复发事件数据的删失分位数回归研究

Quantile regression offers desirable features of easy interpretation and great flexibility in assessing covariate effects on event times, thereby attracting considerable interests in its applications in survival analysis including recurrent event data analysis. However, currently there exists very limited research on developing methodology for analyzing recurrent event data with quantile regression models, extremely lacking for interval-censored recurrent event data. In this proposal, we investigate extending quantile regression to model counting processes arising from recurrent event data and thus lead to a broader regression framework of counting-based modeling which could facilitate the accommodation of various incomplete follow-up scenarios. The proposed martingale-based estimating equations naturally lead to a simple algorithm that involves minimizations of L1-type convex functions, which serves complementarily with another objective function optimization estimation investigated by generalizing the celebrated Powell’s estimator for censored quantile regression. Uniform consistency and weak convergence of the resultant estimators are established utilizing the tools of Glivenko-Cantelli theorem in weak convergence and empirical processes theory, coupled with probability inequalities for empirical processes, stochastic integrals of empirical-type processes, theory of monotone random fields, and production integration theory. For inference procedures, we target at proposing a sample-based covariance estimation procedure, which provides a useful complement to the prevailing bootstrapping approach. Besides aforementioned aspects of research, we accommodate and explore varying covariate effects by employing second-stage inference to serve the ends of summarizing the information provided by the estimators to help understand the underlying effect mechanism, which include but are not limited to robust estimation for some useful summaries of covariate effects, determining whether some covariates have constant effects, and evolving effects. The methodology this proposal establish would help broaden the area of quantile regression modeling methods and thus accelerate the techniques of applying them to analyze recurrent event data.

通过对复发事件数据进行删失分位数回归，可对复发时间条件分布的协变量效应进行更加广泛和细致的刻画。现有的复发事件数据分位数回归分析方法不仅数量极为有限，而且无法应对区间删失复发事件数据的情形。本项目针对复发事件数据，建立基于计数过程的删失分位数回归模型。通过构造目标函数或估计方程，将系数估计转化为目标函数或L1型凸函数的优化问题。借助经验过程理论、经验过程随机积分理论、乘积型积分理论、单调随机域理论等工具，研究所得回归估计在不同分位点处的一致强相合性与弱收敛性等大样本性质。实现基于Bootstrap重抽样估计模拟分布的渐近方差近似估计或基于工作估计方程求解渐近方差显式估计，并进行有关的二级推断，寻找平均协变量效应的稳健估计，检验协变量在特定分位数范围内效应的显著性以及常数效应假定，进一步总结协变量效应机制。本项目是对分位数回归理论的完善和复发事件数据分析技术的推动，具有重要的理论和应用价值。

项目主要对复发事件数据统计推断及相关的数据科学问题进行研究。复发事件数据分析方面的主要研究内容以及取得的进展包括复发事件数据在相依观测过程下的倾向指数加权半参数模型及统计推断、针对复发事件数据基于含治愈个体的半参数比率模型经验似然统计推断、在信息删失的情况下对双变量当前状态数据进行回归分析的vice copula方法的研究、针对随机缺失协变量几种基于逆概率加权和基于重加权的区间删失数据的估计方法的研究、区间删失数据的同时估计和变量选择、不完全事件史的同时估计和变量选择、集群式区间删失失效时间数据的稳健半参数转换混合效应模型、复发间隔时间的半参数风险回归模型、可用于连续协变量的区间删失数据的线性转换模型、当前状态数据在半参数线性转换模型下的稀疏估计等。数据科学方面的主要研究内容以及取得的进展包括算术优化算法与Golden Sine算法结合的混合算术优化算法（HAGSA）、用于全局优化和图像分割任务的改进的远程优化算法（MROA）、用于解决物联网领域恶意软件分类问题的算法、结合多尺度融合与注意力机制的头颈部肿瘤放疗计划中危及器官图像分割方法、改进䲟鱼优化算法并结合熵测度的图像多阈值分割方法、融合哈里斯鹰与正弦波策略的阿奎拉鹰优化算法、基于强化学习的出价策略优化算法、基于准反射的学习方法来增强的改进SMA算法（QRSMA）、基于残差和注意力机制的U-Net的头颈部医学图像危险器官分割方法、处理高维Android恶意软件分类任务的半监督学习算法等。