Nonparametric incidence and latency estimation in mixture cure models

A completely nonparametric method for the estimation of mixture cure models is proposed in this paper. The nonparametric estimator of the incidence introduced by Xu and Peng (2014) is extensively studied and a nonparametric estimator of the latency is presented. These estimators, which are based on the Beran estimator of the conditional survival function, are proved to be the local maximum likelihood estimators. An iid representation is obtained for the nonparametric incidence estimator. As a consequence, an asymptotically optimal bandwidth is found. Moreover, a bootstrap bandwidth selection method for the nonparametric incidence estimator is proposed. The introduced nonparametric estimators are compared with existing semiparametric approaches in a simulation study, in which the performance of the bootstrap bandwidth selector is also assessed. Finally, the presented method is applied to a database of colorectal cancer from the University Hospital of A Coruña (CHUAC).