Joint modeling of longitudinal and survival data with missing and left-censored time-varying covariates

We propose a joint model for longitudinal and survival data with time-varying covariates subject to detection limits and intermittent missingness at random (MAR). The model is motivated by data from the Multicenter AIDS Cohort Study (MACS), in which HIV+ subjects have viral load and CD4 cell count measured at repeated visits along with survival data. We model the longitudinal component using a normal linear mixed model, modeling the trajectory of CD4 cell count by regressing on viral load and other covariates. The viral load data are subject to both left-censoring due to detection limits (17%) and intermittent missingness (27%). The survival component of the joint model is a Cox model with time-dependent covariates for death due to AIDS. The longitudinal and survival models are linked using the trajectory function of the linear mixed model. A Bayesian analysis is conducted on the MACS data using the proposed joint model. The proposed method is shown to improve the precision of estimates when compared to alternative methods