A proportional hazards model taking account of long-term survivors

A proportional hazards (PH) model is modified to take account of long-term survivors by assuming the cumulative hazard to be bounded but otherwise uns pecified to yield an improper survival function. A marginal likelihood is d erived under the restriction for type I censoring patterns. For a PH model with cure, the marginal and the partial likelihood are not the same. In the absence of covariate information, the estimate of the cure rate based on t he marginal likelihood reduces to the value of the Kaplan-Meier estimate at the end of the study. An example of low asymptotic efficiency of the parti al likelihood as compared to the marginal, profile, and parametric likeliho ods is given. An algorithm is suggested to fit the full PH model with cure.