Right Censorship Model and Doubly-Censorship Model Allowing Dependent Survival Time and Censoring Times

在标准右截尾(RC)模型下，研究了种群生存时间的累积分布函数的非参数极大似然估计(NPMLE)的性质。独立假设在应用中有时是不合理的。在这个项目中，引入了一个新的允许相依删失的RC模型。新的模型在许多应用中更加现实，包括在研究人员和他的合作者从事的后续研究中分析癌症患者的生存时间。在新模型下，PI计划建立实线上生存函数的NPMLE的渐近性质。还将研究允许双删失数据和其他类型的区间删失数据的依赖删失的新模型。右删失和双删失数据经常出现在工业实验和医学研究中。研究人员提出的新模型是出于癌症研究的需要，研究人员正在分析纪念斯隆-凯特琳癌症中心提供的某些乳腺癌数据。该项目的结果将有助于分析来自临床试验和工程可靠性研究的数据。理论结果将有助于生存分析统计理论的发展。

The properties of the non-parametric maximum likelihood estimator (NPMLE) of the cumulative distribution function (cdf) of the survival times of a population have been studied for a long time under the standard right censorship (RC) model, which assumes independent censoring. The independent assumption is sometimes not justified in applications. In this project a new RC model that allows dependent censoring is introduced. The new model is more realistic in many applications including the analysis of survival times of cancer patients in a follow-up study that the investigator and his collaborators are engaged in. Under the new model, the PI plans to establish the asymptotic properties of the NPMLE of the survival function on the real line. New models that allow the dependent censoring for doubly censored data and other types of interval-censored data will also be investigated. Right censored and doubly-censored data occur frequently in industrial experiments and medical research. The new models proposed by the investigator are motivated by the needs in the cancer research in which the investigator is analyzing certain breast cancer data provided by the Memorial Sloan-Kettering Cancer Center. The results from this project will be useful in the analysis of the data from clinical trials and engineering reliability studies. The theoretical results will contritute to the advancement of the statistical theory of survival analysis.