Collaborative Research: Extension of Quantile Regression and Empirical Likelihood Analysis for Censored Data

线性模型分析因其结果可直接解释而成为最具吸引力的统计方法之一。加速失效时间(AFT)和删失分位数回归(QR)模型是经典的线性和非删失QR模型的对应模型，是Cox比例风险模型的补充。尤其是，删失QR通过允许跨事件时间分布的非常数协变量效应，丰富了删失数据的线性模型分析。其他回归方法不适当地将协变量效应限制为恒定的，无法提供一致的结果。相比之下，经审查的QR允许对更严重的病例(无事件生存时间较短)的治疗效果为负，但在其他情况下为正。然而，AFT和删失QR模型作为灵活和通用的估计方法没有得到充分的利用，不存在变量选择和推断。这项研究包括发展(A)灵活的估计方法，其在比现有方法更宽松的条件下工作；(B)变量选择的方法，包括高维数据；(C)平行于未删失情况的一般经验似然(EL)方法。此外，所提出的研究和方法的总体思想也适用于截断或其他截尾类型，尽管它们是在随机右截尾机制下发展的。改进用于预测医疗结果的统计模型一直是统计学研究的重要部分。由于最近高通量技术的进步，大量潜在有用的信息，包括患者的基因图谱，都是可用的，并有望导致更好的预测。这项拟议的研究探索了新的方法，将这些数据纳入到建立更好的统计模型中，以更准确地预测患者的生存。待研究的模型类型也更为复杂：它们不是只预测一个“平均”人的存活率，而是允许预测“最高的10%”或“最低的10%”，同时允许存活率受到基因图谱非常不同的影响。

Linear models analysis is one of the most appealing statistical methods for its directly interpretable results. The accelerated failure time (AFT) and censored quantile regression (QR) model serve counterparts of the classical linear and uncensored QR model for censored data, and complement the Cox-proportional hazards model. Censored QR, in particular, enriches linear models analysis for censored data by allowing non-constant covariate effects across the distribution of event times. Other regression methods unduly constrain the covariate effects to be constant and fail to provide consistent results. In contrast censored QR allows the treatment effect to be negative for more severe cases (with shorter event-free survival times) but positive in other cases. The AFT and censored QR model are, however, under-utilized as flexible and general methods for estimation, variable selection and inference do not exist. This investigation includes developing (A) flexible estimation methods that work under less stringent conditions than those for existing methods, (B) methods for variable selection, including high dimensional data, and (C) general empirical likelihood(EL) methods parallel to uncensored case. In addition, the general ideas of the proposed research and method developed are applicable to truncation or other censoring types, although they are developed under random right censoring mechanism.Improving statistical models for predicting medical outcomes is always an important part of statistical research. Thanks to recent advancement in high throughput technologies, a vast amount of potentially useful information, including patient's gene profile, is available and anticipated to lead to much improved prediction. The proposed study investigates novel methods to incorporate those data in building a better statistical model to more accurately predict a patient survival. The type of models to be investigated are also more sophisticated: instead of predicting only an "average" person's survival, they allow prediction for "top 10%, or "bottom 10%", while allowing the survivals can be very differently impacted by the gene profile.