Semiparametric Models, Methodologies and Related Theory for Analysis of Censored Survival Data

本项目涉及与截尾生存数据的半参数回归模型、方法和理论相关的问题。研究人员和他的合作者的目标是开发比例风险混合治愈模型回归参数的半参数有效估计量。将该方法推广到另一类半参数曲线模型。他们提出了一类在医学和计量经济学文献中常见的混合变换模型，并通过估计方程和一些非参数平滑技术来研究它们。此外，他们还计划建立基于边际线性变换模型的多变量失效时间数据估计方程，并提出一类带协变量调整的多变量失效时间数据的独立性检验。他们还导出了从病例队列设计中分析生存数据的相对简单的方法，并讨论了通过投影法进行更有效的参数估计。这里研究的统计学问题的动机是生物医学、工程科学、社会学、经济学和遗传学的应用。该项目开发了适当的统计模型、推理方法和数学理论。这些结果可用于设计临床试验和流行病学研究，特别是在癌症、心血管疾病的研究中，分析工程可靠性和市场渗透率数据，在调整一些环境因素后，评估由于不可测量的影响(如家族遗传效应)而导致的失败次数之间的关联。

This project addresses issues related to semi-parametric regression models, methods and theories with censored survival data. The investigator and his collaborators aim to develop semi-parametric efficient estimators of the regression parameters for the proportional hazards mixture cure model. The approach is extended to another class of semi-parametric cure models. They propose a general class of mixture transformation models, which are common in medical and econometrics literature, and study them via estimating equations as well as some nonparametric smoothing techniques. In addition, they plan to develop estimating equations for multivariate failure time data based on marginal linear transformation models and propose a class of independence tests for multivariate failure time data with the adjustment of covariates. They also derive relatively simple method for analysis of survival data from case-cohort design and discuss more efficient parameter estimation via the projection method. The statistical problems studied here are motivated by applications in biomedical sciences, engineering sciences, sociology, economics and genetics. The project develops appropriate statistical models, inferential methods and mathematical theory. The results can be used to facilitate design of clinical trials and epidemiological studies, particularly in studies of cancer, cardiovascular diseases, to analyze engineering reliability and market penetration data, to assess the association among failure times due to unmeasured effects, such as familial genetic effects, after adjusting some environmental factors.