Causal estimands and confidence intervals associated with Wilcoxon-Mann-Whitney tests in randomized experiments

Statistics in Medicine
Michael P FayErin E Gabriel

Abstract

Although the P value from a Wilcoxon-Mann-Whitney test is used often with randomized experiments, it is rarely accompanied with a causal effect estimate and its confidence interval. The natural parameter for the Wilcoxon-Mann-Whitney test is the Mann-Whitney parameter, ϕ, 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 nonidentifiable causal effect, ψ, 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 ψ 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, ψ is nonidentifiable from a randomized experiment. We review some nonparametric assumptions that rule out Hand's paradox through bounds on ψ and use bootstrap methods to make inferences on those bounds. We explore the relationship of the pr...Continue Reading

References

May 28, 2009·Statistics in Medicine·Michael SchemperGeorg Heinze
Nov 3, 2016·Biometrical Journal. Biometrische Zeitschrift·Markus PaulyFrank Konietschke
Feb 10, 2017·Biometrics·Joanna H Shih, Michael P Fay

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Citations

Jan 10, 2019·Biometrical Journal. Biometrische Zeitschrift·Jan De Neve, Thomas A Gerds
Nov 20, 2019·Biometrics·Jiannan LuPeng Ding
Dec 2, 2020·Statistical Methods in Medical Research·Johan VerbeeckGeert Molenberghs
Feb 11, 2021·Statistics in Medicine·Jan De Neve, Heidelinde Dehaene
Mar 2, 2021·Veterinary World·Ekaterina Romanovna VasilevskayaAngelina Igorevna Fokina
Apr 17, 2021·Statistics in Medicine·Edgar BrunnerTobias Mütze
Oct 12, 2021·Statistical Methods in Medical Research·Brice OzenneJulien Péron

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