Sample size calculations for mixture alternatives in a control group vs. treatment group design

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.

KEYWORDS:

• Wilcoxon test
• power
• mixture models
• treatment effect
• sample size

Acknowledgements

The authors appreciate helpful comments from two referees and an associate editor.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Daniel R. Jeske http://orcid.org/0000-0002-0214-7992

Additional information

Funding

Yao’s research is supported by NSF [grant number DMS-1461677] and Department of Energy [award number 10006272].