A quantile approach to the power transformed location–scale model

The burgeoning growth of health care spending has become a major concern to policy makers, making the modeling of health care expenditure valuable in their decision-making processes. The challenges of health care expenditure analysis are two-fold: the exceptional skewness of its distribution as the top 5% of the population accounted for almost half of all spending and its heteroscedasticity. To address these concerns, the quantile regression model with power transformation has been employed, but at a price of the model complexity and analysis cost. In this article, we introduce a simpler quantile approach to the analysis of expenditure data by employing the location–scale model with an unknown link function to accommodate the heteroscedastic data with non-ignorable outliers. Specifically, in our approach a link function does not depend on quantiles; yet, it effectively fits the data as the slope coefficient depends on the quantiles. This parsimonious feature of our model helps us conduct a more intuitive and easily understood analysis for the whole distribution with fewer computational steps. Thus, it can be more widely applicable in practice. Additionally, simulation studies are conducted to investigate the model performance compared to other competing models. Analysis of the 2007 Medical Expenditure Panel Survey data using our model shows that aging and self-rated health tend to drive up costs. However, uninsured persons do not contribute to the high health cost. These findings suggest that careful monitoring of elderly’s health status and a more aggressive preventive medicare system may contribute to slow down the explosion of medical costs.