A mixture model is an attractive approach for analyzing failure time data in which there are thought to be two groups of subjects, those who could eventually develop the endpoint and those who could not develop the endpoint. The proposed model is a semi-parametric generalization of the mixture model of Farewell (1982). A logistic regression model is proposed for the incidence part of the model, and a Kaplan-Meier type approach is used to estimate the latency part of the model. The estimator arises naturally out of the EM algorithm approach for fitting failure time mixture models as described by Larson and Dinse (1985). The procedure is applied to some experimental data from radiation biology and is evaluated in a Monte Carlo simulation study. The simulation study suggests the semi-parametric procedure is almost as efficient as the correct fully parametric procedure for estimating the regression coefficient in the incidence, but less efficient for estimating the latency distribution.