Statistical Methods for Analyzing Incomplete Lifetime Data

拟议的研究计划旨在开发先进的统计方法，对涉及医学研究、社会科学和系统可靠性中可能出现的潜在过程的事件历史数据进行建模。这些主题建立在我过去的研究经验和最近的文献发展基础上。 第一个主题的研究将考虑长度偏向样本中协变量不完全的数据分析中的问题。在递进多状态马尔可夫过程的研究中，由于进入给定状态的延迟，自然会出现截断数据。大型队列研究可能导致故障时间数据被截断和聚集。多个死因的竞争风险模型和涉及多个过程的半竞争风险模型，其中一个过程可能会审查其他过程，这两者都可能导致截断数据。我计划开发方法来解决参数估计中的挑战，在这种情况下，当事件时间被截断时，样本协变量分布涉及生存分布的参数。 第二个主题的研究是关于需要解决的反复事件过程的分析。我计划使用随机效应来解释移动-滞留模型中的其他异质性，并建立丰富的混合模型，以联合分析事件时间被观测或间隔删失时的重复事件、解决过程和死亡率。将开发具有动留结构的竞争风险模型，以确保正确估计风险函数和协变量影响。我还计划构建灵活的模型来处理临时解析，允许在间歇观察下进入终止状态之前在不同状态之间转换。 第三个主题的研究将探讨观察性研究中的因果推断，在观察性研究中，治疗分配因影响治疗选择和反应预测的潜在混杂因素而不平衡。我计划解决在处理混淆的方法中丢失协变量数据的挑战。这些方法将在半参数加速失效时间模型和附加风险模型的框架下开发，因为COX比例风险假设可能不成立。 建议的研究集中于开发创新的统计方法，通过使用基于似然的技术和推理来处理某些不完整数据问题。这将有助于通过计算有效的方法进行点估计和方差估计，并验证估计量的理论性质。它将提供新的理解和有价值的成果，这将有利于统计方法的发展和在多个领域的应用。它还有望激发研究生和大四本科生的兴趣，并为他们提供大量机会，让他们参与、培训和启发新的研究想法。

The proposed research program aims to develop advanced statistical methods to model event history data involving latent processes that can arise in medical research, social sciences and system reliability. The topics build on my past research experience and recent developments in the literature. Research in the first theme will consider issues in data analysis with incomplete covariates in length-biased samples. Truncated data naturally arise in studies of progressive multi-state Markov processes due to the delayed entry to a given state. Large cohort studies can result in truncated and clustered failure time data. Competing risk models for multiple causes of death and semi-competing risk models involving multiple processes in which one process may censor the others may both result in truncated data. I plan to develop methods to address the challenges in parameter estimation where the sample covariate distribution involves parameters of the survival distribution when event times are truncated. Research in the second theme is on the analysis of recurrent event processes subject to resolution. I plan to use random effects to account for other heterogeneities in a mover-stayer model and build enriched mixture models to jointly analyze the recurrent events, resolution processes and mortality when event times are either observed or interval-censored. Competing risk models with a mover-stayer structure will be developed to ensure that the hazard functions and the covariate effects are correctly estimated. I also plan to construct flexible models to handle the temporary resolution, allowing transitions between different states before entering the terminating state under intermittent observations. Research in the third theme will look into causal inference in observational studies where treatment allocations are unbalanced by potential confounders affecting the treatment selection and prediction of the response. I plan to address the challenge of missing covariate data in methods for dealing with confounding. The methods will be developed in the framework of semiparametric accelerated failure time models and additive hazards models, as Cox proportional hazards assumptions may not hold. The proposed research focuses on developing innovative statistical methods to handle certain incomplete data problems by using likelihood-based techniques and inferences. It will shed light on point and variance estimation via computational effective methods and verify the theoretical properties of the estimators. It will provide new understandings and valuable results that will benefit both statistical methodology development and applications in multiple areas. It is also anticipated to stimulate interests of both graduate students and senior undergraduate students and provide abundant opportunities for them to get involved, trained and inspired for new research ideas.