Abstract
The application of social network analysis to the organization of healthcare delivery is a relatively new area of research that may not be familiar to health services statisticians and other methodologists. We present a methodological introduction to social network analysis with a case study of physicians’ adherence to clinical guidelines regarding use of implantable cardioverter defibrillators (ICDs) for the prevention of sudden cardiac death. We focus on two hospital referral regions in Indiana, Gary and South Bend, characterized by different rates of evidence-based ICD use (86 and 66 %, respectively). Using Medicare Part B claims, we construct a network of physicians who care for cardiovascular disease patients based on patient-sharing relationships. Approaches for weighting physician dyads and aggregating physician dyads by hospital are discussed. Then, we obtain a set of weighted network statistics for the positions of hospitals in their referral region, global statistics for the physician network within each hospital, and of the network positions of individual physicians within hospitals, providing the mathematical specification and sociological intuition underlying each measure. We find that adjusting for network measures can reduce the observed differences between referral regions for evidence-based ICD therapy. This study supports previous reports on how variation in physician network structure relates to utilization of care, and motivates future work using physician network measures to examine variation in evidence-based medicine.
Similar content being viewed by others
References
Al-Khatib, S.M., Hellkamp, A., Curtis, J., Mark, D., Peterson, E., Sanders, G.D., Heidenreich, P.A., Hernandez, A.F., Curtis, L.H., Hammill, S.: Non-evidence-based ICD implantations in the United States. JAMA 305(1), 43–49 (2011)
Bates, D., Maechler, M., Bolker, B., Walker, S.: Fitting linear mixed-effect models using lme4. J. Stat. Softw. 67(1), 1–48 (2015)
Bardy, G.H., Lee, K.L., Mark, D.B., Poole, J.E., Packer, D.L., Boineau, R., Domanski, M., Troutman, C., Anderson, J., Johnson, G., et al.: Amiodarone or an implantable cardioverter-defibrillator for congestive heart failure. N. Engl. J. Med. 352(3), 225–237 (2005)
Barnett, M.L., Christakis, N.A., O’Malley, A.J., Onnela, J., Keating, N.L., Landon, B.E.: Physician patient-sharing networks and the cost and intensity of care in US hospitals. Med. Care 50(2), 152–160 (2012)
Barrat, A., Barthelemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Acad. Sci. USA 101(11), 3747–3752 (2004)
Bastian, M., Heymann, S., Jacomy, M.: Gephi: An open source software for exploring and manipulating networks. International AAAI Conference on Weblogs and Social Media (2009)
Bonarich, P.: Some unique properties of eigenvector centrality. Soc. Netw. 29(4), 555–564 (2007)
Borgatti, S.P., Halgin, D.S.: Analyzing affiliation networks. In: The Sage Handbook of Social Network Analysis, pp. 433–471. Sage Publications, Thousand Oaks, CA (2011)
Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25, 163–177 (2001)
Bridewell, W., Das, A.K.: Social network analysis of physician interactions: the effect of institutional boundaries on breast cancer care. In: AMIA Annual Symposium Proceedings, pp. 152–160 (2011)
Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30, 107–117 (1998)
Bynum, J.P., Bernal-Delgano, E., Gottlieb, D., Fisher, E.: Assigning ambulatory patients and physicians to hospitals: a method for obtaining population-based provider performance measurements. Health Serv. Res. 41(1), 45–58 (2007)
Cabana, M.D., Rand, C.S., Powe, N.R., Wu, A.W., Wilson, M.H., Abboud, P.C., Rubin, H.R.: Why don’t physicians follow clinical practice guidelines? A framework for improvement. JAMA 282(15), 1458–1465 (1999)
Csardi, G., Nepusz, T. (2006): The igraph software package for complex network research. InterJ. Complex Syst. 1695. http://igraph.org
Curtis, L.H., Al-Khatib, S.M., Shea, A.M., Hammill, B.G., Hernandez, A.F., Schulman, K.A.: Sex differences in the use of implantable cardioverter-defibrillators for primary and secondary prevention of sudden cardiac death. JAMA 298(13), 1517–1524 (2007)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)
Fattore, G., Frosini, F., Salvatore, D., Tozzi, V.: Social network analysis in primary care: the impact of interactions on prescribing behaviour. Health Policy 92(2–3), 141–148 (2009)
Freeman, L.C.: Centrality in social networks: conceptual clarification. Soc. Netw. 1, 215–239 (1979)
Goodreau, S.M.: Advances in exponential random graph (p*) models applied to a large social network. Soc. Netw. 29(2), 231–248 (2007)
Handcock, M.S.: Assessing Degeneracy in Statistical Models of Social Networks. Working Paper report No. 39, Center for Statistics and the Social Sciences. University of Washington, Seattle, WA (2003a)
Handcock, M.S., Hunter, D.R., Butts, C.T., Goodreau, S.M., Morris, M.: Statnet: software tools for the Statistical Modeling of Network Data. http://statnetproject.org. (2003b)
Hunter, D.R.: Curved exponential family models for social networks. Soc. Netw. 29(2), 230–231 (2007)
Hunter, D.R., Handcock, M.S., Butts, C.T., Goodreau, S.M., Morris, M.: ergm: A package to fit, simulate and diagnose exponential-family models for networks. J. Stat. Softw. 24(3), 54860 (2008)
Iacobucci, D., Wasserman, S.: Social networks with two sets of actors. Psychometrika 55(4), 707–720 (1990)
Kadish, A., Dyer, A., Daubert, J.P., Quigg, R., Estes, M., Anderson, K.P., Calkins, H., Hoch, D., Godlberger, J., Shalaby, A., et al.: Prophylactic defibrillator implantation in patients with nonischemic dilated cardiomyopathy. N. Engl. J. Med. 350(21), 2151–2158 (2004)
Landon, B.E., Keating, N.L., Barnett, M.L., Onnela, J.P., Paul, S., O’Malley, A.J., Keegan, T., Christakis, N.A.: Variation in patient-sharing networks of physicians across the United States. JAMA 308(3), 265–273 (2012)
Latapy, M., Magnien, C., Del Vecchio, N.: Basic notions for the analysis of large two-mode networks. Soc. Netw. 30(1), 31–48 (2008)
Lomas, J., Anderson, G.M., Domnick-Pierre, K., Vayda, E., Enkin, M.W., Hannah, W.J.: Do practice guidelines guide practice? The effect of a consensus statement on the practice of physicians. N. Engl. J. Med. 321(19), 1306–1311 (1989)
Luke, D.A., Harris, J.K.: Network analysis in public health: history, methods, and applications. Annu. Rev. Public Health 28, 69–93 (2007)
Lurie, S.J., Fogg, T.T., Dozier, A.M.: Social network analysis as a method of assessing institutional culture: three case studies. Acad. Med. 84(8), 1029–1035 (2009)
Matlock, D.D., Peterson, P.N., Heidenreich, P.A., Lucas, F.L., Malenka, D.J., Wang, Y., Curtis, J.P., Fisher, E.S., Masoudi, F.A.: Regional variation in the use of implantable cardioverter-defibrillators for primary prevention: results from the National Cardiovascular Data Registry. Circ. Cardiovasc. Qual. Outcomes 4(1), 114–121 (2011)
Mehra, M.R., Yancy, C.W., Albert, N.M., Curtis, A.B., Stough, W.G., Gheorghiade, M., Heywood, J.T., McBride, M.L., O’Connor, C.M., Reynolds, D., et al.: Evidence of clinical practice heterogeneity in the use of implantable cardioverter-defibrillators in heart failure and post-myocardial infarction left ventricular dysfunction: Findings from IMPROVE HF. Heart Rhythm. 6(12), 1727–1734 (2009)
Moss, A.J., Zareba, W., Hall, W.J., Klein, H., Wilber, D.J., Cannom, D.S., Daubert, J.P., Higgins, S.L., Brown, M.W., et al.: Prophylactic implantation of a defibrillator in patients with myocardial infarction and reduced ejection fraction. N. Engl. J. Med. 346(12), 877–883 (2002)
Newman, M.E.J.: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Phys. Rev. E 64, 016132 (2001)
Newman, M.E.: Analysis of weighted networks. Phys. Rev. E 70(5), 056131 (2004)
O’Malley, A.J., Marsden, P.V.: The analysis of social networks. Heath Serv. Outcomes Res. Methodol. 8(4), 222–269 (2008)
O’Malley, A.J.: The analysis of social network data: an exciting frontier for statisticians. Stat. Med. 32(4), 539–555 (2013)
O’Malley, A.J., Onnela, J.P.: Topics in Social Network Analysis and Network Science (2014). arXiv:1404.0067 [physics.soc-ph]
Opsahl, T., Agneessens, F., Skvoretz, J.: Node centrality in weighted networks: generalizing degree and shortest paths. Soc. Netw. 32(3), 245–251 (2010)
Pollack, C.E., Soulos, P.R., Gross, C.P.: Physician’s peer exposure and the adoption of a new cancer treatment modality. Cancer 121(16), 2799–2807 (2015)
Porter, M.A., Mucha, P.J., Newman, M.E., Friend, A.J.: Community structure in the united states house of representatives. Phys. A 386(1), 414–438 (2007)
R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna Austria. ISBN 3-900051-07-0. http://www.R-project.org (2008)
Rinaldo, A., Fienberg, S.E., Zhou, Y.: On the geometry of discrete exponential families with application to exponential random graph models. Electron. J. Stat. 3, 446–484 (2009)
Robins, G., Snijders, T., Wang, P., Handcock, M., Pattison, P.: Recent developments in exponential random graph (p*) models for social networks. Soc. Netw. 29(2), 192–215 (2007)
Ruhnau, B.: Eigenvector-centrality—a node-centrality? Soc. Netw. 22(4), 357–365 (2000)
Russo, A.M., Stainback, R.F., Bailey, S.R., Epstein, A.E., Heidenreich, P.A., Jessup, M., Kapa, S., Kremers, M.S., Lindsay, B.D., Stevenson, L.W.: ACCF/HRS/AHA/ASE/HFSA/SCAI/SCCT/SCMR 2013 appropriate use criteria for implantable cardioverter-defibrillators and cardiac resynchronization therapy: a report of the American College of Cardiology Foundation appropriate use criteria task force, Heart Rhythm Society, American Heart Association, American Society of Echocardiography, Heart Failure Society of America, Society for Cardiovascular Angiography and Interventions, Society of Cardiovascular Computed Tomography, and Society for Cardiovascular Magnetic Resonance. J. Am. Coll. Cardiol. 61(12), 1318–1368 (2013)
Snijders, T.A.B., Pattison, P.E., Robins, G.L., Handcock, M.S.: New specifications for exponential random graph models. Sociol. Methodol. 36, 99–153 (2006)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)
Wennberg, J.E., Cooper, M.M.: The Dartmouth atlas of health care. American Health Association, Chicago (1996)
Funding
This study was funded by U01AG046830 (to J.S.S.).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All the authors declares that they have no conflicts of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Appendix
Appendix
The centrality measures discussed herein can be calculated for unweighted and weighted networks. We specify the descriptions for weighted networks to reflect our use of a weighted network. Unweighted counterparts can be derived by simplifying the weighted measures in the case when all the weights equal 1. The unweighted measures are presented or described explicitly below when they have a particularly intuitively interpretable form.
The weighted closeness centrality (C wc) is the inverse of the total weighted geodesic distance from a node to all other nodes in the network. Thus, if \(g_{ij}^{w}\) denotes the weighted geodesic distance from node i to node j, it follows that
Closeness centrality measures both the direct and indirect connections of node i to quantify its closeness to all other nodes in the network. Therefore, if node i has smaller geodesic distances than all other nodes, it is considered most central in the network and subsequently will have a larger centrality measure. Multiplying \(C_{i}^{wc}\) by N − 1 yields the inverse of the average geodesic distance of node i to the other nodes and is the measure used herein. If \(g_{ij}^{w} = \infty\) for any nodes j ≠ i then \(C_{i}^{wc} = 0\). For studies interested in computing closeness centrality for a network containing multiple components, or subnetworks of nodes with no connecting dyads between them, a common practice is to use the largest connected component of the network (the set of nodes for which a finite length path exists between every pair of nodes) to compute closeness centrality and other network measures that depend on distance measures between nodes.
The weighted betweenness centrality (C wb) measures the relative frequency with which node i appears on the weighted geodesic path between all two pairs of nodes (j, k) such that j ≠ i and k ≠ i. A standardized measure of betweenness centrality is obtained by dividing the relative frequency by the total number of geodesic paths that could have included the focal node, yielding the measure:
where \(0 \le \sigma_{jk\left( i \right)} /\sigma_{jk} \le 1\) is the sum of the weights along the weighted geodesic paths between nodes j and k that pass through node i, denoted σ jk(i), divided by the sum of the weights along all of the weighted geodesic paths between nodes j and k, denoted σ jk . If there is a unique weighted geodesic path between nodes j and k then σ jk = g w jk and the numerator of C wb i reduces to a binary indicator variable.
Eigenvector centrality (C e) represents the importance of a node based on the importance of the nodes it shares edges with. Let C denote a vector of centrality values defined such that the centrality of node i, denoted, \(C_{i}^{e}\) is proportional to a linear combination of the centrality of the nodes with whom node i is directly connected, implying the mathematical relation
where W is the weighted adjacency matrix (equal to A for binary networks). Therefore, the eigenvector centrality measure satisfies the matrix equation WC = λC, which is immediately recognized as being equivalent to the characteristic equation whose solution yields the eigenvalues and eigenvectors of W. Intuitively, the solution that best discriminates between the nodes’ positions in the network is the eigenvector associated with the principal (largest) eigenvalue of W, representing the axis along which most of the variability in W occurs. Furthermore, because A is real-valued and square, the Perron-Frobenius theorem implies that the eigenvector associated with the largest unique eigenvalue of W contains only positive elements thereby yielding a quantity suitable for use as a centrality measure (Ruhnau 2000). Weighted eigenvector centrality \(WC_{i}^{e}\) for node i is therefore defined as the ith element of the vector WC e that solves the equation:
The generalization of eigenvector centrality to a weighted network is still the leading eigenvector of the adjacency matrix, but ties that are valued at twice the weight will contribute twice as much to the vertex’s eigenvector centrality (Newman 2004). Compared with closeness and betweenness centrality measures, eigenvector centrality is more informative for binary-valued networks when centrality is driven by differences in degree, and it is more informative in situations where a high degree node is tied to many low degree nodes or vice versa (Bonarich 2007).
Another important network measure is network clustering. The clustering coefficient is a measure of how complete the neighborhood of the node is (Latapy et al. 2008) and does not directly involve the focal node nor its edges. The igraph package uses the weighted clustering coefficient as defined by Barrat et al. (2004):
where \(d_{i}^{w}\) is the strength of node i, d i is the degree of node i, w ij is the weight of the edge between nodes i and j, and a ij are elements of the adjacency matrix. The unweighted counterpart to this can be calculated intuitively with the following definition:
In the case of a binary-valued network, the clustering coefficient reduces to the ratio of the number of triangles (or closed triads) involving node i, denoted t i , divided by the number of two-paths with node i at the apex (a “two-star”), denoted d i (d i − 1). In other words, \({\text{ClustCoef}}_{i}\) is the ratio of the sum of the weighted products over the closed triads to the sum of the weighted products over all open or closed triads with respect to node i (the weighted products reduce to binary indicators in the case of binary networks). A network with a high level of clustering implies if nodes i and j have highly weighted edges to node k, it is more likely i and j will also have highly weighted edges (or have ties in a binary network) than in a network with little clustering.
Rights and permissions
About this article
Cite this article
Moen, E.L., Austin, A.M., Bynum, J.P. et al. An analysis of patient-sharing physician networks and implantable cardioverter defibrillator therapy. Health Serv Outcomes Res Method 16, 132–153 (2016). https://doi.org/10.1007/s10742-016-0152-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10742-016-0152-x