Sample Size Determination Based on Rank Tests in Clinical Trials

The problem of sample size determination based on three commonly used non-parametric rank based tests, namely, one-sample Wilcoxon's rank sum test, two-sample's Wilcoxon's rank sum test, and the rank-based test for independence is studied. Explicit formulas for variabilities of the test statistics under the alternative hypotheses are derived. Consequently, close forms of power functions of these test statistics are obtained for sample size determination utilizing the concept of higher order polynominal equations. Simulation studies were performed to evaluate the finite samples performance of the derived sample size formulas. The results indicates that the derived methods work well with moderate sample size.