复发事件过程中混杂偏倚的调整和统计分析

Recurrent event data usually occur in long-term studies which concern recurrence rates of certain events. In some circumstances of these studies, subjects can only be observed at discrete time points rather than continuously and thus only the numbers of the events that occur between the observation times, not their occurrence times, are observed. This type of data can also be referred to as interval-censored recurrent event data, or panel count data. In panel count data, the observation times or process may differ from subject to subject and more importantly, and may contain relevant information about the underlying recurrent event process, therefore can be viewed as dependent observation process. Methods have been proposed for regression analysis of interval-censored recurrent event data, but most of the existing research focuses on situations where observation times are independent of longitudinal response variables given covariates. However, the independence assumption may not hold. Among others, some inference procedures were also proposed by incorporating observation history into the semiparametric regression models for recurrence event process. However, confounding bias may arise due to the dependence of observation process on covariates. That is, recurrent event process, observation times and covariates may mutually be correlated. Therefore, we propose semiparametric analysis and nonparametric tests of recurrent event process with adjusting for confounding effects caused by dependent observation process. In our approach, the observation filtration will be adjusted by parametric estimates of propensity scores using the idea of inverse probability weighting, to avoid any confounding bias produced. The results of this research will serve as new methodologies for analyzing interval censored recurrent event data with dependent observation process, without producing any confounding bias.

复发事件过程和观测过程是区间删失复发事件数据中两个重要的点过程，两者之间的相依性对复发事件率的研究起着至关重要的作用，是目前统计界对复发事件乃至一般纵向数据研究的热点之一。本项目主要应用倾向指数以及逆概率加权的方法对复发事件过程中的如下几个问题进行研究：复发事件过程中相依观测时间具有混杂效应的系统判定方法；相依观测过程对复发事件率的估计所造成混杂偏倚的调整；含有相依观测过程的复发事件过程建模和协变量效应的参数估计；估计方程的构造以及估计的相合性与渐近正态性的证明；相依观测过程下复发事件过程的非参数假设检验等，希望给出复发事件分析中相依观测过程所造成混杂偏倚的理论描述，设计出调整混杂偏倚的有效方法和步骤，完成调整混杂偏倚后复发事件过程的统计推断，为复发事件的理论研究提供有力的工具和支持。该研究亦可广泛地应用到生物学，医学，社会和经济学，工业可靠性等领域中，具有重要的现实意义和应用价值。

复发事件过程和观测过程是复发事件数据中两个重要的点过程，两者之间的相依性对复发事件的研究起着至关重要的作用，是目前统计界对复发事件乃至一般纵向数据研究的热点之一。本项目研究了含有治愈率的复发事件数据的半参数比率模型及相应的统计分析，有信息的观测时间及相关终止事件的面板计数数据的联合统计分析，带有时变协变量及有信息观测过程下面板计数数据的统计分析，工艺参数过程相关的统计分析， GINAR(p)过程的正则估计，基于零截尾泊松分布的二元INAR(1)模型，高维可加风险模型中加权LASSO的Oracle不等式及选择相合性，高维表观基因组研究中介效应的估计和检验，稀疏高维多元回归的正则估计，统计模拟中代表点的选择，以及基于互信息量和熵值的特征选择方法。通过本项目的研究，给出了复发事件分析中相依观测过程所造成混杂偏倚的理论描述，设计出了调整混杂偏倚的有效方法和步骤，完成了调整混杂偏倚后复发事件过程的统计推断，为复发事件的理论研究提供了有力的工具和支持。该研究亦可广泛地应用到生物学，医学，社会和经济学，工业可靠性等领域中，具有重要的现实意义和应用价值。