Multiple decrement modeling in various censoring and masking contexts

本课题的研究范围具有创新性、实践性和应用的广泛性。该程序的主要目的是将B.Turnbull(Cornell)的单变量生存函数的经典自洽和非参数最大似然估计(NPMLE)推广到多个减量的平台。此外，在新提出的模型中，将保留掩蔽的可能性(其中一些可能的故障模式可以作为特定观测的潜在候选者而被排除)和删减的存在(其中没有准确地观察到故障时间)。与迄今文献中发现的任何以前的模型不同，将开发的迭代算法将完全是数据驱动和无分布的，足够灵活地处理掩蔽故障模式的任何组合。这些算法提供了每个竞争风险的累积关联函数或相关的单一风险生存函数的估计器。此外，在研究计划的每一步，都将对模型进行许多改进。除了开发可以在许多不同的审查和掩蔽方案(如区间截断数据、信息掩蔽等)以及不同的模型假设(如相关竞争风险)存在的情况下发挥作用的模型外，还将对模型进行核心修改。借鉴W.J.布劳恩(西部)、T.Duschesne(Laval)和J.Stafford(多伦多)在单变量设置下所做的工作，通用算法将以一系列方式进行增强，最显著的是在收敛、精度和效率方面。简而言之，这项研究的结果将在精算学以及任何其他遇到多次递减失败的领域，如生物统计学或工程学中得到广泛应用。

The scope of this research program is innovative, practical, and far-reaching in its application. The primary thrust of the program is to generalize the classic self-consistent and nonparametric maximum likelihood estimators (NPMLE's) of the univariate survival functions of B. Turnbull (Cornell) to the plateau of multiple decrements. In addition, the possibility of masking (where some of the possible failure modes can be eliminated as potential candidates for a particular observation) and the presence of censoring (where the time-to-failure is not observed exactly) will be retained in the new proposed models. The iterative algorithms that will be developed, unlike any previous models found in the literature to date, will be exclusively data-driven and distribution-free, being flexible enough to handle any combination of masked failure modes. These algorithms provide estimators of either the cumulative incidence functions for each competing risk or the associated single risk survival functions. Furthermore, there will be many enhancements made to the models at each step of the research program. Apart from developing models that can function in the presence of many diverse censoring and masking schemes (such as interval-truncated data, informative masking, etc.), as well as different model assumptions (such as dependent competing risks), a kernel modification to the models will also be implemented. Drawing on the work of W.J. Braun (Western), T. Duschesne (Laval), and J. Stafford (Toronto) conducted in a univariate setting, the generalized algorithms will be enhanced in a litany of ways, most notably in the areas of convergence, accuracy, and efficiency. In short, the results from this research will find generous application in actuarial science, as well as any other field that encounters multiple decrement failures, such as biostatistics or engineering.