Bayesian Tobit quantile regression model for medical expenditure panel survey data

High expenditure on healthcare is an important segment of the U.S. economy, making healthcare cost modelling valuable in decision-making processes over a wide array of domains. In this paper, we analyze medical expenditure panel survey (MEPS) data. Tobit regression model has been popularly used for the medical expenditures. However, it is no longer sufficient for the MEPS data because: (i) the distribution of the expenditures shows skewness, heavy tails and heterogeneity; (ii) most predictors are categorical, including binary, nominal and ordinal variables; (iii) there are a few predictors which may be nonlinearly related to the response. We therefore propose a Bayesian Tobit quantile regression model to describe a complete distributional view on how the medical expenditures depend on the various predictors. Specifically, we assume an asymmetric Laplace error distribution to adapt the quantile regression to a Bayesian setting. Then, we propose a modified group Lasso for categorical factor selection, and a smoothing Gaussian prior for modelling the nonlinear effects. The estimates and their uncertainties are obtained using an efficient Monte Carlo Markov Chain sampling method. The effectiveness of our approach is demonstrated by modelling 2007 MEPS data.