Extension of Fisher's least significant difference method to multi-armed group-sequential response-adaptive designs.

Multi-armed multi-stage designs evaluate experimental treatments using a control arm at interim analyses. Incorporating response-adaptive randomisation in these designs allows early stopping, faster treatment selection and more patients to be assigned to the more promising treatments. Existing frequentist multi-armed multi-stage designs demonstrate that the family-wise error rate is strongly controlled, but they may be too conservative and lack power when the experimental treatments are very different therapies rather than doses of the same drug. Moreover, the designs use a fixed allocation ratio. In this article, Fisher's least significant difference method extended to group-sequential response-adaptive designs is investigated. It is shown mathematically that the information time continues after dropping inferior arms, and hence the error-spending approach can be used to control the family-wise error rate. Two optimal allocations were considered. One ensures efficient estimation of the treatment effects and the other maximises the power subject to a fixed total sample size. Operating characteristics of the group-sequential response-adaptive design for normal and censored survival outcomes based on simulation and redesigning the NeoSphere trial were compared with those of a fixed-sample design. Results show that the adaptive design attains efficient and ethical advantages, and that the family-wise error rate is well controlled.