Actuarial Modeling of Competing Risks Under Various Dependence Structures

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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.