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

Guanjie Lyu, Mohamed Belalia, Abdulkadir Hussein

Abstract

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.

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

Abstract

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.
Paper Structure (14 sections, 1 theorem, 22 equations, 2 figures, 5 tables, 1 algorithm)

This paper contains 14 sections, 1 theorem, 22 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The proposed method
  3. Semicontinuous distributions and conditional quantiles
  4. Copula based quantile regression model
  5. The proposed estimator
  6. Weak consistency
  7. Simulation study
  8. Simulation setting
  9. Finite sample performance
  10. Misspecifications and robustness
  11. Healthcare data analysis
  12. Motivating dataset
  13. Model results
  14. Concluding remarks

Key Result

Theorem 2.2

Under ass:2024-06-10, 10:11AM, we have, for $\tau \in (0, 1)$ and $\bm{x}\in {\mathbb{R}}^d$, where "$\xrightarrow[n\to \infty]{P}$" stands for convergence in probability.

Figures (2)

  • Figure 1: Uncompensated care burden versus SDI score, all pointwise confidence bands are derived from $300$ bootstrap samples. TopLeft: The estimated probability of occurrence for uncompensated care with logistic regression (green dash line) and copula binary model (red solid line); TopRight: The quantile estimates of level $50\%$ for linear quantile regression (orange dotted line), logistic/linear quantile regression (green dash line) and copula-based two-part model (red solid line); BottomLeft: The quantile estimates of level $70\%$ for the three models; BottomRight: The quantile estimates of level $90\%$ for the three models.
  • Figure 2: Charity care burden versus SDI score, all pointwise confidence bands are derived from $300$ bootstrap samples. TopLeft: The estimated probability of occurrence for charity care with logistic regression (green dash line) and copula binary model (red solid line); TopRight: The quantile estimates of level $50\%$ for linear quantile regression (orange dotted line), logistic/linear quantile regression (green dash line) and copula-based two-part model (red solid line); BottomLeft: The quantile estimates of level $70\%$ for the three models; BottomRight: The quantile estimates of level $90\%$ for the three models.

Theorems & Definitions (2)

  • Theorem 2.2
  • proof