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 paper 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.

翻译：删失分位数回归已成为理论统计学与应用统计学中经典Cox比例风险模型或加速失效时间模型的重要替代方法。尽管分位数回归在右删失生存数据中已得到广泛研究，但生存分析文献中针对区间删失数据的分析方法仍十分有限。本文提出一种新颖的局部加权方法用于估计线性删失分位数回归，特别适用于处理多种形式的区间删失生存数据。回归参数的估计方程及相应的凸目标函数可构建为两个区间端点处分位数损失贡献的加权平均。权重分量采用局部核平滑或集成机器学习技术进行非参数估计。为估计区间删失数据的非参数分布质量，通过引入个体特异性潜在泊松变量，采用改进的非参数极大似然估计EM算法。通过大量模拟研究与两项HIV/AIDS数据集的真实数据分析，验证了所提方法的实证性能。