  A 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 paper, we investigate properties of
the method of moment estimators for the treatment effect and demonstrate their
usefulness for obtaining approximate confidence intervals without any
parametric assumptions about the distribution of responses.
