非递进多状态复发事件数据统计建模及变量选择

Multi-state recurrent event processes arise frequently in a wide range of applied areas such as clinical trials, financing and banking research, industry and human behavioral research. Traditionally most studies have focused on progressive multistate processes which are either completely ordered or at least irreversible. The motivation of this project is to assist analyzing data for a couple observation study which aim to detecting the underlying patterns in the behaviors of couple interactions and identify the factors that can significantly alter these patterns. It involved non-progressive multi-state recurrent event process. A general framework for non-progressive multi-state models and an associated model selection methodology have not been studied yet in the literature. The challenges in establishing such a framework come from the untraceable multivariate joint distribution of the gap times. Also several known issues such as the non-identifiability problem, dependence among the gap times, and the induced dependent censoring are to be addressed for the non-progressive models. In this project, a class of new marginal conditional models for the transition-specific gap times will be proposed on one hand allowing arbitrary dependence among the gap times and on the other hand resolving the bias introduced by the induced dependent censoring. The corresponding estimation methods will be given and the asymptotic property of the proposed estimators are expected to be studied using the empirical process theory. Also high dimensional model selection methods based on penalized imputed-pseudo likelihood methods will be study. The property of these penalties are expect to be detected and proved.

多状态复发事件过程数据在临床医学、行为学等领域研究中经常遇到。传统的研究大多集中在递进的多状态过程。然而，实际问题中多个状态间的转换是非递进的情况更为常见。非递进多状态复发事件的状态转移过程本身也是随机的，状态转移间隔时间的联合分布难以获得。关于非递进的多状态复发事件模型及其相关的变量选择方法的研究很少，且多基于马尔科夫性假设。本项目拟对非递进多状态复发事件过程在非马尔科夫相依下建立几类新的条件边缘模型，包括：Cox形式的常系数模型、变系数模型；加速失效时间常系数模型、变系数模型；带脆弱变量的联合模型等。进而，提出相应的估计方法、证明理论性质，同时将建议模型与惩罚似然方法相结合研究变量选择方法及相关理论性质。该项目的研究既有重要的理论意义，又有广泛的应用价值。

多状态模型是描述纵向生存资料十分常见的模型，用于对个体在有限多个不同离散状态间逗留及转换的连续时间随机过程进行建模。这种模型在实际中有着非常广泛的应用背景。相关模型和方法可用于预测贷款违约风险问题、工业生产中自动化生产线的变点问题、人类行为学中研究人类交往中的基本模式、在心理学研究中可以研究心理状态、情感等的变化过程及其影响因素等等。本项目主要研究非递进多状态复发事件的一类状态转移重复发生的间隔时间建模问题,目的是尽可能捕捉到非递进多状态复发事件过程重要的或是感兴趣的特征，以满足预测及进一步的研究需要，同时提出有效的参数估计方法并给出估计的渐近性质等理论结果。进一步丰富和发展了非递进多状态复发事件过程的统计分析方法和理论。其中，Cox形式的常系数特定状态转移模型，采用逆概率剖面插值伪似然的方法给出模型参数估计并给出大样本理论性质，得到较好效果；针对协变量与时间有关的问题提出的变系数模型更加适用性，采用样条、局部多项式等方法给出参数估计；类似的方法也被用于加速失效时间常系数模型、变系数模型、带脆弱变量的联合模型等，提出相应的估计方法、证明理论性质，同时将建议模型与惩罚似然方法相结合研究变量选择方法及相关理论性质。该项目的研究既有重要的理论意义，又有广 泛的应用价值，能为实际工作者提供有力分析方法和工具。