Abstract

In the context of comparing a treatment group to a control group, a mixture model for the observations from the treatment group allows for being able to make inference about the existence of responders and non-responders in the treatment group. A generalized treatment effect for the model is represented by the probability a treated patient is a responder and the magnitude of a shift in the control group distribution that models the responses from patients that respond to the treatment. Pseudolikelihood (PSL) and method of moment (MOM) estimators for the generalized treatment effect are derived that account for the inclusion of covariates. Confidence intervals based on the asymptotic properties of the MOM estimator are also developed. Except when the overall treatment effect is small, simulation results demonstrate that the PSL estimator is preferred over the MOM estimator and that the confidence intervals have satisfactorily close to nominal coverage probabilities.