混合半参数模型下生存数据的亚组分析

When the “personalized medicine” has been one of the hottest topics in this big-data era, subgroup analysis for survival data undoubtedly becomes an important subject in statistics. Currently there exist two frameworks for subgroup analysis: post-hoc framework and pre-hoc framework. In the post-hoc framework, the current literature for subgroup analysis with right censored data all assumed that there exist subgroups. However, much less attention has been paid to the more important topic of subgroup detection. Meanwhile, the models in post-hoc framework are usually complicated and difficult to interpret, being easily affected by the randomness in sample data. By contrast, the pre-hoc framework is more systematic from the perspective of methodology, but no much effort has been made in this area, with even less achievement for censored survival data. In this project, under the pre-hoc framework, we propose semiparametric mixture models for subgroup analysis. Specifically, we utilize the idea of EM test to develop testing procedure for subgroup detection and develop approach for subgroup estimation as well. The related large sample properties and the diagnostic methods are also explored. From the theoretical perspective, the research of this project will effectively complement the subgroup analysis techniques in the pre-hoc framework. Moreover, there is great potential for real applications. For instance, the subgroup analysis would help doctors to understand the disease nature so that reasonable personalized decision can be made.

当“精准医疗”已成为大数据时代最热门的话题之一时，对生存数据的亚组分析无疑成为统计学中重要的研究课题。目前亚组分析大致可以分成事后与事前两种分析框架。在事后框架下，现有对右删失持续时间数据的研究都假设亚组已经存在，而对于更为重要的亚组识别问题研究较少，且模型的复杂性偏高，解释性偏低，受数据的随机性影响也较大。在亚组分析的事前框架下，从方法论角度而言更加体系化，不过其现有成果相对于事后分析法要少得多，针对删失持续时间数据的研究成果几乎空白。本课题将在事前框架下构建半参数有限混合模型，利用EM思想构造识别亚组的检验方法、参数估计，讨论相应的统计性质及相关模型的诊断等。本项目的研究，在理论上将为有效填补事前框架下持续时间数据亚组分析技术的空白打下基础，在应用上空间很大，如：帮助医疗者理解疾病的本质，从而做出合理的差异化决策。

在个性化医疗、精准营销等领域，亚组分析是一个重要的话题。亚组分析包括亚组探测、亚组识别以及亚组估计等。从亚组分析的统计技术角度而言，混合模型是一种较为常用的分析技术。本项目主要考虑构建各类半参数混合模型，对于带有删失的持续时间数据进行亚组识别与亚组估计，并对模型中的参数进行统计推断。. 在本项目研究期间，项目负责人与团队成员依照项目计划开展研究工作，在一系列相关的研究课题中取得进展与成果。研究方面，项目团队考虑了基于线性变换模型与加速失效模型的混合模型，设计了相应的亚组识别检验方法，探索了亚组估计EM算法的性质，并推导了一些理论结果。项目团队也对半参数混合模型下EM算法和EM检验的性质进行了一些探索与研究。这些研究的主要思想和成果被应用于一些相关的研究中，所获得的研究成果发表在国际顶级统计学术期刊JASA、国际主流统计学术期刊TEST、Statistics & Probability Letters以及Journal of Applied Statistics上。人才培养方面，项目资金辅助了培养了博士研究生5人、硕士研究生2人。在项目资金的支持下，项目负责人与项目成员也多次参加国内外学术会议，报告研究成果，并与国内外同行进行了密切的互动与交流。