Graphical models allow scientific prior knowledge to be incorporated into the statistical analysis of data, whilst also providing a vivid way to represent and communicate this knowledge. In this paper we develop a graphical model of the immune system as a means of analyzing immunological data from the Manchester Asthma and Allergy Study (MAAS). The analysis is achieved using the Infer.NET tool which allows Bayesian inference to be applied automatically to a specified graphical model.
Our immune system model consists firstly of a Hidden Markov Model representing how allergen-specific skin prick tests (SPTs) and serum-specific IgE tests (SITs) change over time. By introducing a latent multinomial variable, we also cluster the children in an unsupervised manner into different sensitization classes. For 2 sensitization classes, the children who are vulnerable to allergies and have a high probability of having asthma (22%) are identified. For 5 sensitization classes, children in the first cluster, those who are vulnerable to allergies, have an even higher probability of having asthma (42%). The second part of the model involves using the inferred sensitization class as a label and 8 exposure variables in a Bayes Point Machine. Using multiple permutation tests, we conclude that the level of endotoxins and gender have a significant effect on a child’s vulnerability to allergies.