"Semiparametric Shared Parameter Model of Longitudinal and Survival Data"
February 22, 2011 @ 3:30 p.m. - 4:30 p.m.
Liang Li, Ph.D., Department of Quantitative Health Sciences, Cleveland Clinic
Location: 701 Blockley Hall
Semiparametric Shared Parameter Model of Longitudinal and Survival Data
In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientiﬁc interest to relate these prognostic quantities to a later time-to-event clinical endpoint such as patient survival. This is often done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). We study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log-likelihood with the frailties eliminated as nuisance parameters. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis (HEMO) Study on patients with kidney disease. Extensions of the methodology to more general joint models for longitudinal and survival data are discussed.