The Annals of Statistics

Asymptotic Inference with Response-Adaptive Treatment Allocation Designs

William F. Rosenberger

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

Article information

Ann. Statist., Volume 21, Number 4 (1993), 2098-2107.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

Martingale central limit theorem permutation test randomized play-the-winner rule


Rosenberger, William F. Asymptotic Inference with Response-Adaptive Treatment Allocation Designs. Ann. Statist. 21 (1993), no. 4, 2098--2107. doi:10.1214/aos/1176349412.

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