Assessing the Impact of Efficacy Stopping Rules on the Error Rates Under the Multi-arm Multi-stage Framework

Background: The multi-arm multi-stage framework uses intermediate outcomes to assess lack-of-benefit of research arms at interim stages in randomised trials with time-to-event outcomes. However, the design lacks formal methods to evaluate early evidence of overwhelming efficacy on the definitive outcome measure. We explore the operating characteristics of this extension to the multi-arm multi-stage design and how to control the pairwise and familywise type I error rate. Using real examples and the updated nstage program, we demonstrate how such a design can be developed in practice.

Methods: We used the Dunnett approach for assessing treatment arms when conducting comprehensive simulation studies to evaluate the familywise error rate, with and without interim efficacy looks on the definitive outcome measure, at the same time as the planned lack-of-benefit interim analyses on the intermediate outcome measure. We studied the effect of the timing of interim analyses, allocation ratio, lack-of-benefit boundaries, efficacy rule, number of stages and research arms on the operating characteristics of the design when efficacy stopping boundaries are incorporated. Methods for controlling the familywise error rate with efficacy looks were also addressed.

Results: Incorporating Haybittle-Peto stopping boundaries on the definitive outcome at the interim analyses will not inflate the familywise error rate in a multi-arm design with two stages. However, this rule is conservative; in general, more liberal stopping boundaries can be used with minimal impact on the familywise error rate. Efficacy bounds in trials with three or more stages using an intermediate outcome may inflate the familywise error rate, but we show how to maintain strong control.

Conclusion: The multi-arm multi-stage design allows stopping for both lack-of-benefit on the intermediate outcome and efficacy on the definitive outcome at the interim stages. We provide guidelines on how to control the familywise error rate when efficacy boundaries are implemented in practice.