Joint Models for Longitudinal and Time-to-Event Data

这项建议的主要重点是制定统计方法，以量化依赖时间的协变量与发生特别感兴趣的事件之前的时间之间的联系。例如，在工程应用中，研究关键单元的可靠性对于保证系统的整体功能能力至关重要。在这样的研究中，目的是评估机组的退化信号是否与整个系统的故障风险显著相关。在这种研究中遇到的一个常见问题是，依赖于时间的协变量(例如，退化信号)的测量通常带有误差，并且在分析中没有考虑到这种误差导致对协变量与事件发生的时间之间的关联的偏向估计。分析这些类型数据的现代方法涉及两个独立的模型：一个考虑时间依赖协变量中的测量误差以估计其真实值的模型(纵向模型)，以及另一个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的模型(时间到事件模型)。联合建模技术背后的激励思想是将事件间隔时间模型与纵向模型相结合。标准方法是考虑时变协变量(即纵向响应)的线性模型和关联分析的相对风险模型。但是，在某些情况下，需要更灵活的技术来适当地对这两个流程进行建模。我将强调标准方法不能正确处理的三个主要问题，需要进一步的方法学发展。第一个主题考虑了事件发生时间过程涉及一系列事件的情况，对于这些事件，需要使用多状态相对风险模型来表征状态/事件之间的转变。第二个主题考虑了纵向轨迹在两个线性阶段之间呈现过渡的情况，因此线性假设不成立。第三个专题涉及两个或更多纵向二元反应，需要考虑它们之间的内在联系，以调查它们对事件发生前时间的影响。我的长期目标是开发纵向数据和事件间隔时间数据的联合建模方法。这将通过三个短期目标来实现，每个短期目标都涉及适合博士生的新统计方法。事实上，我的研究目标是创新统计方法，包括理论和计算，以及在自然科学中的应用。学生的参与和培训有助于完成这项提案的目标，这是相当重要的。所有学生都将接受培训，开始从事研究或鼓舞人心的就业。

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.