Network Model with Application to Allergy Diseases

We propose a new graphical model to describe the comorbidity of allergic diseases. We present our model in two versions. First, we introduce a generative model that reflects the variables' causal relationships. Then, we propose an approximation of the generative model by a misspecified model, which is computationally more efficient and easily interpretable. In both versions of our model, we consider typical allergic disease symptoms and covariates. We consider two directed acyclic graphs (DAGs). The first one describes information about the coexistence of certain allergic diseases (binary variables). The second graph describes the relationships between particular symptoms and the occurrence of these diseases. In the generative model, the edges lead from diseases to symptoms, corresponding to causal relations. In the misspecified model, we reverse the direction of edges: they lead from symptoms to diseases. The proposed model is evaluated on a cross-sectional multicentre study in Poland (www.ecap.pl). An assessment of the stability of the proposed model is obtained using the bootstrap and jackknife techniques. Our results show that the misspecified model is a good approximation of the generative model and helps predict the incidence of allergic diseases.