Nonparametric Maximum Likelihood Estimators for Multivariate Distributions and Related Inference Problems with Various Types of Censored Data

多元分布的非参数最大似然估计以及各种类型截尾数据的相关推理问题

• 批准号: 1407461
• 负责人: Jian-Jian Ren
• 金额: $ 12万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1407461&HistoricalAwards=false
• 关键词: Nonparametric; Maximum; Likelihood; Estimators; Multivariate

In the analysis of multivariate survival data, we frequently encounter the situation where one or more components of a vector are not completely observable due to censoring. One common type of such data is when the survival time is subject to various types of censoring, and the covariate variables, such as treatments, gender, etc., are completely observable. Data examples of this type have been encountered in important medical research on bone marrow transplant, breast cancer, AIDS research, heart disease, etc. Another common type of censored survival data occurs when both components of the random vector are survival times that are subject to univariate or bivariate right censoring. Data examples of such type have been encountered in medical studies on skin grafts and kidney disease. The objective of this project is to study the empirical likelihood-based nonparametric maximum likelihood estimator (NPMLE) for multivariate distribution function with various types of censored multivariate survival data and to provide solutions and theoretical understanding of several important nonparametric and semi-parametric inference problems in survival analysis. The statistical methodology developed in this project will provide tools for multivariate survival data analysis, which has direct impact to medical research, epidemiology, and social and behavioral sciences. It is well-known that nonparametric distribution estimator of that of random vector X based on multivariate survival data is of great importance, because it provides tools to study the relation among the components of X and plays vital roles in modeling and testing, etc. It is also known that to study the effects of covariate Z on survival time T under semi-parametric model assumptions, such as linear models, the Cox model, accelerated life model, etc., the estimators under the model setting often can be expressed as statistical functional of the distribution estimator, thus the asymptotic properties of these estimators can be studied via the differentiability of these statistical functionals and the asymptotic properties of distribution estimators. However, most existing estimators with above mentioned survival data are ad hoc, and are not likelihood-based in the usual sense. Also, most of them either contain negative probability masses, or are kernel and bandwidth dependent. Since Owen (1988), the empirical likelihood function has been generally accepted as the nonparametric likelihood function. The essential idea of empirical likelihood-based NPMLE ensures that it is a proper multivariate distribution function, which is desirable in practice. But, the empirical likelihood-based NPMLE for aforementioned multivariate survival data had not been carefully considered in literature until a recent paper by the PI of this project, in which she discovered many surprisingly nice properties of the bivariate NPMLE with censored survival data, and studied its asymptotic properties for discrete covariate Z. In this proposed empirical likelihood, weighted empirical likelihood, asymptotic methods and simulations will be mainly used, and the issues under consideration include: (a) Derivation of empirical likelihood-based NPMLE for various types of censored multivariate survival data; (b) Computation algorithms and asymptotic properties of the resulting NPMLE; (c) Derivation and asymptotic properties of the statistical functionals under several important semi-parametric survival models. This project will provide a general methodology for constructing the multivariate distribution estimators with various types of censored multivariate survival data, which generally possesses desirable properties, and will provide solutions to several important and challenging statistical inference problems associated with some widely used survival models.

在对多元生存数据的分析中，我们经常遇到由于审查而无法完全观察到的一个或多个成分的情况。这种数据的一种常见类型是，生存时间受到各种类型的检查，而协变量变量（例如治疗，性别等）是完全可观察到的。在骨髓移植，乳腺癌，艾滋病研究，心脏病等的重要医学研究中，这种类型的数据示例已遇到单变量或双变量右审查。这种类型的数据示例已在有关皮肤移植物和肾脏疾病的医学研究中遇到。该项目的目的是研究基于经验可能性的非参数最大似然估计器（NPMLE），用于多元分布功能，具有各种审查的多变量生存数据，并提供了对几种重要的非参数和半参数性问题的解决方案和理论理解生存分析。该项目中开发的统计方法将为多元生存数据分析提供工具，该数据对医学研究，流行病学以及社会和行为科学有直接影响。众所周知，基于多元生存数据的随机向量X的非参数分布估计值非常重要，因为它提供了研究X组件之间关系的工具，并在建模和测试中起着至关重要的作用。还知道，在半参数模型假设下研究协变量Z对生存时间t的影响，例如线性模型，COX模型，加速寿命模型等，模型设置下的估计器通常可以表示为统计分布估计量的功能，因此可以通过这些统计功能的不同性和分布估计量的渐近性质来研究这些估计值的渐近性能。但是，大多数具有上述生存数据的现有估计量都是临时的，并且在通常的意义上不是基于可能性的。同样，其中大多数要么包含负概率质量，要么依赖于内核和带宽。自Owen（1988）以来，经验可能性功能普遍被认为是非参数可能性函数。基于经验可能性的NPMLE的基本思想确保它是适当的多元分布函数，在实践中是可取的。但是，直到该项目的PI最近的一篇论文，她才仔细考虑了基于经验的基于上述多元生存数据的NPMLE，在文献中，她发现了许多具有审查生存数据的双变量NPMLE的精美属性，并研究了。它用于离散协变量Z的渐近特性。将主要使用此拟议的经验可能性，加权经验可能性，渐近方法和仿真，所考虑的问题包括：（a）基于经验可能性的NPMLE的衍生。生存数据； （b）所得NPMLE的计算算法和渐近特性； （c）在几个重要的半参数存活模型下，统计功能的衍生和渐近特性。该项目将提供一种通用方法，用于构建具有多种审查的多元生存数据的多元分布估计量，这些数据通常具有理想的特性，并将为与某些广泛使用的生存模型相关的几种重要且具有挑战性的统计推断问题提供解决方案。