Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up

When analyzing time-to-event data, it often happens that some subjects do not experience the event of interest. Survival models that take this feature into account (called ‘cure models’) have been developed in the presence of covariates. However, the nonparametric cure models with covariates, in the current literature, cannot be applied when the follow-up is insufficient, i.e., when the right endpoint of the support of the censoring time is strictly smaller than that of the survival time of the susceptible subjects. New estimators of the conditional cure rate and the conditional survival function are proposed using extrapolation techniques coming from extreme value theory. The proposed methodology can also be used to estimate the conditional survival function when no cure rate is present. The asymptotic normality of the proposed estimators is established and their performances for small samples are shown by means of a simulation study. Their practical applicability is illustrated through the analysis of two short applications with real datasets on the repayment of student bullet loans and the employee's turnover in a company.