There has been considerable recent success in the detection of gene-disease associations. We consider here the development of tools that facilitate the more detailed characterization of the effect of a genetic variant on disease. We replace the simplistic classification of individuals according to a single binary disease indicator with classification according to a number of subphenotypes. This more accurately reflects the underlying biological complexity of the disease process, but it poses additional analytical difficulties. Notably, the subphenotypes that make up a particular disease are typically highly associated, and it becomes difficult to distinguish which genes might be causing which subphenotypes. Such problems arise in many complex diseases. Here, we concentrate on an application to Crohn disease (CD). We consider this problem as one of model selection based upon log-linear models, fitted in a Bayesian framework via reversible-jump Metropolis-Hastings approach. We evaluate the performance of our suggested approach with a simple simulation study and then apply the method to a real data example in CD, revealing a sparse disease structure. Most notably, the associated NOD2.908G-->R mutation appears to be directly related to more severe disease behaviors, whereas the other two associated NOD2 variants, 1007L-->FS and 702R-->W, are more generally related to disease in the small bowel (ileum and jejenum). The ATG16L1.300T-->A variant appears to be directly associated with only disease of the small bowel.