Some New Developments in Competing Risks Models -- Extensions and Applications

在本项目中，研究者研究了竞争风险模型的扩展，以允许连续的竞争风险，其中失败的原因被替换为仅在未删失的失败时间观察到的连续标记变量，及其在HIV疫苗有效性研究中的应用。研究者开发标记特异性比例风险模型的统计方法，允许回归参数非参数依赖于标记，基线风险非参数依赖于时间和标记。这项研究的动机是需要评估HIV疫苗的有效性，同时考虑到试验参与者感染HIV病毒与疫苗中所含HIV毒株的差异，并调整协变量效应。疫苗有效性用标记特异性比例风险模型中的一个回归函数表示。该研究也可以应用于其他医学研究。研究了当标记变量为双线性/连续、单变量/多变量时，标记特异性比例风险模型及其在疫苗有效性试验中的应用。它是在病例队列设计下研究的，其中一些协变量可能仅在样本的一个子集中观察到。研究了半参数标记特异性比例风险模型。关于标记特定危害函数的统计程序自然扩展了已开发的用于离散标记竞争风险数据和单一失效原因失效时间数据的方法的范围。 由于特定于标记的相对风险不仅衡量给定标记的终点事件发展的相对风险，而且还取决于对标记的不同暴露，因此在解释它们时需要谨慎。为了允许更大的灵活性，考虑直接建模的条件风险函数的故障时间给定的标记和协变量。 对新方法进行了理论验证、仿真验证和应用于HIV疫苗有效性试验，研究了经典竞争风险模型的扩展和新应用。本研究的目的是开发统计学上有效的和生物学上可解释的方法来评估和获得有效的HIV疫苗。统计方法的理论依据非常具有挑战性。通过这些研究，可以在竞争风险模型理论及其应用方面取得重大进展。本研究开发的方法将用于分析从HIV疫苗有效性试验中收集的数据，并为开发更有效的疫苗提供有用的输入。这里提出的问题的研究也将产生许多适合研究生和本科生学习的不同层次的研究课题，从而促进学生参与当前科学的研究。

In this project, the investigator studies an extension of the competing risks model to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark variable only observed at the uncensored failure times, and its applications in the HIV vaccine efficacy studies. The investigator develops statistical methods for the mark-specific proportional hazards model, allowing the regression parameters to depend nonparametrically on the mark and the baseline hazard to depend nonparametrically on both time and mark. This research is motivated by the need to assess HIV vaccine efficacy, while taking into account the divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. The vaccine efficacy is expressed in terms of one of the regression functions in a mark-specific proportional hazards model. The research can find applications in other medical researches as well. The mark-specific proportional hazards model and its applications to vaccine efficacy trials is investigated when the mark variable is dsicrete/continuous and univariate/multivariate. It is studied under the case-cohort designs where some of the covariates may only be observed for a subset of the sample. The semiparametric mark-specific proportional hazards model is also studied. The statistical procedures concerning the mark-specific hazards functions naturally extend the scope of methods that have been developed for competing risks data with discrete marks and for failure time data with single cause of failure. Since the mark-specific relative risks measure not only the relative risks of developing the end-point event given the marks, but also depend on differential exposure to the marks, one needs to be careful in their interpretations. To allow for greater flexibility, direct modeling of the conditional hazard function of failure time given the mark and covariate is considered. The new methods are justified theoretically, evaluated in simulations and applied to the HIV vaccine efficacy trials.The investigator studies an extension and new applications of the classical competing risks model. The goal of the reseach is to develop statistically efficient and biologically interpretable methods for evaluating and achieving efficacious HIV vaccines. The theoretical justifications for the statistical methods are very challenging. By pursuing this research, significant progress could be made in the theory of competing risks models and its applications. The methods developed in this research will be used to analyze the data collected from the HIV vaccine efficacy trials and provide useful input for developing more effective vaccines. The research of the problems proposed here will also generate many research topics at different levels suitable for graduate and undergraduate studies, therefore promotes involvements of students in the research of current sciences.