Maximum Likelihood Estimation for Semiparametric Regression Models with Interval-Censored Multi-State Data

TL;DR

This paper develops a semiparametric maximum likelihood estimation method for analyzing interval-censored multi-state data in chronic disease studies, providing consistent, efficient estimators and demonstrating their performance through simulations and real data application.

Contribution

It introduces a stable EM algorithm for NPMLE in semiparametric multi-state models with interval censoring, achieving asymptotic normality and efficiency.

Findings

Estimators are consistent and asymptotically normal.

The covariance matrix attains the semiparametric efficiency bound.

Simulation studies show good performance in realistic scenarios.

Abstract

Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur over a broad time interval. We formulate the effects of potentially time-dependent covariates on multi-state processes through semiparametric proportional intensity models with random effects. We adopt nonparametric maximum likelihood estimation (NPMLE) under general interval censoring and develop a stable expectation-maximization (EM) algorithm. We show that the resulting parameter estimators are consistent and that the finite-dimensional components are asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we demonstrate through extensive simulation studies that the proposed numerical and inferential procedures perform well in realistic settings. Finally, we provide an application to a major epidemiologic cohort study.