Empirical Likelihood and Censored Quantile Regression

经验似然和截尾分位数回归

• 批准号: 0604920
• 负责人: Mai Zhou
• 金额: --
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604920&HistoricalAwards=false
• 关键词: Empirical; Likelihood; Censored; Quantile; Regression

This project is concerned with the development of statistical methodologies in the regression analysis of censored data that can model both the average and extreme responses. The investigators will develop a novel empirical likelihood (EL) approach for the accelerated failure time (AFT) model and censored quantile regression. Empirical likelihood is a recently developed nonparametric inference method with asymptotic properties similar to the parametric maximum likelihood. The novel EL approach uses sample points casewise and is less stringent than previously proposed residual based empirical likelihood: the sample points are not required to be identically distributed, and a more general form of heteroscedasticity is permitted. An interesting application of the proposed approach is to censored quantile regression. While quantile regression has appeared as an alternative to the least squares with uncensored data as it provides more complete information about the conditional distribution of the response, its application to censored data has been limited due to the lack of an efficient inference method, among other reasons. The proposed EL approach will advance quantile analysis in censored regression and extend the domain of EL inference in general.The proposed research is of high federal strategic interest because the results will accelerate many health, medical, and economic research projects where data is incomplete and abnormal cases rather than the average are of interest, such as low birth weight, high ozone concentration, cancer survival rates, or high yield stock, among others. Traditional analyses focus on the center of the data and implicitly assume that the results found for the average group are generalizable to the entire patient group. However, this is usually not the case. For example, an investigator in a survival study of cancer patients may find that certain molecular biomarkers are prognostic factors only for those ovarian cancer patients who die exceptionally early compared to others in the same reference group. The quantile regression technique with the proposed inference procedure permits the investigation of the biomarkers without constraining their effects for different subpopulations to be same as for the average group. Therefore, the proposed method can better inform health professionals of the effects of physiological and molecular biomarkers on different subpopulations and provide a useful prognostic tool for the overall and progression free survival times.

该项目涉及发展对删失数据进行回归分析的统计方法，这种方法可以模拟平均和极端反应。研究人员将为加速失效时间（AFT）模型和删失分位数回归开发一种新的经验似然（EL）方法。经验似然法是近年来发展起来的一种非参数推断方法，具有类似于参数极大似然法的渐近性质。新的EL方法使用样本点casewise和不太严格比以前提出的基于残差的经验似然：样本点不需要是同分布的，和一个更一般形式的异方差是允许的。一个有趣的应用所提出的方法是删失分位数回归。虽然分位数回归已经出现作为一种替代最小二乘与未经审查的数据，因为它提供了更完整的信息的条件分布的响应，其应用已被限制，由于缺乏一个有效的推理方法，除其他原因。建议的EL方法将推进删失回归中的分位数分析，并扩展EL推断的领域。建议的研究具有高度的联邦战略利益，因为其结果将加速许多健康，医学和经济研究项目，其中数据不完整，异常情况而不是平均情况，如低出生体重，高臭氧浓度，癌症存活率，或高收益股票等等。传统的分析集中在数据的中心，并隐含地假设平均组的结果可推广到整个患者组。然而，通常情况并非如此。例如，在癌症患者的生存研究中，研究人员可能会发现某些分子生物标志物仅对那些与同一参考组中的其他人相比死亡特别早的卵巢癌患者是预后因素。分位数回归技术与建议的推理程序允许调查的生物标志物，而不限制其影响不同的亚群是相同的平均组。因此，所提出的方法可以更好地告知卫生专业人员生理和分子生物标志物对不同亚群的影响，并为总体和无进展生存时间提供有用的预后工具。