Intuitive Nonparametric Effect Size Index for Treatment Trials

• Activity Number: 200
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 9:00 AM to 10:50 AM
• Sponsor: Biometrics Section
• Author(s): Laura Acion*+ and Scott Temple and Stephan Arndt
• Companies: University of Iowa and University of Iowa College of Medicine and University of Iowa
• Keywords: effect size ; treatment trials ; Mann-Whitney U statistic ; Kendall's tau

Abstract

Effect size indices (ESI) tell the magnitude of the difference between treatments and, ideally, should tell clinicians how likely their patients will benefit from the treatment. The currently used ESIs are expressed in statistical rather than clinically useful terms and may not give clinicians the appropriate information. We restrict our discussion to a study of two groups: one with n patients receiving treatment X and the other with m receiving treatment Y. Cohen's d (d = (Xmean - Ymean) / SD) is a well known ESI for continuous outcomes. There is some intuitive value to d, but measuring improvement in SDs is a statistical concept that may not help a clinician. How much improved is a half SD? A more intuitive and simple ESI is the probability that a patient receiving X does better than a randomly chosen patient on Y, i.e., p(X>Y), where larger values mean better outcomes. This probability is related to the Mann-Whitney U statistic and Kendall's tau. We define criteria for good ESI, propose p(X>Y) as an alternative index, and show the relation of p(X>Y) with d under the uniform distribution. We discuss advantages and disadvantages of both ESIs and illustrate with clinical data.