Statistical Methods for the Analysis of Recurrent Events and Event History Data

基于单个事件发生的统计方法不足以全面理解具有复杂事件历史的事件过程的数据产生机制。因此，许多研究领域都需要设计用于分析重复事件和其他复杂事件历史的统计方法和模型。忽略事件流程过去的模型无法全面理解底层流程。动态模型是基于强度的随机过程模型，用于检查过去事件发生对过程当前或未来演变的影响。动态模型包括动态协变量，它本质上是内部时间相关的解释变量。动态协变量的固有性质及其与干预措施、治疗效果和异质性的复杂关系使得在存在动态协变量时建模和推理具有挑战性。另一个重要的问题是在事件历史设置中使用结果依赖研究设计。这种设计提供了一种经济有效的方法来分析事件历史数据。然而，在事件历史设置中存在许多方法论问题。该研究计划的总体目标是解决周期性事件和事件历史数据统计分析中的重要问题，其动机是工程和科学设置中对复杂模型和相关分析方法的需求。因此，我将探索动态模型和结果依赖的研究设计，用于复发事件和事件历史，并在各种设置中开发新的统计方法。在流行病学，医学和可靠性工程中出现的新兴方法和具有挑战性的问题激励了本研究计划。通过该计划开展的研究将对加拿大的重要应用领域产生直接影响。例如，所开发的新模型将有助于了解加拿大卫生服务中反复发生的事件，为卫生政策决策者提供具体证据，以改善护理活动和医院利用，并降低住院总费用。该研究的预期结果也将有利于加拿大的发电公司改善其可靠性计划，并确定其维护政策，从而最大限度地降低运营总成本，最大限度地提高可修复系统的可用性。

Statistical methods based on the occurrence of a single event are not adequate for a comprehensive understanding of data producing mechanisms of event processes with complex event histories. Therefore, statistical methods and models designed for the analysis of recurrent events and other complex event histories are needed in many fields of study. Models that ignore the past of an event process are incapable of comprehensive understanding of the underlying process. Dynamic models are intensity-based stochastic process models which are used to examine the effect of past event occurrences on the present or future evolution of a process. Dynamic models include dynamic covariates, which are essentially internal time-dependent explanatory variables. The inherent nature of dynamic covariates and their complex relations with interventions, treatment effects and heterogeneity make modelling and inference challenging issues when dynamic covariates are present. Another important issue is the use of the outcome-dependent study designs in event history settings. Such designs provide a cost-effective way to analyze event history data. However, there are many methodological problems in event history settings. The overarching goal of this research program is to address important issues in the statistical analysis of recurrent events and event history data, motivated by the need for complex models and related methods of analysis in engineering and scientific settings. Therefore, I will explore dynamic models and outcome-dependent study designs for recurrent events and event history, and develop novel statistical methods in various settings. Emerging methodological and challenging issues that arise in epidemiology, medicine and reliability engineering motivate this research program. Research carried out through this program will have direct impact on important application areas in Canada. For example, the developed novel models will be instrumental in understanding the recurrent event occurrences in health services in Canada, providing concrete evidence to decision-makers in health policy to improve care activities and hospital utilization, and to reduce the total hospitalization cost. The anticipated outcomes of the research will also be beneficial for power generation companies in Canada to improve their reliability programs and to determine their maintenance policies, which minimize the total cost of operation and maximize the availability of repairable systems.