Weighted quantile regression for analyzing health care cost data with missing covariates

Abstract

Analysis of health care cost data is often complicated by a high level of skewness, heteroscedastic variances and the presence of missing data. Most of the existing literature on cost data analysis have been focused on modeling the conditional mean. In this paper, we study a weighted quantile regression approach for estimating the conditional quantiles health care cost data with missing covariates. The weighted quantile regression estimator is consistent, unlike the naive estimator, and asymptotically normal. Furthermore, we propose a modified BIC for variable selection in quantile regression when the covariates are missing at random. The quantile regression framework allows us to obtain a more complete picture of the effects of the covariates on the health care cost and is naturally adapted to the skewness and heterogeneity of the cost data. The method is semiparametric in the sense that it does not require to specify the likelihood function for the random error or the covariates. We investigate the weighted quantile regression procedure and the modified BIC via extensive simulations. We illustrate the application by analyzing a real data set from a health care cost study.

A General Framework for Quantile Estimation with Incomplete Data

“…For quantile regression with missing covariates, Sherwood et al . () took the IPW approach to study healthcare cost data. Under a non‐ignorable missingness mechanism, Zhao et al .…”

“…Yi and He (2009) investigated a similar method under different model assumptions focusing on median regression. For quantile regression with missing covariates, Sherwood et al (2013) took the IPW approach to study healthcare cost data. Under a non-ignorable missingness mechanism, Zhao et al (2013) proposed an augmented IPW method to estimate the distribution function and quantiles of a response variable.…”

Empirical likelihood for quantile regression models with response data missing at random

“…Since the seminal work of Koenker [1], quantile regression (QR) has been an indispensable and versatile tool for statistical research due to its promising performance and elegant mathematical properties, and attracted immediately considerable attention, resulting in numerous papers (e.g., see [1][2][3][4][5][6][7]) devoted to various theoretical extensions of this significant topic. Moreover, QR has been widely applied to a variety of fields such as economics, finance, biology, and medicine.…”

“…Lv [5] discussed smoothed empirical likelihood analysis with missing response in partially linear quantile regression. Sherwood [6] recently proposed an inverse probability weighting QR approach for analyzing health care cost data when the covariates are MAR. Sun [14] studied QR for competing risk data when the failure type was missing.…”

Variable selection for additive partial linear quantile regression with missing covariates

“…Lipsitz et al (1997) and Yi and He (2009) proposed IPW methods for longitudinal quantile regression models with dropouts. Sherwood et al (2013) used the IPW approach with linear quantile regression and proposed a BIC type procedure with a weighted objective function for model selection. Liu and Yuan (2015) proposed a weighted empirical likelihood quantile regression estimator for missing covariates that achieves semiparametric efficiency.…”