Efficient stage-wise allocation ratios in multi-arm multi-stage designs

Abstract

Background

Multi-arm multi-stage (MAMS) designs allow the simultaneous evaluation of multiple treatments across several stages. Due to their potential to accelerate drug development, researchers are continuously seeking ways to improve MAMS designs. This study focuses on the impact of varying allocation ratios at each stage on statistical power and the expected sample size (ESS).

Methods

We present a methodology for calculating the operating characteristics of MAMS designs with varying stage-wise allocation ratios, where the maximum sample size is fixed. We evaluate the impact of various common allocation ratio combinations on three types of power: marginal, disjunctive, and conjunctive, assuming equal sample size across stages. The allocation ratio at any stage is assumed to be equal for all experimental arms, and outcomes are assumed to follow a normal distribution. The parameters used in our evaluation, such as sample size and treatment effects, are derived from a real trial.

Results

Our results demonstrate that efficient stage-wise allocation ratios vary by power type. Both marginal and disjunctive power increase when more patients are allocated to the control arm, but the efficient stage-wise allocation ratio differs for each. Conversely, conjunctive power benefits from a more balanced allocation between control and experimental arms. Variations in allocation ratios resulted in minor changes to ESS.

Conclusions

Our findings highlight the importance of considering stage-wise allocation ratios to align with the specific objectives of a trial. Stage-wise allocation ratios can enhance power and efficiency in MAMS trials, facilitating better decision-making and minimising resource use.