Edgar R. Mendoza

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Dynamic Algorithms for Time-to-Event Processes Edgar R. Mendoza

Mentor: Emmanuel Appiah Department of Chemical Engineering and Department of Mathematics

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 is based on the assumption that the underlying survival distribution belongs to some specific family of distributions (e.g., Page 123 normal, Weibull, exponential). On the other hand, a of 3

nonparametric approach is centered around the best-fitting member of a class of survival distribution functions [5]. Moreover, Kaplan-Meier(KME)[5] and Nelson-Aalen [1, 8] type nonparametric approach do not assume either distribution class or closed-form distributions. In fact, it just depends on the 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 the usage of the probabilistic analysis approach. The closed-form representation of the survival function coupled with the mathematical statistics method (parametric approach) is used to estimate both 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, financial, medical, economical, 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: (a) develop an innovative alternative dynamic modeling approach for time-to-event processes. (b) introduce time-dependent covariates (external and internal) in the developed models and consider more complex timeto-event dynamic studies (c) introduction of the discrete-time dynamic intervention process (d) formulation of continuous and discrete-time interconnected dynamic system (e) introduction of conceptual and computational state and parameter estimation procedures (f) exhibit well-known results are exhibited as special cases in a systematic and unified manner.

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. [3] David W Hosmer, Stanley Lemeshow, and Susanne May. Applied survival analysis. 2011. [4] John D Kalbfleisch and Ross L Prentice. The statistical analysis of failure time data, volume 360. John Wiley & Sons, New Jersey, 2011. [5] Edward L Kaplan and Paul Meier. Nonparametric estimation from incomplete observations. Journal of the American statistical association, 53(282):457–481, 1958. [6] Jerald F Lawless. Statistical models and methods for lifetime data, volume 362. John Wiley & Sons, New Jersey, 2011. [7] Ganesh Malla and Hari Mukerjee. A new piecewise exponential estimator of a survival function. Statistics & probability letters, 80(23):1911–1917, 2010. [8] Wayne Nelson. Hazard plotting for incomplete failure data. Journal of Quality Technology, 1(1), 1969. [9] Olusegun M Otunuga, Gangaram S Ladde, and Nathan G Ladde. Local lagged adapted generalized method of moments and applications. Stochastic Analysis and Applications, pages 1–34, 2016.