Consistent estimation of a joint model for multivariate longitudinal and survival data with latent variables

Abstract

The investigation of the relationship between a time-to-event outcome and time-dependent risk factors is often of great interest in longitudinal studies. However, the time-dependent risk factors may not be directly observed or simply measured by a single variable. Instead, they are latent and should be characterized by several observed variables from different aspects. In this article, we consider a novel joint modeling framework to examine the effects of latent time-dependent risk factors on the hazard of interest. A factor analysis model is used to depict the dependence between time-dependent latent variables and multivariate longitudinal observed variables, and a proportional hazard model is adopted for linking latent time-dependent factors to the hazard of interest. We develop a hybrid procedure that combines an asymptotically distribution-free generalized least square approach and a conditional score method. Theoretical results are provided on the consistency and asymptotic normality of parameter estimators. The method is evaluated through simulation studies and applied to a dataset about Alzheimer’s disease.