Dynamic Modeling of Recurrent Events and Its Applications

本项目将开发一些新的统计方法来研究复发性事件。提出这项研究的动机是需要为疟疾疫苗试验和其他生物计量学研究开发新的统计方法。所提出的统计方法可用于评估事件发生的危险因素，以及伴随变量、干预措施、过去历史对事件发生和事件类型的影响，以及不同类型事件之间的关联。所提出的研究在理论发展和统计计算上都具有挑战性。拟议的统计方法可促进对疟疾疫苗试验的分析，并有助于开发有效的疟疾疫苗，以控制和消除疟疾。概述研究的发展将丰富了解事件历史的统计工具集合，并有助于克服医疗和公共卫生等方面的挑战。研究生资助将用于疟疾控制理论的研究。本研究旨在建立循环事件的非参数和半参数动态模型，以改进现有的循环事件统计方法。提出了统计方法来建模和评估事件发生的风险因素，以及伴随变量、干预措施和事件历史如何影响事件的发生和事件类型。新的统计方法也被提出来调查不同类型事件之间的关联。这项拟议的研究的动机是分析疟疾疫苗效力试验所产生的挑战，并在生物医学、可靠性和经济学等其他领域提出了应用。本文的研究包括两个部分。第一部分对事件发生的动态变系数强度模型进行了研究，介绍了三种模型：非参数动态变系数强度模型、半参数动态变系数强度模型和多类型重复事件的动态模型。第二部分提出了对不同类型复发事件之间的关联进行建模和评估的研究。基于似然原理和局部线性平滑技术对非参数动态变系数强度模型进行估计。剖面估计方法将用于半参数动态变系数强度模型。我们将研究具有科学意义的推理程序。大样本理论将发展为提出的估计和假设检验程序。提出了一种两阶段估计方法来估计循环事件过程的条件速率函数模型，其中在第一阶段估计边缘半参数模型，在第二阶段估计速率比模型。提出了研究各种模型的条件费率比。新的统计方法、理论和计算算法将得到发展。拟议的统计方法可促进对疟疾疫苗试验的分析，并有助于开发有效的疟疾疫苗，以控制和消除疟疾。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop some novel statistical methods for the recurrent events. The proposed research is motivated by the need to develop new statistical methodology for the malaria vaccine trial and other biometrical researches. The proposed statistical methods can be used to assess the risk factors of event occurrences, how the occurrences of events and event types are affected by concomitant variables, intervention, the past history, as well as the associations among different types of events. The proposed research is challenging in theoretical development and in statistical computation. The proposed statistical methods can facilitate the analysis of the malaria vaccine trial and contribute to develop efficacious malaria vaccines toward control and elimination of malaria. The development of the outlined research would enrich a collection of statistical tools for understanding the event histories and contribute to the efforts to overcome the medical and public health challenges and beyond. The graduate student support will be used for research on the theory of malaria control. The research aims to develop nonparametric and semiparametric dynamic models for the recurrent events that will advance the existing statistical methods for recurrent events. The statistical methods are proposed to model and assess the risk factors of event occurrences, how the occurrences of events and event types are affected by concomitant variables, interventions, and the event history. New statistical methods also proposed to investigate the associations among different types of events. The proposed research is motivated by the challenges arising from analyzing the malaria vaccine efficacy trialand has broach applications in other fields such as biomedical, reliability and economics. The proposed research includes two parts. The research for the dynamic varying-coefficient intensity models of event occurrences is described in Part I which introduces three models: the nonparametric dynamic varying-coefficient intensity model, the semiparametric dynamic varying-coefficient intensity model, and the dynamic models for multiple type of recurrent events. Research for modeling and assessing the associations among different types of recurrent events is proposed in Part II. The nonparametric dynamic varying-coefficient intensity models will be estimated based on the likelihood principle and the local linear smoothing technique. The profile estimation approach will be utilized for the semiparametric dynamic varying-coefficient intensity models. The inference procedures that are of scientific interest will be investigated. Large sample theory will be developed for the proposed estimation and hypothesis testing procedures. A two-stage estimating procedure is proposed to estimate the models for the conditional rate function of the recurrent event processes where the marginal semiparametric models are estimated in the first stage and the models for the rate ratio are estimated in the second stage. Studies are proposed to investigate a variety of models for the conditional rate ratio. New statistical methods, theory and computational algorithms will be developed. The proposed statistical methods can facilitate the analysis of the malaria vaccine trial and contribute to develop efficacious malaria vaccines toward control and elimination of malaria.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.