Algebraic Methods for Studying Interactions Between Epidemiological Variables

Independence models among variables is one of the most relevant topics in epidemiology, particularly in molecular epidemiology for the study of gene-gene and gene-environment interactions. They have been studied using three main kinds of analysis: regression analysis, data mining approaches and Bayesian model selection. Recently, methods of algebraic statistics have been extensively used for applications to biology. In this paper we present a synthetic, but complete description of independence models in algebraic statistics and a new method of analyzing interactions, that is equivalent to the correction by Markov bases of the Fisher's exact test.