A log-linear analytics approach to cost model regularization for inpatient stays through diagnostic code merging

Healthcare cost models that use a great number of detailed ICD-10 diagnostic codes produce unstable results, yet the underlying causes of this instability have not been well understood. This study provides a mathematical framework linking the variability of model coefficients to the uneven, power-law distribution of diagnostic codes and the structure of the regression model. We propose a transparent approach that improves coefficient stability by merging similar codes through hierarchical truncation. Using Medicare data, we demonstrate how this method clarifies the trade-off between code detail and model reliability, offering analysts and policymakers a practical and interpretable tool for diagnosis-based cost modeling. • Model inpatient stay costs using log-linear regression with diagnostic code indicators. • Link the Hessian matrix to diagnostic code occurrence and co-occurrence patterns. • Propose a metric to measure inconsistency in regression coefficients. • Improve coefficient stability by grouping diagnostic codes through truncation. • Show that grouping diagnostic codes enhances interpretability in healthcare cost models.