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A challenge when dealing with survival analysis data is accounting for a curefraction, meaning that some subjects will never experience the event ofinterest. Mixture cure models have been frequently used to estimate both theprobability of being cured and the time to event for the susceptible subjects,by usually assuming a parametric (logistic) form of the incidence. We propose anew estimation procedure for a parametric cure rate that relies on apreliminary smooth estimator and is independent of the model assumed for thelatency. We investigate the theoretical properties of the estimators and showthrough simulations that, in the logistic/Cox model, presmoothing leads to moreaccurate results compared to the maximum likelihood estimator. To illustratethe practical use, we apply the new estimation procedure to two studies ofmelanoma survival data.

A presmoothing approach for estimation in semiparametric mixture cure models