Semiparametric estimation of GLMs with interval-censored covariates via an augmented Turnbull estimator

TL;DR

This paper introduces a new likelihood-based method, GELc, for estimating generalized linear models with interval-censored covariates, demonstrating its consistency, asymptotic normality, and good finite-sample performance through simulations and real data applications.

Contribution

We develop a novel GELc estimator that extends Turnbull's nonparametric estimator for better inference in GLMs with interval-censored covariates.

Findings

GELc estimator is consistent and asymptotically normal.

Simulation studies show favorable finite-sample performance.

Method applied successfully to real-world biomedical data.

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.