Hospital Pricing Estimation by Gaussian Conditional Random Fields Based Regression on Graphs

Accurate estimation of what a day in a hospital costs and what the hospital charges is of high interest to many parties, including health care providers, medical insurance companies, health researchers, and uninsured patients. The problem is complex, as the cost-to-charge ratio varies greatly from hospital to hospital and over time. In addition, the cost-to-charge ratio is often not reported, and in such cases group average values from similar hospitals are used. In this study we address the problem of estimating the cost-to-charge ratio at the hospital level by utilizing structured regression on a temporal graph of more than 4,000 hospitals, observed over 8 years, constructed from the National Inpatient Sample database. In the proposed approach, the cost-to-charge estimates at individual hospitals for a certain month obtained by an artificial neural network were used as unstructured components in the Gaussian Conditional Random Fields (GCRF) model. The diagnosis codes of treatments in each hospital were used to create a similarity metric that represents correlation among hospital specializations. The estimates of cost-to-charge ratio obtained using convex optimization of the GCRF parameters on the constructed graph were much better than those relying on group average based cost-to-charge estimates. In addition, cost-to-charge ratio estimates by our GCRF model outperformed regression by nonlinear artificial neural networks.