Precise and Accurate Power of the Rank-Sum Test for a Continuous Variable

• Activity Number: 251 - SPEED: Biopharmaceutical Methods and Application I, Part 2
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 2:45 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Katie Rose Mollan* and Ilana Trumble and Sarah Reifeis and Orlando Ferrer and Camden P Bay and Pedro L. Baldoni and Michael Hudgens
• Companies: University of North Carolina Chapel Hill and University of Colorado Denver and University of North Carolina at Chapel Hill and University of North Carolina Chapel Hill and Harvard Medical School and University of North Carolina At Chapel Hill and University of North Carolina at Chapel Hill
• Keywords: Mann-Whitney test; Wilcoxon rank-sum test; Monte Carlo simulation; non-parametric; power analysis

Abstract

Accurate power calculations are essential in small studies containing expensive experimental units or high-stakes exposures. Herein, power of the Wilcoxon Mann-Whitney rank-sum test for a continuous variable is formulated using a Monte Carlo approach combined with defining P(X < Y) = p as a measure of effect size, where X and Y denote random observations from two distributions hypothesized to be equal under the null hypothesis. Effect size p fosters productive communications when researchers understand p = 0.5 is analogous to a fair coin toss. This approach is feasible with or without background data. Simulations were conducted comparing this Monte Carlo approach to power approaches by Rosner & Glynn (2009), Shieh et al. (2006), Noether (1987), and O'Brien-Castelloe (2006). Approximations by Noether and O'Brien-Castelloe are shown to be inaccurate for small sample sizes. The Rosner & Glynn and Shieh et al. approaches performed well in many small sample scenarios, though both are restricted to location-shift alternatives and neither is theoretically justified for small samples. The Monte Carlo method is recommended and available for convenient use in the R package wmwpow.