A presmoothing approach for estimation in the semiparametric Cox mixture cure model

A challenge when dealing with survival analysis data is accounting for a cure fraction, meaning that some subjects will never experience the event of interest. Mixture cure models have been frequently used to estimate both the probability of being cured and the time to event for the susceptible subjects, by usually assuming a parametric (logistic) form of the incidence. We propose a new estimation procedure for a parametric cure rate that relies on a preliminary smooth estimator and is independent of the model assumed for the latency. On a second stage one can assume a semiparametric model for the latency and estimate also the survival distribution of the uncured subject. For the particular case of the logistic/Cox model, we investigate the theoretical properties of the estimators and show through simulations that presmoothing leads to more accurate results compared to the maximum likelihood estimator. To illustrate the practical use, we apply the new estimation procedure to two studies of melanoma survival data.