Sample size planning for multiple contrast tests.

Sample size calculations for two (independent) samples are well established and applied in (pre-)clinical research. When planning several samples, which is common in, for example, preclinical studies, sample size planning tools based on analysis of variance methods are available. Since the underlying effect sizes of these methods are often hard to interpret and to provide for the sample size planning, we employ multiple contrast test procedures for sample size computations in both parametric (under normality assumption) and nonparametric designs using Steel-type tests. Since the exact distributions of the test statistics are unknown under the alternative and variance heterogeneity, we use approximate solutions. Furthermore, since no closed formula for the sample size is available, we use numerical approximations for their computation. Extensive simulation studies are finally conducted to assess the quality of the approximations. It turns out that the methods are accurate in the sense that the multiple contrast test procedures reach the target power to detect the alternative of interest with the sample size computed. The developed procedures are a valuable tool to plan (pre-)clinical trials with several samples and are easily accessible in publicly available software.