Abstract
Abstract For comparing two treatment effects in a clinical trial under a univariate set-up, a sampling design called randomized play-the-winner (RPW) rule was used by different authors (see, e.g., Wei, 1979 Wei, 1988 ; Wei and Durham, 1978 ). The objective of using such a rule was to allocate more patients to the better treatment. The present work suggests a bivariate version of the RPW rule. The rule is used to propose some sequential-type nonparametric tests for the equivalence of two bivariate treatment effects against a class of restricted alternatives. Some exact and asymptotic results associated with the tests are studied and examined. The limiting proportions of allocations to the two treatments are also obtained.
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