Joint Modelling of Multivariate Longitudinal and Time-to-Event under Bayesian Inference: With Application to Type 2 Diabetes and Hypertension Disease.

In medical research, it is common to collect multivariate data by measuring subjects multiple times across different outcomes. Researchers often use univariate mixed-effects models to analyse this data by assuming that both the random effects and errors follow a normal distribution. Additionally, the response variables are assumed to be linear functions of the unknown regression parameters. However, the assumption of normal distribution may not always provide reliable results if the data exhibit skewness; outcome variables may have a nonlinear relationship with covariates, such as time. Furthermore, a univariate mixed-effects model applied to correlated multivariate longitudinal outcomes without considering their correlation may lead to biased parameter estimates. To simultaneously overcome these issues, we presented a flexible semiparametric multivariate mixed-effects model that incorporates multiple correlated longitudinal outcomes, exhibits skewness, and uses a nonparametric function to capture nonlinear time effects. The proposed models are illustrated through an application to correlated glucose concentration and blood pressure data, aiming to study the association between glucose concentration and blood pressure in individuals with type 2 diabetes and hypertension. A simulation study is conducted to evaluate the performance of the proposed models. The results from both the application and simulation studies suggest that the semiparametric mixed effect model, which utilizes a multivariate normal distribution for the random errors, has better performance than other proposed models since it accommodates the nonlinear effects of covariates and asymmetrical characteristics of longitudinal measurements. In our application, we found a strong association between the changes in glucose concentration and blood pressure, with the rate of change increasing over time.