Actuarial Modeling of Competing Risks Under Various Dependence Structures

考虑到NSERC的主要目的是支持“正在进行的研究项目(具有长期目标)，而不是单一的短期项目或项目集合”，这项拨款提案旨在建立在现有的创新研究项目的基础上，该项目能够对精算和统计学科做出重大额外贡献--不仅在学术文献中，而且在精算师、统计学家和其他人的日常工作中。到目前为止，我的主要研究领域一直集中在开发一整套完全非参数的算法，我称之为自洽竞争风险(SC-CR)算法，作为对故障时间分布建模的一种方式。*按照我到目前为止完成的研究计划的总体轨迹，目前的提案代表着该计划的下一个阶段，主要是为了将统计相关性的维度纳入SC-CR算法。尽管我们到目前为止提出的模型在精算师和其他人遇到的许多情况下都有充分的应用，但在实践中，它们确实倾向于严重依赖统计独立性的假设。为了更实际地发挥作用，通常是非常强有力的假设的独立性假设将需要放松。依赖可以通过许多不同的方式表现出来：依赖掩蔽、依赖审查、掩蔽和审查之间的依赖、递减之间的依赖等等。我们将考虑不同的方法来建模依赖，最显著的是使用Copula理论。将有意识地努力使关联函数的估计器保持非参数，或尽可能接近这一点。简而言之，将在本研究计划中开发的模型通过提供能够对竞争风险数据进行建模的非参数模型来弥补文献中的显著空白，同时允许对可能性进行审查、掩蔽和相关性。*随着这些相关性模型的理论结果的出现，将需要大量的统计模拟。统计属性，如一致性(不要与上面提到的自我一致性属性混淆)、非参数最大似然和无偏性，都应该得到验证。我特别计划利用硕士学生的帮助来执行研究计划的各种计算方面的工作，就像我过去所做的那样，作为进一步推进HQP培训的一种方式。此外，由于大多数方案编制预计将使用统计软件R执行，因此也有可能创建和/或促成一个R统计包，然后可供从业人员使用。随着每一种相关性模型的建立和估计者的统计属性的确立，结果可以传播给更广泛的精算界和统计界。*****

Mindful of NSERC's principle aim of supporting, "ongoing programs of research (with long-term goals) rather than a single short-term project or collection of projects", this grant proposal is designed to build upon an already existing innovative research program that is capable of significant additional contributions to the actuarial and statistical disciplines --- not only in the academic literature, but also in the day-to-day work of actuaries, statisticians, and others. To date, my main area of research has centered on developing a whole class of fully nonparametric algorithms, which I have called Self-Consistent Competing Risks (SC-CR) Algorithms, as a way to model failure time distributions. ******Following the overall trajectory of my research program accomplished so far, the current proposal, representing the next phase in the program, is primarily designed to incorporate the dimension of statistical dependence into the SC-CR Algorithms. Although the models we have proposed to date have ample application to many circumstances encountered by actuaries and others, in practice they do tend to rely heavily on the assumption of statistical independence. To be of even more practical use then, the independence assumption, which is often a very strong assumption, will need to be relaxed. Dependence can be manifested in many different ways: dependent masking, dependent censoring, dependence between masking and censoring, dependence between decrements, etc. Different approaches to modeling dependence will be considered, most notably with the use of copula theory. A conscious effort will be made to keep the estimators of the incidence functions nonparametric, or as close to this as possible. In short, the models that will be developed in this research program address a significant void in the literature by providing nonparametric models capable of modeling competing risks data while allowing for the possibility censoring, masking, and dependence.******As the theoretical results of each of these dependence models emerges, a significant amount of statistical simulation will be warranted. Statistical attributes such as consistency (not to be confused with the property of self-consistency mentioned above), nonparametric maximum likelihood, and unbiasedness should all be verified. I especially plan to utilize the aid of Master's students to execute various computational aspects of the research program, as I have done in the past, as a way to further advance HQP training. Furthermore, since most of the programming is anticipated to be implemented with the statistical software R, there is also the possibility of creating, and/or contributing to, an R statistical package that can then be used by practitioners. As each of the dependence models are developed, and the statistical attributes of the estimators established, the results can then be disseminated to the wider actuarial and statistical communities. *****