A Latent Supervised Cluster Method on Comorbidities for Risk Adjustment in Diagnosis-Related Groups

Medical costs within diagnosis-related groups (DRGs) exhibit substantial vari- ability, yet traditional clustering approaches prove inadequate for risk adjustment due to the high-dimensional curse of comorbidities. This paper proposes a latent supervised clustering method that incorporates the dependent variable (cost) as a latent supervisor to generate more informative cluster labels for regression anal- ysis. The method addresses the sparsity and complexity inherent in comorbidity data by guiding the clustering process toward configurations that enhance pre- dictive accuracy for healthcare costs. Theoretically, we establish the consistency of this approach and demonstrate that with sufficient weighting on the latent supervisor, the true clustering mechanism can be recovered. Empirically, using the CMS SynPUF database, we demonstrate significant improvements in both model fitting performance and overfitting control compared to traditional meth- ods. Our approach achieves an R2 of approximately 0.3, representing a substantial improvement over conventional risk adjustment models that typically achieve around 0.16. The proposed method offers dual benefits: it optimizes cluster for- mation for cost prediction while simultaneously controlling overfitting through the filtering of irrelevant characteristics. This enhanced predictive capability has practical implications for healthcare economics, potentially reducing financial risks for hospitals and improving fairness in insurance reimbursement systems.