Multiple decrement modeling in various censoring and masking contexts

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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.