Heterogeneity-Aware Regression with Nonparametric Estimation and Structured Selection for Hospital Readmission Prediction

Readmission prediction is a critical but challenging clinical task, as the inherent relationship between high-dimensional covariates and readmission is complex and heterogeneous. Despite this complexity, models should be interpretable to aid clinicians in understanding an individual's risk prediction. Readmissions are often heterogeneous, as individuals hospitalized for different reasons, particularly across distinct clinical diagnosis groups, exhibit materially different subsequent risks of readmission. To enable flexible yet interpretable modeling that accounts for patient heterogeneity, we propose a novel hierarchical-group structure kernel that uses sparsity-inducing kernel summation for variable selection. Specifically, we design group-specific kernels that vary across clinical groups, with the degree of variation governed by the underlying heterogeneity in readmission risk; when heterogeneity is minimal, the group-specific kernels naturally align, approaching a shared structure across groups. Additionally, by allowing variable importance to adapt across interactions, our approach enables more precise characterization of higher-order effects, improving upon existing methods that capture nonlinear and higher-order interactions via functional ANOVA. Extensive simulations and a hematologic readmission dataset (n=18,096) demonstrate superior performance across subgroups of patients (AUROC, PRAUC) over the lasso and XGBoost. Additionally, our model provides interpretable insights into variable importance and group heterogeneity.