Semiparametric copula-based quantile regression for semicontinuous outcomes with application to healthcare data

A semiparametric copula-based two-part quantile regression framework is developed for the analysis of semicontinuous outcomes characterized by a point mass at zero and a continuous positive component. The proposed approach models the occurrence and magnitude processes separately and links them through copula-based conditional distributions, allowing for flexible dependence structures and nonlinear covariate effects across quantiles. Large-sample properties of the resulting estimator are established, and extensive simulation studies demonstrate improved finite-sample performance relative to logistic/linear quantile regression, particularly under nonlinear dependence and substantial zero inflation. An application to healthcare data illustrates how the proposed method provides a nuanced characterization of the association between social deprivation and uncompensated and charity care burdens, revealing heterogeneous and nonlinear effects that are not captured by competing approaches.