Multiple decrement modeling in various censoring and masking contexts

本研究项目的范围具有创新性、实用性和深远的应用意义。该程序的主要推力是将B. Turnbull （Cornell）的单变量生存函数的经典自一致和非参数最大似然估计（NPMLE’s）推广到多重递减的平台。此外，在新提出的模型中，屏蔽的可能性（其中一些可能的失效模式可以作为特定观测的潜在候选而被消除）和审查的存在（其中未准确观察到失效时间）将被保留。将要开发的迭代算法，与迄今为止在文献中发现的任何模型不同，将完全是数据驱动和无分布的，足够灵活，可以处理任何隐藏故障模式的组合。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。此外，在研究计划的每个步骤中将对模型进行许多增强。除了开发可以在许多不同的审查和屏蔽方案（如间隔截断数据，信息屏蔽等）以及不同的模型假设（如依赖竞争风险）存在下运行的模型之外，还将实现对模型的内核修改。借鉴W.J. Braun（西方）、T. Duschesne（拉瓦尔）和J. Stafford（多伦多）在单变量环境下进行的工作，广义算法将以一系列方式得到增强，最显著的是在收敛、准确性和效率方面。简而言之，这项研究的结果将广泛应用于精算科学，以及任何其他遇到多重递减失败的领域，如生物统计学或工程学。

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.