  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. We investigate the theoretical properties of the estimators and show
through simulations that, in the logistic/Cox model, 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.
