Semiparametric Bayesian regularized quantile regression to mixed effect model for health insurance data

In longitudinal health insurance studies, modeling medical expenditures and their complex covariate effects is of considerable interest. Traditional mean regression models may perform poorly in the presence of outliers or heavy-tailed responses. To address this issue, we develop a Bayesian semiparametric quantile mixed-effects model with Lasso regularization for simultaneous estimation and variable selection. Assuming the Asymmetric Laplace distribution (ALD) for the errors and using cubic splines to capture nonlinear effects, posterior inference is conducted via Gibbs sampling. The proposed method is applied to Medical Expenditure Panel Survey (MEPS) data and further assessed through simulation studies.