Variation in patient-sharing networks of physicians across the United States

Abstract

Context: Physicians are embedded in informal networks that result from their sharing of patients, information, and behaviors.

Objectives: To identify professional networks among physicians, examine how such networks vary across geographic regions, and determine factors associated with physician connections.

Design, setting, and participants: Using methods adopted from social network analysis, Medicare administrative data from 2006 were used to study 4,586,044 Medicare beneficiaries seen by 68,288 physicians practicing in 51 hospital referral regions (HRRs). Distinct networks depicting connections between physicians (defined based on shared patients) were constructed for each of the 51 HRRs.

Main outcomes measures: Variation in network characteristics across HRRs and factors associated with physicians being connected.

Results: The number of physicians per HRR ranged from 135 in Minot, North Dakota, to 8197 in Boston, Massachusetts. There was substantial variation in network characteristics across HRRs. For example, the mean (SD) adjusted degree (number of other physicians each physician was connected to per 100 Medicare beneficiaries) across all HRRs was 27.3 (range, 11.7-54.4); also, primary care physician relative centrality (how central primary care physicians were in the network relative to other physicians) ranged from 0.19 to 1.06, suggesting that primary care physicians were more than 5 times more central in some markets than in others. Physicians with ties to each other were far more likely to be based at the same hospital (69.2% of unconnected physician pairs vs 96.0% of connected physician pairs; adjusted rate ratio, 0.12 [95% CI, 0.12-0.12]; P < .001), and were in closer geographic proximity (mean office distance of 21.1 km for those with connections vs 38.7 km for those without connections, P < .001). Connected physicians also had more similar patient panels in terms of the race or illness burden than unconnected physicians. For instance, connected physician pairs had an average difference of 8.8 points in the percentage of black patients in their 2 patient panels compared with a difference of 14.0 percentage points for unconnected physician pairs (P < .001).

Conclusions: Network characteristics vary across geographic areas. Physicians tend to share patients with other physicians with similar physician-level and patient-panel characteristics.

Figure A1

US Map with HRRs highlighted

Figure A2

Number of Shared patients by doctor pairs across the 51 HRRs Pre (Panel a) and Post (panel b) Thresholding

Figure A3

Scatter Plots of Mean Network Attributes for 51 Hospital Referral Regions by Log Number of Physicians

Figure 1

A schematic illustrating a projection from a two-mode (bipartite) to a one-mode (unipartite) network. Medicare records link each doctor to a number of patients, which naturally leads to a bipartite network consisting of two types of nodes, doctors and patients. An edge can only exist between nodes of different type (a doctor and a patient), and the network is fully described by the (in this case 6 × 3) bipartite adjacency matrix B. A one-mode projection of the doctor-patient network is obtained by multiplying the bipartite adjacency matrix B by its transpose. The resulting symmetric one-mode adjacency matrix A is square in shape (in this case 6 × 6), and its elements indicate the number of patients the two physicians have in common. For example, A(3,4) = 1 shows that physicians 3 and 4 provide care for one common patient (patient B), whereas A(4,5) = 2 shows that physicians 4 and 5 have two patients in common (patients B and C). The diagonal elements of matrix A correspond to the number of patients the given physician provides care for, e.g. A(4,4) = 2 (in other words, physician 1 has degree 2).

Figure 2

This schematic illustrates some fundamental social networks concepts. (A) Nodes and ties are the elementary building blocks of networks. A tie connecting two nodes (physicians) indicates that the two physicians share one or more patients. (B) The degree of a node quantifies the number of connections a given node has. For example, the red node at the center of the figure has a degree of five, i.e. the physician shares patients with five other physicians. In our work, we present adjusted degree (degree divided by the number of Medicare patients cared for by each physician). (C) The clustering coefficient is a metric that quantifies the extent to which the network neighbors of a given node are directly connected to one another. More specifically, the clustering coefficient of the physician at the center of the figure (red node) is given by the number of ties that exist among his or her colleagues (the dashed four ties) divided by the number of ties that could exist between them (in this case 10), yielding a value of 4/10 or 0.4. This number can also be interpreted as the probability that any two randomly chosen network neighbors of the individual at the center are directly connected to one another. (D) Betweenness centrality quantifies the structural centrality of a node in the network. The betweenness centrality of a node is proportional to the number of times the node lies on shortest paths in the network, where one considers all shortest paths, i.e. shortest paths from every node in the network to every other node in the network. In the schematic, the size of a node is proportional to its betweenness centrality score, and the betweenness centrality scores are shown for four nodes in increasing order of centrality. In our work, we present relative PCP or specialist centrality, where we divide the mean PCP or specialist centrality for all physicians in the network by the mean centrality of all other physicians in the network.

Figure 3

Depictions of two networks: Albuquerque, NM (panels A and B, ~1000 physicians) and Minneapolis/St. Paul, MN (Panels C and D, ~1700 physicians). On the left (panels A and C), hospital affiliations are coded (each hospital is represented by a different color and on the right (panels B and D) specialty is coded. Depictions of two networks: Albuquerque, NM (panels A and B, ~1000 physicians) and Minneapolis/St. Paul, MN (Panels C and D, ~1700 physicians) using “spring embedder” methods, which position objects with strong connections (i.e., physicians with more shared patients) in closer physical proximity. On the left (panels A and C), hospital affiliations are coded (each hospital is represented by a different color and on the right (panels B and D) specialty is coded.

Figure 4

Scatter Plots of Mean Network Attributes for 51 Hospital Referral Regions by Log Number of Physicians (Nodes)

Figure 5

Depictions of two networks: Albuquerque, NM (panels A and B, ~1000 physicians) and Minneapolis/St. Paul, MN (Panels C and D, ~1700 physicians). On the left (panels A and C), hospital affiliations are coded (each hospital is represented by a different color and on the right (panels B and D) specialty is coded.