  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.
