The single‐index/Cox mixture cure model

In survival analysis, it often happens that a certain fraction of the subjects under study never experience the event of interest, that is, they are considered “cured.” In the presence of covariates, a common model for this type of data is the mixture cure model, which assumes that the population consists of two subpopulations, namely the cured and the non‐cured ones, and it writes the survival function of the whole population given a set of covariates as a mixture of the survival function of the cured subjects (which equals one), and the survival function of the non‐cured ones. In the literature, one usually assumes that the mixing probabilities follow a logistic model. This is, however, a strong modeling assumption, which might not be met in practice. Therefore, in order to have a flexible model which at the same time does not suffer from curse‐of‐dimensionality problems, we propose in this paper a single‐index model for the mixing probabilities. For the survival function of the non‐cured subjects we assume a Cox proportional hazards model. We estimate this model using a maximum likelihood approach. We also carry out a simulation study, in which we compare the estimators under the single‐index model and under the logistic model for various model settings, and we apply the new model and estimation method on a breast cancer data set.