Nonparametric Bayesian Methods for Joint Analysis of Recurrent Events and Survival Time

该研究项目将开发灵活的统计模型，用于联合分析复发事件和生存时间。在长期随访研究中，受试者可能多次经历复发事件，其中对受试者特异性复发事件的观察在研究结束时终止，或出现死亡等终末事件。涉及此类数据结构的科学相关问题在生物医学科学以及计量经济学和工程学中普遍存在。分析此类数据的一个关键问题是，复发事件的历史和最终事件的风险是相互关联的。因此，联合建模潜在的随机机制是很重要的，通常，在存在预测变量的情况下，这些预测变量预计会影响复发事件的发生和生存时间。该项目的一个关键目标是通过开发新的统计模型，放宽最先进方法的限制性假设，扩大现有技术的推断和预测范围，以联合分析复发事件和生存时间。为了方便研究人员和实践者使用这些方法，将开发可公开使用的软件来实施若干统计模型。该项目将为研究生创造教育和研究培训机会，并设法促进妇女和代表性不足的群体参与研究。该研究项目将开发通用贝叶斯建模方法，用于联合分析复发事件和生存时间。建模框架建立在生存反应的贝叶斯非参数混合Erlang分布的基础上，协变量效应比比例风险回归模型更灵活。通过将非参数生存回归建模方法与协变量相关的重复事件点过程强度的参数模型相结合，将制定不同类别的联合模型。联合模型将捕获复发事件和生存过程之间的一般依赖性，同时允许受试者之间的异质性。主要目标是开发一个全面的联合建模框架，相对于最先进的共享脆弱性建模方法，该框架显著改善了模型拟合和预测性能。在生存反应的回归建模的背景下，该项目还将扩展贝叶斯非参数的新兴领域的方法。该研究项目在研究各种模型的理论性质方面具有实质性的分析成分，以及在实现计算可处理的模型拟合方面具有重要的计算成分。新方法的实际效用将通过模拟研究和涉及癌症患者数据分析的应用进行调查。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 research project will develop flexible statistical models for joint analysis of recurrent events and survival time. In long-term, follow-up studies, subjects may experience a recurrent event at multiple times, where the observation of subject-specific recurrent events is terminated by end of the study, or a terminal event such as death. Scientifically relevant problems involving such data structures are prevalent in the biomedical sciences, as well as in econometrics and engineering. A critical issue in analyzing such data is that the history of the recurrent events and the risk of terminal event are interrelated. It is thus important to jointly model the underlying stochastic mechanisms, typically, in the presence of predictor variables that are expected to affect the occurrence of recurrent events and the survival time. A key objective of this project is to expand the inferential and predictive scope of existing techniques for joint analysis of recurrent events and survival time by developing novel statistical models that relax restrictive assumptions of state-of-the-art methods. To facilitate use of the methods by researchers and practitioners, publicly available software will be developed for implementing several of the statistical models. The project will create educational and research training opportunities for graduate students and seek to foster the participation of women and underrepresented groups in the research.This research project will develop general Bayesian modeling approaches for joint analysis of recurrent events and survival time. The modeling framework builds from Bayesian nonparametric mixtures of Erlang distributions for the survival responses, with covariate effects accommodated more flexibly than proportional hazard regression models. Different classes of joint models will be formulated by combining the nonparametric survival regression modeling methods with parametric models for the covariate-dependent recurrent event point process intensities. The joint models will capture general dependence between the recurrent event and survival processes, while allowing for heterogeneity between subjects. The primary objective is to develop a comprehensive joint modeling framework that significantly improves on model fit and predictive performance relative to the state-of-the-art shared frailty modeling methods. In the context of regression modeling for survival responses, the project will also expand the methodology in the burgeoning field of Bayesian nonparametrics. The research project has a substantial analytic component with regards to study of theoretical properties for the various models, as well as a significant computational component with regards to achieving computationally tractable model fitting. The practical utility of the new methods will be investigated with simulation studies and through applications involving analysis of data from cancer patients.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.