Statistical Methods for Repeated Events

作为一名统计学家，我开发了新的统计方法来改进研究的设计和分析，在许多项目上合作，并进一步培训HQP。虽然我的提案的主题是由真实的管理数据（即，常规收集的数据主要用于研究以外的目的，我的方法可以应用于许多学科领域，如生物科学和工业，收集大型数据集，研究对象可能会随着时间的推移发生多个事件（甚至可能有多种类型）。我的研究建议的主要目标是：（A）制定一个多变量聚类检测方法，（B）开发马尔可夫和半马尔可夫模型，调整变量删失和粗化，和（C）模拟随时间变化的系数效应的经常性事件数据。统计方法的发展和审查是重要的科学努力，以确保从数据分析中得出的结论是正确的，错误的发现不会扩散。 对于目标（A），我想开发一些方法，可以检测不同类型事件的地理聚集。地理数据的统计分析在许多领域都很重要，我计划的贡献将使用户能够及时确定汇总。例如，这项研究的结果对于监测任何地理系统都很重要，例如森林中不同昆虫的侵扰或全省的医疗索赔。 目标（B）关注相关数据的不同方面，其中数据可能随时间推移连续观察到受试者集合，并且可能存在事件的确切时间未知或删失的情况（即，事件未被观察到）。我将在马尔可夫和半马尔可夫模型中加入这种粗化数据的复杂性。所开发的方法将影响对某些关键时间不完整的数据的分析，并且应该比其他方法偏差更小。用我的新方法，得出的结论将是有效的，粗化数据的不便将被克服。这些方法上的进步对于任何粗化数据的分析都是必不可少的。 随着计算机性能的进步，模拟研究已成为评估统计方法的关键工具。仅当生成的数据具有适当的属性时，评估才有效。对于复杂的数据结构，数据的生成可能不是微不足道的。目标（C）将侧重于生成复发事件数据，其额外复杂性是协变量将与时间无关，但这些协变量的系数估计值将与时间相关。这项创新对我自己的研究调查很重要，也将帮助自然科学和工程领域的其他人对这类数据进行模拟研究。

As a statistician, I develop novel statistical methods to improve the design and analysis of studies, work collaboratively on many projects, and further the training of HQP. While my proposal features topics that are motivated by real administrative data (i.e., routinely collected data primarily assembled for purposes other than research), my methodology could be applied to many subject areas, such as biological sciences and industry, where large datasets are collected and study subjects may have multiple events over time (perhaps even with multiple types). The main objectives of my research proposal are to: (A) formulate a multivariate cluster detection method, (B) develop Markov and semi-Markov models that adjust for variable censoring and coarsening, and (C) simulate recurrent event data with time-varying coefficient effects. The development and examination of statistical methods are important scientific endeavours to ensure that the conclusions reached from the analysis of data are correct and that false findings are not proliferated. For Objective (A), I want to develop methods that will allow for the detection of geographic aggregations of different types of events. The statistical analysis of geographic data is important in many fields and my planned contributions will enable users to identify aggregations in a timely manner. For example, the results of this research would be important for monitoring any system over geography such as infestations of different insects in a forest or medical claims across a province. Objective (B) focuses on a different aspect of correlated data where data may be continuously observed over time for a collection of subjects and there may be instances when the exact times of events are unknown or censored (i.e., event is unobserved). I will incorporate the complexity of this coarsened data in Markov and semi-Markov models. The methods developed will impact the analysis of data that are incomplete for some key times and should be less biased than other methods. With my new methods, the conclusions drawn will be valid and the inconvenience of coarsened data will be overcome. These methodological advances are essential for any analysis of coarsened data. With advances in computer performance, simulation studies have become a key tool for the assessment of statistical methods. The assessment can only be valid if the generated data generated have the appropriate properties. With complicated data structures, the generation of data may not be trivial. Objective (C) will focus on generating recurrent event data with the additional complexity that the covariates will be time-independent but the estimates of the coefficients for these covariates will be time-dependent. This innovation will be important for my own research investigations and will also assist others in the natural sciences and engineering wanting to perform simulation studies for this type of data.