Derivation and Validation of the Health State Function Form of a Population

In this chapter the very important point of Health State Function derivation, application and validation by performing stochastic simulations is analyzed. The used first exit time or hitting time theory of a stochastic processes crossing a barrier for the first time is used to model the health state process of a member of a population. The health state of the population is expressed as the average of the particular health states of all the members of the population. In the simplest form, the mean health state of the population is modeled as a smooth declining curve crossing the zero health state level at the horizontal axis X. Following the related stochastic theory we can estimate this smooth health state function if we have a good information for the death probability density function as is the case of the majority of the nowadays countries. Accordingly we propose the related Health State forms, we apply these forms to life table data, and we perform stochastic simulations verifying the good applicability of the proposed health state forms. After proposing the simpler but yet quite good model of the health state function, we have developed a detailed methodology for finding and applying a Final Health State form. This form appears as an extension of the simple model by using the mortality data sets and a technique including smoothing of data sets and adaptation to the Simple Model, the latter be used to locate the trajectory where the final form model approaches.