Two‐stage adaptive randomization for delayed response in clinical trials

Summary Despite the widespread use of equal randomization in clinical trials, response‐adaptive randomization has attracted considerable interest. There is typically a prerun of equal randomization before the implementation of response‐adaptive randomization, although it is often not clear how many subjects are needed in this prephase, and in practice the number of patients in the equal randomization stage is often arbitrary. Another concern that is associated with realtime response‐adaptive randomization is that trial conduct often requires patients' responses to be immediately available after the treatment, whereas clinical responses may take a relatively long period of time to exhibit. To resolve these two issues, we propose a two‐stage procedure to achieve a balance between power and response, which is equipped with a likelihood ratio test before skewing the allocation probability towards a better treatment. Furthermore, we develop a non‐parametric fractional model and a parametric survival design with an optimal allocation scheme to tackle the common problem caused by delayed response. We evaluate the operating characteristics of the two‐stage designs through extensive simulation studies and illustrate them with a human immunodeficiency virus clinical trial. Numerical results show that the methods proposed satisfactorily resolve the arbitrary size of the equal randomization phase and the delayed response problem in response‐adaptive randomization.