A double-semiparametric approach for extending mixture cure models with interval-censored data

Mixture cure models (MCMs) have become a valuable tool for analyzing failure time data in settings where a subset of individuals is considered to be "cured" or no longer experience the failure event of interest. Under the MCM framework, the latency component typically postulates a semiparametric survival model for the failure times of uncured individuals, while the incidence component models the probability of being uncured using logistic regression. However, in many practical applications, assuming linear covariate effects or imposing a fully parametric form on the incidence may be unrealistic, given that cure status is inherently unobserved for right-censored individuals. We introduce a more general mixture cure model for interval-censored data by incorporating nonparametric covariate effects in the incidence component. Our method allows semiparametric frameworks for both components of the mixture cure model, offering flexibility in capturing complex relationships between susceptibility and risk factors while preserving interpretability. We develop a spline-based sieve maximum likelihood estimator for both the model parameters and the unknown functions, and establish its desirable asymptotic properties. The finite-sample performance and practical utility of the proposed method are demonstrated through a simulation study and an analysis of data from a cardiac allograft vasculopathy study, respectively.