through a clinical trial example.

Contribution

It extends existing methodologies to include abcd multi-arm multi-stage designs with controlled generalized error rates and provides a computationally efficient approach for design optimization.

Findings

Ensures strong control of the a-generalized type-I familywise error-rate.

Achieves power to reject at least b out of c false hypotheses.

Demonstrates the impact of design parameters on trial performance.

Abstract

Primarily motivated by the drug development process, several publications have now presented methodology for the design of multi-arm multi-stage experiments with normally distributed outcome variables of known variance. Here, we extend these past considerations to allow the design of what we refer to as an abcd multi-arm multi-stage experiment. We provide a proof of how strong control of the a-generalised type-I familywise error-rate can be ensured. We then describe how to attain the power to reject at least b out of c false hypotheses, which is related to controlling the b-generalised type-II familywise error-rate. Following this, we detail how a design can be optimised for a scenario in which rejection of any d null hypotheses brings about termination of the experiment. We achieve this by proposing a highly computationally efficient approach for evaluating the performance of a candidate design. Finally, using a real clinical trial as a motivating example, we explore the effect of the design's control parameters on the statistical operating characteristics.