A Mixed Integer Programming Formulation for Risk Stratification

Risk stratification is the process of segmenting patients into distinct groups of similar complexity and care needs in order to improve resource allocation. Patients are typically risk stratified using statistical or machine learning methods that generate an individual risk score for some measure of resource use. One of the main limitations of existing methods is reduced interpretability, which is often inherent to artificial intelligence techniques. In this work, we propose a novel risk stratification approach that optimizes the representation of different patient groups and generates interpretable risk profiles. We associate risk scores to patient profiles and determine the optimal combination of representative profiles for each patient group using a Mixed Integer Programming (MIP) formulation. We generate continuous ratings for patient risk scores ranging from 0 to 1 that allow for dynamic thresholding. Our method stratifies patients into several risk groups (e.g., low, medium, high risk), which is frequently more clinically significant than binary classification. We apply our approach to both public and proprietary real data in the context of accidental fall risk assessment and show that the generated risk profiles provide clinical insights that can be used for the design of targeted interventions.