Bayesian quantile regression joint models: Inference and dynamic predictions

In the traditional joint models of a longitudinal and time-to-event outcome, a linear mixed model assuming normal random errors is used to model the longitudinal process. However, in many circumstances, the normality assumption is violated and the linear mixed model is not an appropriate sub-model in the joint models. In addition, as the linear mixed model models the conditional mean of the longitudinal outcome, it is not appropriate if clinical interest lies in making inference or prediction on median, lower, or upper ends of the longitudinal process. To this end, quantile regression provides a flexible, distribution-free way to study covariate effects at different quantiles of the longitudinal outcome and it is robust not only to deviation from normality, but also to outlying observations. In this article, we present and advocate the linear quantile mixed model for the longitudinal process in the joint models framework. Our development is motivated by a large prospective study of Huntington's disease where primary clinical interest is in utilizing longitudinal motor scores and other early covariates to predict the risk of developing Huntington's disease. We develop a Bayesian method based on the location-scale representation of the asymmetric Laplace distribution, assess its performance through an extensive simulation study, and demonstrate how this linear quantile mixed model-based joint models approach can be used for making subject-specific dynamic predictions of survival probability.