Functional Censored Quantile Regression

We propose a functional censored quantile regression model to describe the time-varying relationship between time-to-event outcomes and corresponding functional covariates. The time-varying effect is modeled as an unspecified function that is approximated via B-splines. A generalized approximate cross-validation method is developed to select the number of knots by minimizing the expected loss. We establish asymptotic properties of the method and the knot selection procedure. Furthermore, we conduct extensive simulation studies to evaluate the finite sample performance of our method. Finally, we analyze the functional relationship between ambulatory blood pressure trajectories and clinical outcome in stroke patients. The results reinforce the importance of the morning blood pressure surge phenomenon, whose effect has caught attention but remains controversial in the medical literature. Supplementary materials for this article are available online.

本文提出功能删失分位数回归模型（functional censored quantile regression model），用以刻画事件发生时间结局与对应功能协变量间的时变关联。该研究将时变效应建模为一类未指定形式的函数，并通过B样条（B-splines）对其进行近似。本文开发了广义近似交叉验证方法，通过最小化期望损失以选择样条节点数量，并推导了所提方法及节点选择流程的渐近性质。此外，本文开展了大量模拟实验，以评估所提方法的有限样本表现。最后，本文针对脑卒中患者的动态血压轨迹与临床结局间的功能关联展开实证分析，分析结果印证了晨间血压骤升现象的重要性——该现象的效应已受到学界关注，但目前医学文献中对此仍存在争议。本文的补充材料可在线获取。