A Test for Generalized Behrens-Fisher Problem with an Adaptive Interim Analysis

Abstract

Abtsrcat The present paper considers a generalization of the Behrens-Fisher problem without assuming that the underlying distribution functions are continuous so that the proposed procedure is also applicable to count or ordered categorical data. The proposed test is based on a generalization of the Wilcoxon-Mann-Whitney statistic where the data correspond to sequentially observed responses from patients allocated at random to two treatments in two stages. At stage 1, patients are allocated completely at random between two treatments. At the end of stage 1, the accumulated responses corresponding to the treatments are compared. At stage 2, the patients are assigned to the treatments in such a way that the more promising treatment receives more patients. Simulation comparisons of the proposed procedure with some natural competitors show a considerably larger number of allocations to the better treatment and a smaller average sample number with a little loss in power.