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 models have been frequently used to estimate both probability being cured and time susceptible subjects, by usually assuming parametric (logistic) form incidence. We propose new estimation procedure rate relies on preliminary smooth estimator independent model assumed latency. On second stage one can assume semiparametric latency also distribution uncured subject. For particular case logistic/Cox model, we investigate theoretical properties estimators show through simulations presmoothing leads more accurate results compared maximum likelihood estimator. To illustrate practical use, apply two studies melanoma data.