Estimation of survival based on proportional hazards when cure is a possibility

Inference based on the proportional hazards model is discussed in the presence of long-term survivors. The model is formulated as a cure model yielding an improper survivor function. An algorithm is proposed to fit the proportional hazards model restricted by the fixed survival rates at the end of observation period. A parametric cure model is used to estimate the proportion of long-term survivors. To combine the stability of the parametric method with the flexibility of the nonparametric one, the survival function is estimated nonparametrically conditional on the cure rates provided by the parametric analysis. The methods are applied to the data collected in clinical trials on Hodgkin's disease.