Causal Estimands and Confidence Intervals Associated with Wilcoxon-Mann-Whitney Tests in Randomized Experiments

• Activity Number: 72 - Recent Advances in Nonparametric Statistical Methods II
• Type: Contributed
• Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael Fay* and Erin Gabriel and Joanna H Shih and Dean Follmann and Erica H Brittain
• Companies: National Institute of Allergy and Infectious Diseases and Karolinska Institute and National Cancer Institute and NIAID and National Institute of Allergy and Infectious Diseases
• Keywords: Mann-Whitney; causal; randomized experiment; proportional odds; confidence interval; proportion benefited by treatment

Abstract

Although the p-value from a Wilcoxon-Mann-Whitney (WMW) test is used often with randomized experiments, it is rarely accompanied with a causal effect estimate. The natural parameter for the WMW test is the Mann-Whitney parameter, phi, which measures the probability that a randomly selected individual in the treatment arm will have a larger response than a randomly selected individual in the control arm (plus an adjustment for ties). We show that the Mann-Whitney parameter may be framed as a causal parameter and show that it is not equal to a closely related and non-identifiable causal effect, psi, the probability that a randomly selected individual will have a larger response under treatment than under control (plus an adjustment for ties). We review the paradox, first expressed by Hand, that the psi parameter may imply that the treatment is worse (or better) than control, while the Mann-Whitney parameter shows the opposite. Unlike the Mann-Whitney parameter, psi is non-identifiable from a randomized experiment. We review some nonparametric assumptions which rule out Hand's paradox through bounds on psi, and use bootstrap methods to make inferences on those bounds.