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）和截尾分位数回归（QR）模型是对截尾数据的经典线性和无截尾QR模型的对应，是对cox比例风险模型的补充。特别是截尾QR，通过允许跨事件时间分布的非恒定协变量效应，丰富了截尾数据的线性模型分析。其他回归方法不恰当地将协变量效应约束为常数，无法提供一致的结果。相比之下，截尾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，但对其他病例的治疗效果为正。然而，AFT和删节QR模型没有得到充分利用，因为不存在灵活和通用的估计、变量选择和推理方法。这项研究包括开发(A)灵活的估计方法，在不像现有方法那样严格的条件下工作，(B)变量选择方法，包括高维数据，以及(C)与未审查情况平行的一般经验似然（EL）方法。此外，本研究的总体思路和方法虽然是在随机权利审查机制下发展起来的，但也适用于截断或其他审查类型。改进预测医疗结果的统计模型一直是统计研究的重要组成部分。由于最近高通量技术的进步，大量潜在有用的信息，包括患者的基因谱，是可用的，并有望导致大大改进预测。提出的研究探讨了新的方法，将这些数据纳入建立更好的统计模型，以更准确地预测患者的生存。要研究的模型类型也更复杂：它们不仅可以预测“平均”人的生存，还可以预测“前10%”或“后10%”，同时允许生存受到基因谱的不同影响。

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.