Calculation of power and sample size with bounded outcome scores

The two-sample Wilcoxon rank sum test is the most popular non-parametric test for the comparison of two samples when the underlying distributions are not normal. Although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic, parametric assumptions are often made to determine the power of the test or the sample size. We encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients. It is shown that, for power and sample size estimation, it can be dangerous to apply the classical formulae routinely, especially with outcome scores having a U-shaped or a J-shaped distribution. As an example we have taken the Barthel index, a quality-of-life outcome measure in stroke patients. Further, we have investigated alternative methods by means of Monte Carlo simulation. The distributional characteristics of the estimated powers were compared. Our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non-parametric method.