生存分析中的子群分析

How to confirm and quantify the treatment (e.g., new therapy) effect is often the primary objective of a randomized clinical trial and otherwise statistical applications. Sophisticated statistical methods yield the final result (positive or negative) of the trial that is a conclusion with respect to the average treatment effect on the entire study population. However, it is frequently encountered that a treatment may be quite effective for some subset of a population, but mildly effective, ineffective, or even harmful for others. Different magnitudes of treatment effects among the entire population would eventually classify it into several pieces; each piece is called a subgroup. Its identification is of critical importance. On the other hand, as responses of interest, the right censored survival times of some subjects make the identification challengeable in the clinical trial. It is eager to develop statistical methods tailored to the subgroup analysis in survival analysis (SASA). Novelly taking different views respectively from the penalty function, the latent variable, the threshold effect, and the interaction effect, this proposal will offer deep insight into SASA. It aims to systematically establish the identification and evaluation methods for subgroups by employing and developing modern statistical theory and techniques, and comprehensively describe the effect mechanisms of treatment on the survival times within each subgroup. Remarkably, the output of this proposal will afford investigators the solid theoretical basis and methodological guidance, based on which the clinical conclusions can be scientifically achieved.

如何科学地衡量某种处理(如新的治疗方法)的效应是临床试验以及其它统计应用中的首要问题。传统的统计分析方法通常衡量处理的相对于整个样本而言的平均效应。然而，在临床试验中通常发现处理对某些个体是有效的，而对其他个体的效用是不明显的，甚至是负面的。按照处理的效应的大小不同将把整个样本分为若干组；每一组被称为一个子群。因此，如何识别子群尤为重要。另一方面，作为响应变量，临床试验中个体的生存时间通常会发生删失；这使得子群的识别更具挑战性。生存分析中子群问题的统计分析方法亟待建立与发展。本项目创造性地从惩罚函数、潜在变量、门限作用以及交互作用四个不同的角度对生存分析中子群问题深入地进行研究，采用和发展现代统计理论与技巧，系统地建立子群的识别与评估的统计方法，科学而全面地刻画在每个子群中处理对生存时间的影响方式，从而为临床试验者提供理论基础与方法指导。

本项目主要围绕高维生存数据的子群分析问题进行研究。受本项目的资助，我们提出了基于高维变量分组和样本量分组的模型平均方法，建立了其最优性准则；讨论了不同时间区间的点过程的强度函数出现突变的现象，建立了变点检测的相合性；探讨了存在应答和不应答两种类型的样本的统计建模问题，建立了样本识别和模型参数的统计推断方法；研究了生存数据下超高维变量的筛选方法，建立了筛选方法的相合性。此外，本项目还研究了其他统计方法与应用问题。这些工作大部分都已经在统计学和机器学习领域的主流刊物上正式发表，少量处于审稿阶段。申请者的研究表明，本项目提出的统计分析方法是可行的，可为临床试验者的数据分析提供理论保障与应用支持。