Maximum likelihood estimation for semiparametric regression models with interval-censored multistate data

• Published in: Biometrika Vol. 111; no. 3; pp. 971 - 988
• Main Authors: Gu, Yu, Zeng, Donglin, Heiss, Gerardo, Lin, D Y
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.09.2024; Oxford Publishing Limited (England)
• Subjects: Algorithms; Covariance matrix; Epidemiology; Mathematical models; Maximum likelihood estimation; Parameter estimation; Regression analysis; Regression models; Time dependence; Multistate model; Nonparametric likelihood; Time-dependent covariate; Proportional intensity; Semiparametric efficiency; Transition probability; Random effect; EM algorithm
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asad073

Summary Interval-censored multistate 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 relate potentially time-dependent covariates to multistate processes through semiparametric proportional intensity models with random effects. We study nonparametric maximum likelihood estimation under general interval censoring and develop a stable expectation-maximization 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.