Martingale methods and the martingale invariance principle are used to derive central limit theorems and related results for biased coin designs of the kind previously studied by Efron, Wei and many others. The results are applied to the study of selection bias. The method is developed for the simplest two-treatment case and then extended, first to the case of several treatments, and secondly to the case of two treatments with prognostic factors.
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Richard L. Smith (1984) studied this question.
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