Saddlepoint Approximations for Survival Analysis

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Re: NSF DMS-9704570 Saddlepoint Approximations for Survival Analysis Snehalata V. Huzurbazar University of Wyoming The primary goal of this research is to develop saddlepoint approximations to survival and hazard functions used for bio-medical data or alternatively, approximations to reliability functions used for engineering data. Modelling of survival data results in complicated waiting times whose exact distributions are intractable but they can be approximated using saddlepoint methods. The latter are based on `higher-order' asymptotic methods and yield extremely accurate approximations for density and distribution functions which can then be combined to give approximate survival and hazard functions. The methodology is extremely computer-intensive due to the nature of the calculations. Survival analysis is primarily concerned with the modelling of waiting time distributions arising from various scenarios. The investigator studies models for linear as well as acyclic progression of diseases, models for competing risks, models with feedback for cyclic behaviour as well as frailty models for populations which are heterogeneous. Due to the complexity of the distributions that describe waiting time behaviour in these situations, conventional methods are restricted to models which mainly use the exponential distribution. Use of saddlepoint methods removes this restriction, yielding much more flexibility in modelling. The above models are tremendously useful in studying the progression of various diseases. For example, progression of the HIV virus is mainly from one stage to the next; but in some cases, patients can skip stages and also get better before getting worse. Progression of diseases is also studied using frailty models, that is, situations in which the whole population does not have the same risk for a disease. For example, certain subgroups are more susceptible to diabetes than other subgroups, or subpopulations may have different ri sks due to exposure to different environmental factors. Again, modelling the progression of a disease in the different subgroups can lead to fairly complicated models which tax currently used methodology but can be handled using saddlepoint methods. Finally, the methods obtained from this research are easily transferred into reliability models used in engineering and manufacturing.