Bayesian Analysis of Joint Modeling of Longitudinal and Time to Event Data Using Some Skew-Elliptical Distributions

Abstract

Joint modeling of longitudinal and time to event data have been widely used for analyzing medical data, where longitudinal measurements is gathered with a time to event or survival data. In most of these studies, distributional assumption for modeling longitudinal response is normal, which leads to vulnerable inference in the presence of outliers in longitudinal measurements and violation of this assumption. Violation of the normality assumption can also make the statistical inference vague. Powerful distributions for robust analyzing and relaxing normality assumption, are skew-elliptical distributions, which include univariate and multivariate versions of the student's t, the Laplace and normal distributions. In this paper, a linear mixed effects model with skew-elliptical distribution for both random effects and residuals and a Cox's model for time to event data are used for joint modeling. This strategy allows for the skewness and the heavy tails of random effect distributions and thus makes inferences robust to the violation. For estimation, a Bayesian parametric approach using Markov chain Monte Carlo is adopted. The method is illustrated in a real Intensive Care Unit (ICU) data set and the best model is selected using some Bayesian criteria for model selection.