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

Abstract

ABSTRACTWe 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.