Quantile calculus and censored regression
分位数微积分与删失回归AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究删失条件下的分位数回归及随分位水平变化的协变量效应，因此归入分位数与分布效应方向。
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分位数微积分与删失回归
- 研究问题
- 研究删失时间未必可见且可能依赖协变量时，如何估计随分位水平变化的协变量效应，并避免算法复杂性与概率网格依赖。
- 方法与思路
- 作者在累积概率尺度上建立分位数微积分，通过积分估计方程构造删失分位数回归，并提出渐进局部最小化算法。
- 材料陈述的贡献
- 摘要称，该方法在特定情形退化为 Kaplan–Meier 或普通分位数回归，且在正则条件下具有一致性与高斯过程极限。
- 阅读关注点
- 读全文时应核对删失机制、正则条件与积分方程的定义，关注算法如何处理概率与时间尺度不能一一对应的情形。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；具体正则条件、算法复杂度及模拟结果未提供，不能判断一般删失情形下的适用性。
原文摘要
Quantile regression has been advocated in survival analysis to assess evolving covariate effects. However, challenges arise when the censoring time is not always observed and may be covariate-dependent, particularly in the presence of continuously-distributed covariates. In spite of several recent advances, existing methods either involve algorithmic complications or impose a probability grid. The former leads to difficulties in the implementation and asymptotics, whereas the latter introduces undesirable grid dependence. To resolve these issues, we develop fundamental and general quantile calculus on cumulative probability scale in this article, upon recognizing that probability and time scales do not always have a one-to-one mapping given a survival distribution. These results give rise to a novel estimation procedure for censored quantile regression, based on estimating integral equations. A numerically reliable and efficient Progressive Localized Minimization (PLMIN) algorithm is proposed for the computation. This procedure reduces exactly to the Kaplan-Meier method in the k-sample problem, and to standard uncensored quantile regression in the absence of censoring. Under regularity conditions, the proposed quantile coefficient estimator is uniformly consistent and converges weakly to a Gaussian process. Simulations show good statistical and algorithmic performance. The proposal is illustrated in the application to a clinical study.