Towards symbolic regression for interpretable clinical decision scores

Abstract: Medical decision-making makes frequent use of algorithms that combine risk equations with rules, providing clear and standardized treatment pathways. Symbolic regression (SR) traditionally limits its search space to continuous function forms and their parameters, making it difficult to model this decision-making. However, due to its ability to derive data-driven, interpretable models, SR holds promise for developing data-driven clinical risk scores. To that end we introduce Brush, an SR algorithm that combines decision-tree-like splitting algorithms with non-linear constant optimization, allowing for seamless integration of rule-based logic into symbolic regression and classification models. Brush achieves Pareto-optimal performance on SRBench, and was applied to recapitulate two widely used clinical scoring systems, achieving high accuracy and interpretable models. Compared to decision trees, random forests, and other SR methods, Brush achieves comparable or superior predictive performance while producing simpler models.