H3: A Healthcare Three-Hop Index for Physician Referral Network Prediction

2026-05-03

AI Summary

Existing approaches struggle to accurately predict physician referral relationships due to their inability to effectively capture key topological properties of medical referral networks—namely sparsity, disassortative mixing, and hub dominance. To address this limitation, this work proposes the H3 metric, which introduces, for the first time, a modeling framework based on three-hop indirect referral paths. By integrating degree normalization and a redundancy penalty mechanism, H3 enhances prediction accuracy while preserving interpretability: each prediction can be traced back to specific intermediary physicians, thereby overcoming the opacity of black-box models. Empirical evaluation using Medicare shared-patient data demonstrates that H3 significantly outperforms both traditional heuristic methods and deep learning baselines in both concurrent and cross-temporal prediction scenarios, achieving high accuracy alongside strong robustness.

Abstract

Accurate prediction of physician referral links is essential for optimizing care coordination and reducing fragmentation in healthcare delivery. However, existing computational methods, ranging from triadic closure heuristics to graph neural networks, fail to capture the intrinsic properties of physician referral networks, including sparsity, disassortative degree mixing, and hub-dominated topology. Here, we propose H3, a healthcare three-hop index that addresses these limitations by modeling indirect referral pathways through intermediate physicians, with degree-based normalization and a redundancy penalty to mitigate hub-mediated noise. Using Medicare Physician Shared Patient Patterns data, we evaluate H3 under two complementary prediction regimes: within-period prediction, which assesses recovery of contemporaneous referral links under sparse conditions, and cross-period prediction, which tests robustness to temporal shift as referral windows expand. Across both regimes, H3 consistently outperforms classical heuristics and deep learning-based baselines. Unlike black-box neural network approaches, H3 produces fully decomposable predictions traceable to specific intermediary physicians, offering a transparent and deployable solution for referral network completion.

Problem

• physician referral network
• link prediction
• network sparsity
• disassortative mixing
• hub-dominated topology

Innovation

• three-hop index
• physician referral network
• degree normalization
• redundancy penalty
• interpretable prediction