Bayesian joint relatively quantile regression modeling of multivariate ordinal longitudinal data with latent mixed effects models for an application to diagnosis and treatment of lung cancer

In this paper, we propose a Bayesian joint quantile regression approach to model multivariate ordinal longitudinal data with multi-response mixed effects model. A multivariate asymmetric Laplace (MAL) distribution is employed to construct the working likelihood of the considered model. LASSO-type penalization priors of regression parameters are incorporated into the working likelihood to implement Bayesian joint QR inference. MCMC algorithm is employed to derive the fully posterior distributions of all parameters. For multivariate ordinal longitudinal data, in order to give more efficient estimation results, we propose the joint relatively QR approach for regression coefficients. Some simulation studies are presented to illustrate the performance of the proposed joint relatively QR estimation approach. Finally, we analyze a multivariate ordinal longitudinal dataset from a clinical study in diagnosis and treatment of lung cancer using the proposed approach.