Evaluating subject-treatment interaction when comparing two treatments

Clinical and other studies that evaluate the effect of a treatment relative to a control often focus on estimating a mean treatment effect; however, the mean treatment effect may be misleading when the effect of the treatment varies widely across subjects. Methods are proposed to evaluate individual treatment heterogeneity (i.e., subject-treatment interaction) and its consequences in clinical experiments. The method of maximum likelihood is used to derive estimators and their properties. A bootstrap procedure that requires fewer assumptions is also presented as a small sample alternative to the maximum likelihood approach. It is shown that estimators for subject-treatment interaction are sensitive to an inestimable correlation parameter. This sensitivity is illustrated using some example data sets and using graphical plots. The practical consequence of subject-treatment interaction is that a proportion of the population may be not be responding to the treatment as indicated by the average treatment effect. Results obtained from the methods reported here can alert the practitioner to the possibility that individual treatment effects vary widely in the population and help to assess the potential consequences of this variation. Applications of the proposed procedures to clinical decision making, pharmacogenetic studies, and other contexts are discussed.