Cox-Integrated Spline Sieve Estimation for Doubly Censored Cure Models

Abstract Doubly censored data arise when the failure time represents the duration between an initial and terminal event, both of which are subject to censoring. Existing cure models typically assume independence between these events, limiting their ability to capture inherent associations in disease processes. We propose a novel spline-based semiparametric sieve maximum likelihood estimator for doubly censored cure models that jointly assesses covariate effects on both cure probability (incidence) and failure time distribution among susceptibles (latency). Our approach incorporates the initial event time as a covariate in both incidence and latency components, explicitly modeling their association. To our knowledge, this represents the first application of I-splines and M-splines to flexibly approximate the cumulative and baseline hazard functions in doubly censored cure models. The method integrates multiple imputation to handle exact, interval-censored, and right-censored observations. We establish the estimator’s consistency and asymptotic normality, and demonstrate through comprehensive simulations that it achieves reduced bias and improved efficiency compared to existing approaches. In an application to AIDS cohort data, our method reveals that the timing of HIV infection significantly predicts the probability of developing AIDS but not the incubation period among progressors, offering new insights into disease progression mechanisms.