Title: A presmoothing approach for estimation in mixture cure models
Authors: Eni Musta - University of Amsterdam (Netherlands) [presenting]
Valentin Patilea - CREST-Ensai (France)
Ingrid Van Keilegom - KU Leuven (Belgium)
Abstract: A challenge when dealing with survival data is accounting for a cure fraction, meaning that some subjects will never experience the event of interest. In this context, 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 and a semiparametric Cox proportional model for the latency. The maximum likelihood estimator, implemented in the R package smcure, is then typically used for estimating the regression parameters and the cumulative hazard. We propose a new estimation procedure which, in the first stage, focuses on direct estimation of the parametric cure probability without using distributional assumptions on the latency. It relies on a preliminary nonparametric estimator for the incidence, which is then projected on the parametric logistic class of functions. In the second stage, the survival distribution of the uncured subjects is estimated by maximizing the Cox component of the likelihood. The estimators are shown to be consistent and asymptotically normally distributed, while simulations suggest that presmoothing often improves parameter estimation for small and moderate sample size. The proposed procedure is applied to two medical datasets about studies of patients with melanoma cancer.