Nonparametric estimation in mixture cure models with covariates

Nonparametric estimation methods for the cure rate and the distribution of the failure time of uncured subjects with covariates for censored survival data have attracted much attention in the last few years. To model the effects of covariates on the distribution of the failure time of uncured subjects, existing works assume that the cure rate is a constant or depends on the same covariate as the distribution of uncured subjects. In this paper, we review the nonparametric estimation methods in the context of the mixture cure model and propose a new nonparametric estimator for the distribution of uncured subjects that relaxes the assumption used in the existing works. The estimation is based on the EM algorithm, which is readily available for mixture cure models, and is strongly consistent. The finite sample performance of the proposed estimator is assessed and compared with existing methods in a simulation study. Finally, the nonparametric estimation methods are employed to model the effects of some covariates on the time to bankruptcy among commercial banks insured by the Federal Deposit Insurance Corporation during the first quarter of 2006.