Semiparametric inference of survival data

在Cox比例风险回归模型中，我们开发了建立可信区间和区间的方法来检测治疗的时变效应。Sundaram博士和她的合作者已经解决了统计推断的需要，在比标准Wald类型(基于正态近似)的可信区间/频带提供更紧密的区间的置信度区间和置信度区间中，统计推断是必要的。这项工作推广了Tian，Zucker和魏(2005，JASA)的结果，并表明所提出的区间/带比Tian，Zucker和魏提出的区间/带更紧。这是通过局部偏似然平滑为随时间变化的回归系数建立经验似然(EL)逐点置信域来实现的。建立了所提方法的渐近性质。大量的数值研究表明，EL逐点/同时置信域/带比Wald型估计器具有更好的性能。所提出的方法在两个真实的例子上进行了说明：胃癌数据和梅奥诊所原发性胆汁性肝硬变数据在更精确(更窄)的可信区间(带)上显示了相似的结果。 另一个项目开发了随机截断数据的方法，当研究设计是回溯性的和/或由于实验设计无法在事件开始之前捕获研究参与者时，经常会遇到这些数据。例如，孕妇是根据她们第一次去妇科医生确认怀孕而被选中的，导致失去了对早孕丢失妇女的随访。基于随机截尾数据的估计变得非常具有挑战性，因为随时间变化的风险集是非单调的，这使得它与随机右截尾截尾非常不同。Sundaram博士解决的问题之一是为这类数据的两个样本加速故障时间数据开发稳健的推断。桑达拉姆博士还开发了稳健的方法来分析随机截断数据的比例优势模型。当风险随时间收敛时，比例优势模型为比例风险提供了一种有用的替代方案(例如，对成功的治疗进行建模)。建立了估计量的渐近正态和强相合性等大样本性质，并通过大量的模拟研究了有限样本性质，表明了其良好的性能。所提出的方法很容易计算，这与基于似然估计的情况不同，因为它不可能像对比例风险和右删失数据所做的那样来描述非参数(基线优势函数)。

We developed methods to build confidence interval and bands to detect time-varying effects of treatments in Cox's proportional hazards regression model. Dr. Sundaram and her collaborators have addressed in the need for statistical inference which in confidence intervals and confidence bands which give more tighter intervals than the standard Wald-type (normal approximation based) confidence intervals/band. This work extended the results of Tian, Zucker and Wei (2005, JASA) and shows that the proposed intervals/bands are tighter than those proposed by Tian, Zucker and Wei. This was achieved by developing empirical likelihood (EL) point-wise confidence regions for the time-dependent regression coefficients via local partial likelihood smoothing. Asymptotic properties were established for the proposed methods. Extensive numerical studies conducted indicated that the EL point-wise/simultaneous confidence regions/bands have better performance than the Wald-type estimators. The proposed methods illustrated on two real examples: the gastric cancer data and the Mayo Clinic primary biliary cirrhosis data showed similar findings of more precise (narrower) confidence intervals (bands). Another project developed method for randomly truncated data which are frequently encountered when the study design is retrospective and/or due to inability of experimental design to be able to capture the study participant before the initiation of the event. For example, pregnant women get selected based on their first visit to the gynecologist for confirming their pregnancy, resulting in loss to follow up of women who had early pregnancy loss. Estimation based on randomly truncated data becomes very challenging as the risk set over time is non-monotonic, making it very different from random right censoring. One of the problems addressed by Dr. Sundaram is developing robust inference for two sample accelerated failure time data for this type of data. Dr. Sundaram has also developed robust methods for analyzing proportional odds model for randomly truncated data. Proportional odds model provides a useful alternative to proportional hazards when the hazards converge over time (e.g., for modeling treatments that are successful). The large sample properties like asymptotic normality and strong consistency of the proposed estimators were established and the finite sample properties investigated through extensive simulations indicating good performance. The proposed methods are easy to compute, which is not the case with likelihood based estimators as it is not possible to profile out the non-parametric (baseline odds function) as is done with proportional hazards and right censored data.