Semiparametric Transformation Models with a Change Point for Interval-Censored Failure Time Data

Change point models are widely used in medical and epidemiological studies to capture the threshold effects of continuous covariates on health outcomes. These threshold effects represent critical points at which the relationship between biomarkers or risk factors and disease risk shifts, often reflecting underlying biological mechanisms or clinically relevant intervention points. While most existing methods focus on right-censored data, interval censoring is common in large-scale clinical trials and follow-up studies, where the exact event times are not observed but are known to fall within time intervals. In this paper, we propose a semiparametric transformation model with an unknown change point for interval-censored data. The model allows flexible transformation functions, including the proportional hazards and proportional odds models, and it accommodates both main effects and their interactions with the threshold variable. Model parameters are estimated via the EM algorithm, with the change point identified through a profile likelihood approach using grid search. We establish the asymptotic properties of the proposed estimators and evaluate their finite-sample performance through extensive simulations, showing good accuracy and coverage properties. The method is further illustrated through an application to the Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial data.