A Novel Statistical Test for Treatment Differences in Clinical Trials using a Response Adaptive Forward Looking Gittins Index Rule

The most common objective for response adaptive clinical trials is to seek to ensure that patients within a trial have a high chance of receiving the best treatment available by altering the chance of allocation on the basis of accumulating data. Approaches which yield good patient benefit properties suffer from low power from a frequentist perspective when testing for a treatment difference at the end of the study due to the high imbalance in treatment allocations. In this work we develop an alternative pairwise test for treatment difference on the basis of allocation probabilities of the covariate-adjusted response-adaptive randomization with forward looking Gittins index rule (CARA-FLGI). The performance of the novel test is evaluated in simulations for two-armed studies and then its applications to multi-armed studies is illustrated. The proposed test has markedly improved power over the traditional Fisher exact test when this class of non-myopic response adaptation is used. We also find that the test's power is close to the power of a Fisher exact test under equal randomization.