Joint Models for Longitudinal and Time-to-Event Data

该提案的主要重点是开发统计方法，以量化时间相关协变量与特定关注事件发生前的时间之间的关联。例如，研究关键单元的可靠性对于保证工程应用中系统的整体功能能力至关重要。在这样的研究中，目的是评估单元的退化信号是否与整个系统的故障风险显著相关。在这些研究中遇到的一个常见问题是，时间依赖性协变量（例如，降解信号）的测量通常存在误差，并且在分析中未能考虑这种误差导致协变量与事件发生时间之间的关联的有偏估计。分析这些类型数据的现代方法涉及两个独立的模型：一个模型考虑了时间依赖协变量中的测量误差以估计其真实值（纵向模型），另一个模型使用这些估计值来量化该协变量与事件发生时间之间的关联（事件时间模型）。联合建模技术背后的激励思想是将时间-事件模型与纵向模型耦合起来。标准方法是考虑时间依赖协变量的线性模型（即，纵向响应）和用于关联分析的相对风险模型。然而，在某些情况下，需要更灵活的技术来适当地建模这两个过程。我将强调标准方法无法适当处理的三个主要主题，需要进一步的方法发展。第一个主题考虑的情况下，时间到事件的过程涉及一系列的事件，需要一个多状态的相对风险模型来表征状态/事件之间的转换。第二个主题考虑的情况下，纵向轨迹表现出两个线性阶段之间的过渡，使线性假设不成立。第三个主题涉及两个或两个以上的纵向二元响应，需要考虑它们之间的内在关联，以调查它们对事件发生时间的影响。我的长期目标是开发纵向和时间事件数据的联合建模方法。这将通过三个短期目标来实现，每个目标都涉及适合博士生的新统计方法。事实上，我的研究旨在创新统计方法，涉及理论和计算，以及在自然科学中的应用。学生的参与和培训，以帮助完成这一建议的目标是相当重要的。所有学生将接受培训，开始走向研究生涯或鼓舞人心的就业。

The main focus of this proposal is to develop statistical methodologies to quantify the association between a time-dependent covariate and the time until an event of particular interest occurs. For example, investigating the reliability of a critical unit is crucial to guarantee the overall functional capabilities of a system in engineering applications. In such a study, the aim is to evaluate whether the degradation signal of the unit is significantly associated with the risk of failure of the entire system. One common problem encountered in such studies is that the time-dependent covariate (e.g., degradation signal) is often measured with error, and failure to account for such error in the analyses leads to a biased estimate of the association between the covariate and the time to the occurrence of the event. The modern approach to analyze these types of data involves two separate models: a model that takes into account the measurement error in the time-dependent covariate to estimate its true values (longitudinal model), and another model that uses these estimated values to quantify the association between this covariate and the time to the occurrence of the event (time-to-event model). The motivating idea behind the joint modeling techniques is to couple the time-to-event model with the longitudinal model. The standard approach is to consider a linear model for the time-dependent covariate (i.e., the longitudinal response) and a relative risk model for the association analysis. However, there are situations where more flexible techniques are required to appropriately model these two processes. I will emphasize three main topics which the standard approach cannot properly handle, and requires further methodological development. The first topic considers situations where the time-to-event process involves a sequence of events for which a multi-state relative risk model is required to characterize the transitions among the states/events. The second topic considers situations where the longitudinal trajectories exhibit a transition between two linear phases, so that the linearity assumption does not hold. The third topic involves two or more longitudinal binary responses for which the inherent association between them needs to be taken into account to investigate their effects on the time to the occurrence of the event. My long-term goal is to develop methods for joint modeling of longitudinal and time-to-event data. This will be pursued via three short-term objectives, each of which involves novel statistical methods appropriate for PhD students. In fact, my research aims at innovative statistical methods, which involve both theory and computation, and applications in natural sciences. The participation and training of students to help complete the objectives of this proposal is quite important. All students will be trained to get started toward a research career or inspiring employment.