Wilcoxon rank-sum tests to detect one-sided mixture alternatives in group sequential clinical trials

Traditional methods based on the assumption that the treatment distribution is a pure shift of the control distribution may not always hold. The possibility that an individual from the treatment group may not respond to the treatment motivates the use of a mixture distribution for the treatment group. This paper considers two test procedures based on the Wilcoxon rank-sum statistic for a group sequential design to detect the one-sided mixture alternative. Error spending functions are used for the allocation of error rates at each stage. The two tests are evaluated individually in determination of critical values and arm sizes and asymptotic multivariate normality is shown to hold for both. Upon comparison, the tests are presented to be asymptotically equivalent. Both test statistics maintain the Type I error rate even if $$ is misspecified in the design alternative. A more general definition of the treatment effect is used with the mixture distribution. Method of moments estimators and constrained $$-means estimators for the treatment effect are evaluated.