Modelling associations in multivariate longitudinal data with INLA

Measuring the relationship between the longitudinal response variable and time-varying covariates is not always trivial in longitudinal studies, and the use of simple linear mixed models is no longer appropriate, especially when covariates depend on the prior values of the outcome (endogenous time-varying covariates). The failure to account for the dependence between the endogenous variable and the outcome history introduces significant bias. Moreover, the longitudinal variables can be measured at different points in time and may contain missing values. All of these motivations led us to use several multivariate models to assess the association between the response variable and the endogenous covariates. Some induce the association via correlated random effects, called Joint Mixed Models; others use a scaling factor to estimate the association, called Joint Scaled Models. Fitting either of these models, however, is not straightforward, and their computational intensity, due to the potentially high-dimensional integration over the random effects terms, limits their applicability. A flexible Bayesian estimation approach, known as INLA, will be used to fill this gap. We will evaluate its performance and applicability in the context of joint longitudinal models. In particular, it has been evaluated in a scenario with a low population dimension, which generally leads to low accuracy and precision of the estimates, small variances and covariaces of the random effects, resulting in a priors selection problem, and longitudinal variables of different types, one being normally distributed and the other following a Beta distribution. We will present analysis results from a simulation study and a clinical study conducted at the Leiden University Medical Center (LUMC).