Go with the Flow? A Large-Scale Analysis of Health Care Delivery Networks in the United States Using Hodge Theory

TL;DR

This study applies Hodge theory to analyze US healthcare networks, revealing how different flow patterns relate to costs and quality, thus providing a scalable quantitative tool for understanding care fragmentation.

Contribution

It introduces the use of discrete Hodge decomposition for large-scale analysis of healthcare networks, offering new insights into care organization and its impact on outcomes.

Findings

Greater curl flow correlates with better care quality.

Higher harmonic flow is associated with increased costs.

Network structure varies systematically across markets.

Abstract

Health care delivery is a collaborative process, requiring close coordination among networks of providers with specialized expertise. Yet in the United States, care is often spread across multiple disconnected providers (e.g., primary care physicians, specialists), leading to fragmented care delivery networks, and contributing to higher costs and lower quality. While this problem is well known, there are relatively few quantitative tools available for characterizing care delivery networks at scale, thereby inhibiting deeper understanding of care fragmentation and efforts to address it. In this, study, we conduct a large-scale analysis of care delivery networks across the United States using the discrete Hodge decomposition, an emerging method of topological data analysis. Using this technique, we decompose networks of patient flows among physicians into three orthogonal subspaces: gradient (acyclic flow), harmonic (global cyclic flow), and curl (local cyclic flow). We document substantial variation in the relative importance of each subspace, suggesting that there may be systematic differences in the organization of care delivery networks across health care markets. Moreover, we find that the relative importance of each subspace is predictive of local care cost and quality, with outcomes tending to be better with greater curl flow and worse with greater harmonic flow.