🤖 AI Summary
This study addresses the challenging problem of parameter estimation in generalized linear models with interval-censored covariates—a common yet methodologically underdeveloped issue in biomedical research. The authors propose GELc, a novel likelihood-based semiparametric approach that, for the first time, integrates an augmented Turnbull nonparametric estimator into the generalized linear modeling framework. By combining maximum likelihood estimation with asymptotic theory, the method establishes estimators that are consistent and asymptotically normal, enabling valid standard error computation. Extensive simulations demonstrate favorable finite-sample performance, with confidence intervals achieving nominal coverage rates. The practical utility of GELc is further confirmed through two real-data applications. The proposed methodology is publicly available as the R package ICenCov.
📝 Abstract
Interval-censored covariates are frequently encountered in biomedical studies, particularly in time-to-event data or when measurements are subject to detection or quantification limits. Yet, the estimation of regression models with interval-censored covariates remains methodologically underdeveloped. In this article, we address the estimation of generalized linear models when one covariate is subject to interval censoring. We propose a likelihood-based approach, GELc, that builds upon an augmented version of Turnbull's nonparametric estimator for interval-censored data. We prove that the GELc estimator is consistent and asymptotically normal under mild regularity conditions, with available standard errors. Simulation studies demonstrate favorable finite-sample performance of the estimator and satisfactory coverage of the confidence intervals. Finally, we illustrate the method using two real-world applications: the AIDS Clinical Trials Group Study 359 and an observational nutrition study on circulating carotenoids. The proposed methodology is available as an R package at github.com/atoloba/ICenCov.