Electronic health records (EHR) provide opportunities for deeper understanding of human phenotypes - in our case, latent disease - based on statistical modeling. We propose a categorical matrix factorization method to infer latent diseases from EHR data. A latent disease is defined as an unknown biological aberration that causes a set of common symptoms for a group of patients. The proposed approach is based on a novel double feature allocation model which simultaneously allocates features to the rows and the columns of a categorical matrix. Using a Bayesian approach, available prior information on known diseases (e.g., hypertension and diabetes) greatly improves identifiability and interpretability of the latent diseases. We assess the proposed approach by simulation studies including mis-specified models and comparison with sparse latent factor models. In the application to a Chinese EHR data set, we identify 10 latent diseases, each of which is shared by groups of subjects with specific health traits related to lipid disorder, thrombocytopenia, polycythemia, anemia, bacterial and viral infections, allergy, and malnutrition. The identification of the latent diseases can help healthcare officials better monitor the subjects' ongoing health conditions and look into potential risk factors and approaches for disease prevention. We cross-check the reported latent diseases with medical literature and find agreement between our discovery and reported findings elsewhere. We provide an R package "dfa" implementing our method and an R shiny web application reporting the findings.
Keywords: Indian buffet process; matrix factorization; overlapping clustering; patient-level inference; tripartite networks.