Analysis of the U.S. patient referral network

Abstract

In this paper, we analyze the US Patient Referral Network (also called the Shared Patient Network) and various subnetworks for the years 2009 to 2015. In these networks, two physicians are linked if a patient encounters both of them within a specified time interval, according to the data made available by the Centers for Medicare and Medicaid Services. We find power law distributions on most state-level data as well as a core-periphery structure. On a national and state level, we discover a so-called small-world structure as well as a "gravity law" of the type found in some large-scale economic networks. Some physicians play the role of hubs for interstate referral. Strong correlations between certain network statistics with health care system statistics at both the state and national levels are discovered. The patterns in the referral network evinced using several statistical analyses involving key metrics derived from the network illustrate the potential for using network analysis to provide new insights into the health care system and opportunities or mechanisms for catalyzing improvements.

Keywords: generative model; hierarchical modeling; network science; physician network; shared patient network; social network analysis.

FIGURE 1

An illustrative directed network. The nodes A, B, C, D, E, and F represent different physicians. The arrow of an edge points from a referring physician to a referred physician (who accepts the patient referral).

FIGURE 2

Counterclockwise from upper right: CP score distribution of LA, DE, and CA (minimu, median, maximum), in 2009 and the distribution of Gini coefficients of CP score among the 50 states over 2009–2015.

FIGURE 3

Out-degree of DE in 2015. P-value distribution of degree-out in 2012 for all states.

FIGURE 4

State map of average p-values of Power Law Test in 2009–2015, for both indegree and outdegree.

FIGURE 5

Degree Power Law of national network.

FIGURE 6

Clustering coefficients of state network in 2009–2015

FIGURE 7

Number of states that a core node with CP score 1.0 connects to, and the number of cross-state referrals for the corresponding core node. Time ranges from 2009–2015. Figure 8 shows the state map. #external states that the core node can directly reach out.

FIGURE 8

The state map of Figure 7 and core node connections.

FIGURE 9

A visualization of the top five out-of-state referrals. Edge width varies by percentage of within-state referrals, and node size varies by size of state’s physician referral network. The map depicts directed edges of each state’s top five states to which they refer patients. Note that nodes for Alaska (AK) and Hawaii (HI) are placed in the bottom left of the figure. As this is a network diagram, the placement position is not relevant.

FIGURE 10

16 kinds of triads

FIGURE 11

Multidimensional scaling (MDS) plot of 50 states based on feature vector in 2014. Two clusters are in red and blue.