Methodology mathematical and program tools of modeling of hierarchical dynamic systems in environmental epidemiology: application for air-pollution health impact assessment

Important problem of modern environmental epidemiology is study and assessment of air-pollution health effects. For reasonable assessment, it is very important that the models used must be epidemiologically sound and robust in terms of the persistence of the model behavior during changes in the model parameters. For the solving this problem, we introduce notion of ”adequate models” which is similar to a concept of ”categorical structures” in Model Theory. Aim of this paper to propose the methodology for constructing adequate models of complex hierarchical dynamic systems in environmental epidemiology and their problemoriented interpretation. This methodology includes: 1. Creating multivariate multilevel hierarchical structural model based on system analysis. 2. General mathematical formalization. 3. Building the statistical model for the study case, based on the generalized estimat-ing equations technique and time-series analysis. At this stage, for a binary dependent variable (like asthma attack), obtained by categorizing a continuous variable, special fuzzy algorithm is built. This algorithm incorporates fuzzy membership functions in order to increase robustness of the regression model. 4. The use of ”multi-layer” approach in the model interpretation, developed by authors. This approach implies creating the special functional time-depended coefficients reflected effects of pollutants at a given time, allows an interpretation full of epidemiological meaning, and finally evaluate air-pollution effects. To realize the methodology, we created special mathematical algorithms and the program module “quickmodelinteract” implemented as an ado-file of Stata software. This methodology was successfully applied for modeling air-pollution health effect for different databases ([1], [2]).