Regression Models with Interval-Censored Variables

Survival analysis is essential for modeling time-to-event data across various fields, including medicine, engineering, and the social sciences. A major challenge in this field is handling censored data, particularly partly interval-censored data, where event times are either precisely recorded or only known to fall within a specific interval. Proper statistical modeling of such data is crucial for drawing valid conclusions and making accurate predictions. This article reviews regression models for analyzing interval-censored responses and their implementation in R. Following an introduction to the nonparametric maximum likelihood estimator, we focus on four major regression models: the accelerated failure time model, the proportional hazards model, the proportional odds model, and the generalized odds-rate model. For each, we review the state of the art, outline its methodology, discuss implementation strategies, and illustrate practical applications using real-world data. The article concludes with a discussion of current challenges, alternative modeling approaches, and potential directions for future research.