A mixed-effects joint model with skew-t distribution for longitudinal and time-to-event data: A Bayesian approach

Abstract

Modelling longitudinal biomarkers and time-to-event processes jointly is becoming essential in medical research and other follow-up studies in order to evaluate their association, obtain unbiased results, and make valid statistical inferences. This study was motivated by follow-up data on chronic kidney disease (CKD), which is a major global health problem. Numerous studies have been conducted in the literature to analyse and assess the kidney function of CKD patients using cross-sectional data. However, joint models on CKD follow-up data have not been extensively studied in the literature. In the construction of joint models on CKD data, most previous studies proposed mixed-effects submodels with Gaussian distributions for longitudinal outcomes. However, longitudinal outcomes may have asymmetric (skewed) distributions. Proposing a normal distribution for skewed longitudinal data may yield biased results and invalid statistical inferences. In this paper, therefore, we propose a mixed-effects joint model with a skew-t distribution for longitudinal and time-to-event data under the Bayesian approach. We assessed the performance of the proposed joint model using simulation studies and applied the model to real CKD data. The proposed joint model with a skew-t distribution was compared with joint models with skew-normal and normal distributions of model errors. The findings of the simulation and application studies showed that the proposed joint model with skew-t distribution performed well.