Interval-Censored Linear Quantile Regression

Censored quantile regression has emerged as a prominent alternative to classical Cox’s proportional hazards model or accelerated failure time model in both theoretical and applied statistics. While quantile regression has been extensively studied for right-censored survival data, methodologies for analyzing interval-censored data remain limited in the survival analysis literature. This article introduces a novel local weighting approach for estimating linear censored quantile regression, specifically tailored to handle diverse forms of interval-censored survival data. The estimation equation and the corresponding convex objective function for the regression parameter can be constructed as a weighted average of quantile loss contributions at two interval endpoints. The weighting components are nonparametrically estimated using local kernel smoothing or ensemble machine learning techniques. To estimate the nonparametric distribution mass for interval-censored data, a modified EM algorithm for nonparametric maximum likelihood estimation is employed by introducing subject-specific latent Poisson variables. The proposed method’s empirical performance is demonstrated through extensive simulation studies and real data analyses of two HIV/AIDS datasets. Supplementary materials for this article are available online.

删失分位数回归（Censored quantile regression）已在理论与应用统计学领域，成为经典考克斯比例风险模型（Cox’s proportional hazards model）与加速失效时间模型（accelerated failure time model）的主流替代方案。此前针对右删失生存数据的分位数回归研究已较为充分，但现有生存分析文献中，面向区间删失数据的分析方法仍相对有限。本文提出一种全新的局部加权方法，用于估计线性删失分位数回归模型，该方法专门适配各类形式的区间删失生存数据。该回归参数的估计方程与对应凸目标函数，可构造为区间两个端点处分位数损失贡献的加权平均形式。权重分量通过局部核平滑或集成机器学习技术完成非参数估计。为估计区间删失数据的非参数分布质量，本文引入个体特异性潜在泊松变量，采用改进的EM算法实现非参数极大似然估计。通过大规模模拟实验与两项HIV/AIDS数据集的真实数据分析，验证了所提方法的实证表现。本文的补充材料可在线获取。