A Bayesian approach to the probability of coronary heart disease subject to the --308 tumor necrosis factor-$α$ SNP
We study the correlation of the occurrence of coronary heart disease (CHD) with the presence of the single-nucleotide polymorphism (SNP) at the -308 position of the tumor necrosis factor alpha (TNF-$α$) gene. We also consider the influence of the occurrence of type 2 diabetes (t2DM). Using Bayesian inference, we first pursue a bottom-up approach to compute the working hypothesis and the probabilities derivable from the data. We then pursue a top-down approach by modelling the signal pathway that causally connects the SNP with the emergence of CHD. We compute the functional form of the probability of CHD conditional on the presence of the SNP in terms of both the statistical and biochemical properties of the system. From the probability of occurrence of a disease conditional on a given risk factor, we explore the possibility of extracting information on the pathways involved in the occurrence of the disease. This is a first study that we want to systematise into a comprehensive formalism to be applied to the inference of the mechanism connecting the risk factors to the disease.