Dynamic Algorithms for Time-to-Event Processes
Edgar R. Mendoza Mentor: Emmanuel Appiah Department of Mathematics and Department of Chemical Engineering Introduction: In the survival and reliability data analysis, parametric and nonparametric methods are applied to estimate the hazard/risk rate and survival functions [4, 6]. A parametric approach assumes that the underlying survival distribution belongs to some specific family of distributions (e.g., normal, Weibull, exponential). On the other hand, a nonparametric approach is centered around the best-fitting member of a class of survival distribution functions [5]. Moreover, Kaplan-Meier (KME) [5] and NelsonAalen [1, 8] type nonparametric approach does not assume neither distribution class, nor closed-form distributions. In fact, it just depends on a data. The Kaplan-Meier and Nelson-Aalen type nonparametric estimation approaches are systematically analyzed by the totally discrete-time hybrid dynamic modeling process in [2]. In the existing literature [4, 6], the closed-form expression for a survival function is based on probabilistic analysis. The closed-form representation of the survival function coupled with the mathematical statistics method (parametric approach) is used to estimate survival and hazard/risk rate functions. In fact, the parametric approach/model has advantages of simplicity, the availability of likelihood-based inference procedures and the ease of use for a description, comparison, prediction, or decision [6]. The goal of this research project is to develop new mathematical models and computational tools for time-to-event dynamic processes in biological, engineering, epidemiological, financial, medical, military, and social sciences. Materials and Methods: Algorithms developed will be validated by applying them to real-world data sets. Conclusion(s) or Summary: In this work, we hope to attempt the following: 1. develop an innovative alternative dynamic modeling approach for time-to-event processes. 2. Introduce time-dependent covariates (external and internal) in the developed models and consider more complex time-to-event dynamic studies. 3. introduction of discrete-time dynamic intervention process 4. formulation of continuous and discrete-time interconnected dynamic system 5. introduction of conceptual and computational state and parameter estimation procedures References: 1. Odd Aalen. Nonparametric inference for a family of counting processes. The Annals of Statistics, pages 701–726, 1978. 2. EA Appiah and GS Ladde. Linear hybrid deterministic dynamic modeling for time-to-event processes: State and parameter estimations. International Journal of Statistics and Probability, 5(6):32, 2016.
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