Empirical Likelihood and Censored Quantile Regression

该项目涉及在审查数据的回归分析中发展统计方法，可以对平均反应和极端反应进行建模。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。经验似然是最近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的渐近性质。新的EL方法使用样本点，并且比以前提出的基于残差的经验似然方法不那么严格：样本点不要求是同分布的，并且允许更一般形式的异方差。提出的方法的一个有趣的应用是删失分位数回归。分位数回归由于提供了关于反应的条件分布的更完整的信息，已经成为非删失数据的最小二乘的替代方法，但由于缺乏有效的推断方法等原因，它在删失数据中的应用受到了限制。建议的EL方法将推进删失回归中的分位数分析，并扩展EL推断的一般领域。建议的研究具有很高的联邦战略意义，因为其结果将加速许多健康、医学和经济研究项目，这些项目的数据不完整且异常情况而不是平均值感兴趣，例如低出生体重、高臭氧浓度、癌症存活率或高产量种群等。传统的分析集中在数据的中心，并隐含地假设针对平均组的结果可推广到整个患者组。然而，情况通常并非如此。例如，癌症患者生存研究中的一名研究人员可能会发现，某些分子生物标记物只对卵巢癌患者的预后有影响，这些患者比同一参照组中的其他人死亡得特别早。分位数回归技术与建议的推断程序允许调查生物标记，而不限制它们对不同亚群的影响与对平均群体的影响相同。因此，所提出的方法可以更好地让卫生专业人员了解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。

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.