Sample size calculations for mixture alternatives in a control group vs. treatment group design. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Jeske, Daniel R.; Yao, Weixin
• Is Part Of: Statistics. Volume 54:Issue 1(2020)
• Page Start: 97
• Page End: 113
• Publication Date: 2020-01-02
• Subjects: Wilcoxon test -- power -- mixture models -- treatment effect -- sample size; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1715407
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We consider a control group versus treatment group experimental design and assert that powering the design for a potential treatment effect that is represented by a pure shift of the control group distribution is usually unrealistic. Instead, we propose the use of a mixture model as the design alternative in anticipation that there might be a sub-population in the treated population whose responses come from the same control group distribution. When the responses in the treatment group follow a mixture model, the sample size found by the traditional pure shift alternative based method is demonstrated to be under-powered. We develop a new sample size formula for the Wilcoxon test statistic and propose a more general definition of the treatment effect. Method of moment estimators of the treatment effect are proposed and their bias and mean squared error properties are evaluated.