Quantile regression and smoothed empirical likelihood for non-ignorable missing data based on semi-parametric response models

Abstract

In the context of quantile regression with non-ignorable missingness in the response variable, we introduce a semi-parametric exponential tilting model that captures the missingness propensity. To address this, we propose three convolution smoothing-based estimators for quantile regression: inverse probability weighting (IPW), estimation equation imputation (EEI), and augmented IPW (AIPW). These estimators provide consistent estimates for quantile regression coefficients, utilizing the framework of empirical likelihood. We establish theoretical results regarding the asymptotic normality of the three quantile regression estimators, as well as the chi-square property of the corresponding adjusted logarithmic empirical likelihood ratios. Furthermore, we conduct numerical simulations to evaluate the finite-sample performance of these estimators, demonstrating their robustness. To further illustrate the effectiveness of the proposed methods, we apply them to HIV-CD4 data. This application allows us to investigate the differential impact of missing data mechanisms across treatment groups and explore the influence of baseline and previous CD4 and CD8 cell levels on current CD4 cell levels.

摘要 在分位回归的响应变量存在不可忽略缺失的情形下,本文引入半参数指数倾斜模型刻画应答概率, 在此基础上提出 3 种卷积平滑分位数回归估计方程: 逆概率加权 (inverse probability weighting, IPW)、估计方程插补 (estimation equation imputation, EEI) 和增强逆概率加权 (augmented IPW, AIPW), 并在经验似然框架下得到倾斜参数和分位回归系数的估计量. 本文在理论上证明3种分位回归估计量等价的渐近正态性和对应调整对数经验似然比函数的渐近χ2性质. 数值模拟比较上述估计量的有限样本表现,验证估计量的稳健性. 本文所提出的方法被应用于CD4(clusterofdifferentiation 4) 数据分析,考察不同治疗组中缺失机制的差异以及基线和前期的CD4和CD8细胞水平对当期CD4细胞水平的影响.