A bayesian joint dispersion model with flexible links

Abstract

The objective is to jointly model longitudinal and survival data taking into account their interdependence in a real HIV/AIDS dataset inside a Bayesian framework. We propose a linear mixed effects dispersion model for the CD4 longitudinal counts with a between-individual heterogeneity in the mean and variance, relaxing the usual assumption of a common variance for the longitudinal residuals. A hazard regression model is considered in addition to model the time since HIV/AIDS diagnostic until failure, where the coefficients accounting for the linking between the longitudinal and survival processes are time-varying. This flexibility is specified using penalized Splines and allows the relationship to vary in time. Because residual heteroscedasticity may be related with the survival, the standard deviation is considered as a covariate in the hazard model thus enabling to study the effect of the CD4 counts’ stability on the survival. The proposed framework outperforms the traditional joint models, highlighting the importance in correctly taking account the individual heterogeneity for the measurement errors variance.