Stochastic interconnected hybrid dynamic modeling for time-to-event processes

Abstract

In this work, an attempt is made to develop an innovative alternative stochastic interconnected hybrid dynamic model for time-to-event processes in a systematic and unified way. The procedure is composed of the following components: (1) development of a continuous-time state dynamic model, (2) formulation of an interconnected hybrid dynamic model composed of both continuous and discrete-time states of time-to-event processes, (3) derivation of conceptual computational interconnected dynamic algorithm for time-to-event data statistic, and (4) construction of conceptual and computational simulation dynamic procedure for state and parameter estimations. The development of the presented approach is motivated by parameter and state estimation of time-to-event processes in biological, chemical, engineering, epidemiological, medical, military, and social dynamic processes under the influence of discrete-time intervention processes. The presented algorithm is independent of any particular form of survival distributions or data sets. Moreover, it does not require a closed form survival function distributions. The introduction of intervention processes provides a measure of influence of new tools/procedures/approaches in continuous-time states of time-to-event dynamic process. In particular, it generates a measure of the degree of sustainability, survivability, reliability of a time-to-event process. In addition, intervention processes provide comparison between the past and currently used tools/procedures/approaches/etc. The developed procedure coupled with modified Local Lagged Adapted Generalized Method of Moments (LLGMM) approach also provides a measure of degree of confidence, prediction, and planning assessments.