A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects

Abstract

This article studies a general joint model for longitudinal measurements and competing risks survival data. The model consists of a linear mixed effects sub-model for the longitudinal outcome, a proportional cause-specific hazards frailty sub-model for the competing risks survival data, and a regression sub-model for the variance–covariance matrix of the multivariate latent random effects based on a modified Cholesky decomposition. The model provides a useful approach to adjust for non-ignorable missing data due to dropout for the longitudinal outcome, enables analysis of the survival outcome with informative censoring and intermittently measured time-dependent covariates, as well as joint analysis of the longitudinal and survival outcomes. Unlike previously studied joint models, our model allows for heterogeneous random covariance matrices. It also offers a framework to assess the homogeneous covariance assumption of existing joint models. A Bayesian MCMC procedure is developed for parameter estimation and inference. Its performances and frequentist properties are investigated using simulations. A real data example is used to illustrate the usefulness of the approach.

Zero-inflated count models for longitudinal measurements with heterogeneous random effects

“…In this case, generalized autoregressive parameters and innovative variance parametrization methods would be required to model the random covariance matrix. In the longitudinal and joint modeling framework, such methods have shown the advantage of computational attractiveness with a logical interpretation of parameters 13,14,26 .…”

Bayesian Joint Modelling of Longitudinal and Survival Data of HIV/AIDS Patients: A Case Study at Bale Robe General Hospital, Ethiopia

“…The standard maximum likelihood method involves integrating out latent variables from the log likelihood function, which is difficult when dealing with highdimensional variables [9]. As a result, the proposed joint models are estimated under a Bayesian framework using Markov chain Monte Carlo (MCMC) methods with Gibbs sampling using Win BUGS software.…”

A joint model of longitudinal and competing risks survival data with heterogeneous random effects and outlying longitudinal measurements

“…Table 1 compares results from a normal joint model with and without the outliers together with a model with a t-distributed error ( k = 3) using all data points. The estimation procedure for the normal joint model is the same except that there is no need to estimate parameter τ ij (Huang, 2008). First, the outliers are observed to be influential to the parameter estimates for the longitudinal endpoint.…”