High dimensional single-index mixture cure models

Abstract

In survival analysis, there are situations in which not all subjects are susceptible to the final event. For example, if the event is a cancer therapy-related adverse effect, there will be a fraction of patients (considered as cured) that will never experience it. Mixture cure models allow to estimate the probability of cure and the survival function for the uncured subjects. In the literature, nonparametric estimation of both functions is limited to continuous univariate covariates. We fill this gap by proposing single-index mixture cure models. They allow working with a vector covariate and assume that the survival function depends on it through an unknown linear combination, that is estimated by maximum likelihood. Besides, a nonparametric estimator for the density function of the uncured individuals is introduced, and its iid representation is derived. Finally, the proposed models are extended to functional covariates and a preprocessing algorithm is implemented to deal with medical images. The methodology is applied to a cardiotoxicity dataset. The goal is to determine whether (and how) certain factors affect the probability of experiencing the cardiovascular problem and the amount of time it takes for it to manifest. Understanding risk factors may lead to a patient-based preventive medicine.