ASYMPTOTIC INFERENCE WITH RESPONSE-ADAPTIVE TREATMENT ALLOCATION DESIGNS

A response-adaptive treatment allocation design for a clinical trial a ttempts to place the majority of patients on the treatment that appear s more successful, based on the responses of patients already treated. One example of such a design is the randomized play-the-winner rule d eveloped by Wei and Durham, which randomizes the treatment assignment probabilities according to the outcomes of treatments previously assig ned. For a trial with dichotomous treatment responses and a randomized play-the-winner assignment scheme, exact small sample permutation tes ts of the hypothesis of equal treatment effects and large sample tests based on a population model have previously been developed. We presen t a large sample permutation test statistic for this case; under certa in conditions on the sequence of responses, the test statistic is show n to be asymptotically normal. For a trial with a continuous response variable, we develop a rank-based analog of the randomized play-the-wi nner assignment scheme. Simulation evidence in both cases suggests tha t a normal approximation to the test statistic works well for moderate -sized trials, with some conservatism in the extreme tails.