Nonparametric inference in mixture cure models

Abstract

A completely nonparametric method for the estimation of mixture cure models is proposed. An incidence estimator is extensively studied and a latency estimator is presented. These estimators, which are based on the Beran estimator of the conditional survival function, are proven to be the local maximum likelihood estimators. Two i.i.d. representations for the incidence and the latency estimators are obtained. Moreover, an asymptotic expression for the mean squared error of the latency estimator is derived, and its asymptotic normality is proven. In addition, bootstrap bandwidth selection methods for each nonparametric estimator are introduced. The proposed nonparametric estimators are compared with existing semiparametric approaches in simulation studies, in which the performance of the bootstrap bandwidth selectors are also assessed. The nonparametric incidence and latency estimators are applied to a dataset of colorectal cancer patients from the University Hospital of A Coruña (CHUAC). Furthermore, a nonparametric covariate significance test for the incidence is proposed. The method is extended to non continuous covariates: binary, discrete and qualitative, and also to contexts with a large number of covariates. The efficiency of the procedure is evaluated in a Monte Carlo simulation study, in which the distribution of the test is approximated by bootstrap. The test is applied to a sarcomas dataset.