A Semiparametric Regression Cure Model for Interval-Censored Data

Abstract

Motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring, we present a semiparametric nonmixture cure model for the regression analysis of interval-censored time-to-event data. We develop semiparametric maximum likelihood estimation for the model using the expectation-maximization method for interval-censored data. The maximization step for the baseline function is nonparametric and numerically challenging. We develop an efficient and numerically stable algorithm via modern convex optimization techniques, yielding a self-consistency algorithm for the maximization step. We prove the strong consistency of the maximum likelihood estimators under the Hellinger distance, which is an appropriate metric for the asymptotic property of the estimators for interval-censored data. We assess the performance of the estimators in a simulation study with small to moderate sample sizes. To illustrate the method, we also analyze a real dataset from a medical study for the biochemical recurrence of prostate cancer among patients who have undergone radical prostatectomy. Supplemental materials for the computational algorithm are available online.

Keywords:  :

• Convex optimization
• Hellinger consistency
• Maximum likelihood estimation
• Primal-dual interior-point method
• Prostate cancer