The mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we introduce inference based on a pseudo-likelihood approach and compare it with an existing method of moment approach. An extensive simulation study is used to compare robust performance of the two approaches regarding point estimation, confidence regions, and confidence intervals. The methods are demonstrated on an illustrative blood pressure data set.
Keywords: Randomized clinical trial; mixture model; non-parametric inference; pseudo-likelihood; responders; treatment effect.