An eigenfunction approach to multivariate and high-dimensional survival analysis

多变量和高维生存分析的特征函数方法

• 批准号: RGPIN-2016-05722
• 负责人: Sen, Arusharka
• 金额: $ 1.09万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=709649
• 关键词: eigenfunction; approach; multivariate; dimensional; survival

Survival analysis is the study of so-called time-to-event data, and typically multivariate survival data arise either as parallel data, where one tries to observe times to events of interest (such as disease onset, death, failure) for several related individuals (such as family members, organs of human body, components of a system), or serial data, where a series of successive events are tracked (such as stages of a disease), or possibly as a combination of these two schemes. Often time to event data is combined with high-dimensional covariates, such as information on genetic markers available from gene expression data. Two major sources of complication in time to event data are random censoring, whereby certain events cannot be observed due to insufficient followup, and random truncation, whereby an event can be observed only if it occurs after a threshold event (such as a disease occuring after age at beginning of study). For univariate survival data (i.e., when only one individual or component is being tracked) subject to random censoring and truncation, there exist two famous, and by now classical, estimation procedures called Kaplan-Meier and Lynden-Bell estimators, respectively. These estimates are widely applicable since they were derived without any parametric model assumption. Moreover, a host of statistical procedures for such data, such as studying effects of covariates on the time to event, can be developed based on these estimators. Unfortunately, no satisfactory multivariate versions of the latter were available until now. Consequently, statisticians were forced to rely on restrictive model assumptions in order to analyze censored or truncated multivariate survival data. For instance, effects of covariates on survival times were studied under the assumption that the former were not subject to censoring or truncation. Recently, my co-author and I have constructed a multivariate Kaplan-Meier estimator under random censoring, which shares all the nice practical and theoretical properties of its univariate counterpart. In fact, our method is dimension-free, in that one needs to solve the same equation in any dimension, and it produces the classical univariate estimator when applied to univariate data. The main goal of the present project is precisely to extend the procedure to multivariate censoring-cum-truncation and a more complicated semi-censoring model, both of which are of great importance in survival studies. Just like the univariate Kaplan-Meier and Lynden-Bell estimators our new method too has the potential to generate a wealth of inference procedures for multivariate survival data, and we propose to explore them systematically. In particular, we shall study high-dimensional covariates in a much more general set-up than has been attempted so far. In addition to opening up a new line of research, our project has immense possibilities for training graduate students.

生存分析是对所谓事件时间数据的研究，通常多变量生存数据要么是平行数据，即试图观察几个相关个体（如家庭成员、人体器官、系统组成部分）感兴趣的事件（如疾病发作、死亡、衰竭）的时间，要么是串行数据，即跟踪一系列连续事件（如疾病的阶段），或者可能是这两种方案的组合。通常，事件发生时间数据与高维协变量相结合，例如从基因表达数据中获得的遗传标记信息。事件数据在时间上出现并发症的两个主要来源是随机审查，即由于随访不足而无法观察到某些事件，以及随机截断，即只有在阈值事件之后才可以观察到事件（例如在研究开始时年龄之后发生的疾病）。