Bayesian exponential random graph modelling of interhospital patient referral networks

Using original data that we have collected on referral relations between 110 hospitals serving a large regional community, we show how recently derived Bayesian exponential random graph models may be adopted to illuminate core empirical issues in research on relational coordination among healthcare organisations. We show how a rigorous Bayesian computation approach supports a fully probabilistic analytical framework that alleviates well-known problems in the estimation of model parameters of exponential random graph models. We also show how the main structural features of interhospital patient referral networks that prior studies have described can be reproduced with accuracy by specifying the system of local dependencies that produce - but at the same time are induced by - decentralised collaborative arrangements between hospitals. Copyright © 2017 John Wiley & Sons, Ltd.

[1]  P. Pattison,et al.  9. Neighborhood-Based Models for Social Networks , 2002 .

[2]  J. Coleman,et al.  Social Capital in the Creation of Human Capital , 1988, American Journal of Sociology.

[3]  N. Christakis,et al.  A Model of Genetic Variation in Human Social Networks , 2010 .

[4]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[5]  Carter T. Butts,et al.  A Perfect Sampling Method for Exponential Random Graph Models , 2017 .

[6]  D. Hunter,et al.  Inference in Curved Exponential Family Models for Networks , 2006 .

[7]  Thomas Brendan Murphy,et al.  Review of statistical network analysis: models, algorithms, and software , 2012, Stat. Anal. Data Min..

[8]  C. Geyer,et al.  Constrained Monte Carlo Maximum Likelihood for Dependent Data , 1992 .

[9]  Martina Morris,et al.  statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data. , 2008, Journal of statistical software.

[10]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[11]  Andrea L. Larson Network Dyads in Entrepreneurial Settings: A Study of the Governance of Exchange Relationships , 1992 .

[12]  Johan Koskinen,et al.  Bayesian Analysis of Exponential Random Graphs : Estimation of Parameters and Model Selection , 2004 .

[13]  Alberto Caimo,et al.  Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks , 2014, Stat. Comput..

[14]  Richard Platt,et al.  Long-Term Care Facilities: Important Participants of the Acute Care Facility Social Network? , 2011, PloS one.

[15]  Jenine K. Harris,et al.  Referrals among cancer services organizations serving underserved cancer patients in an urban area. , 2011, American journal of public health.

[16]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[17]  David Bruce Wilson,et al.  Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996, Random Struct. Algorithms.

[18]  Pavel N Krivitsky,et al.  Exponential-family random graph models for valued networks. , 2011, Electronic journal of statistics.

[19]  見松 健太郎,et al.  Instability , 1997, Essentials of Atmospheric and Oceanic Dynamics.

[20]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: II. Multivariate relations. , 1999, The British journal of mathematical and statistical psychology.

[21]  Martina Morris,et al.  ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. , 2008, Journal of statistical software.

[22]  Tom A. B. Snijders,et al.  Markov Chain Monte Carlo Estimation of Exponential Random Graph Models , 2002, J. Soc. Struct..

[23]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[24]  Peng Wang,et al.  Closure, connectivity and degree distributions: Exponential random graph (p*) models for directed social networks , 2009, Soc. Networks.

[25]  Jukka-Pekka Onnela,et al.  Variation in patient-sharing networks of physicians across the United States. , 2012, JAMA.

[26]  W. Powell,et al.  Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in the Life Sciences1 , 2005, American Journal of Sociology.

[27]  Theodore J Iwashyna,et al.  Quality of Care and Interhospital Collaboration: A Study of Patient Transfers in Italy , 2014, Medical care.

[28]  Mark S Handcock,et al.  MODELING SOCIAL NETWORKS FROM SAMPLED DATA. , 2010, The annals of applied statistics.

[29]  C. Andrieu,et al.  The pseudo-marginal approach for efficient Monte Carlo computations , 2009, 0903.5480.

[30]  Pierre Alquier,et al.  Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels , 2014, Statistics and Computing.

[31]  Steven M. Goodreau,et al.  Advances in exponential random graph (p*) models applied to a large social network , 2007, Soc. Networks.

[32]  Richard G. Everitt,et al.  Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks , 2012, ArXiv.

[33]  Alberto Caimo,et al.  Bayesian model selection for exponential random graph models , 2012, Soc. Networks.

[34]  Alberto Caimo,et al.  Knowledge Sharing in Organizations , 2015 .

[35]  Garry Robins,et al.  Analysing exponential random graph (p-star) models with missing data using Bayesian data augmentation , 2010 .

[36]  Pavel N Krivitsky,et al.  A separable model for dynamic networks , 2010, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[37]  Theodore J Iwashyna,et al.  The Structure of Critical Care Transfer Networks , 2009, Medical care.

[38]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp , 1996 .

[39]  Alberto Caimo,et al.  Simultaneous modeling of initial conditions and time heterogeneity in dynamic networks: An application to Foreign Direct Investments , 2015, Network Science.

[40]  Ove Frank,et al.  http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained , 2007 .

[41]  Mark S Handcock,et al.  Improving Simulation-Based Algorithms for Fitting ERGMs , 2012, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[42]  Antonietta Mira,et al.  Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods , 2014, 1408.4663.

[43]  Richard Platt,et al.  Social network analysis of patient sharing among hospitals in Orange County, California. , 2011, American journal of public health.

[44]  P. Diaconis,et al.  Estimating and understanding exponential random graph models , 2011, 1102.2650.

[45]  Theodore J Iwashyna,et al.  Revenue, relationships and routines: the social organization of acute myocardial infarction patient transfers in the United States. , 2012, Social science & medicine.

[46]  A. Mira,et al.  Auxiliary Parameter MCMC for Exponential Random Graph Models , 2016, Journal of Statistical Physics.

[47]  Edward O. Laumann,et al.  Community Structure as Interorganizational Linkages , 1978 .

[48]  Alberto Caimo,et al.  Bayesian inference for exponential random graph models , 2010, Soc. Networks.

[49]  J. Møller,et al.  An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants , 2006 .

[50]  Jenine K. Harris,et al.  How does network structure affect partnerships for promoting physical activity? Evidence from Brazil and Colombia. , 2011, Social science & medicine.

[51]  Andrew B. Whitford Bayesian Methods: A Social and Behavioral Sciences Approach , 2003, Journal of Politics.

[52]  Alberto Caimo,et al.  Bergm: Bayesian Exponential Random Graphs in R , 2012, 1201.2770.

[53]  Daniel A. Levinthal,et al.  ABSORPTIVE CAPACITY: A NEW PERSPECTIVE ON LEARNING AND INNOVATION , 1990 .

[54]  A James O'Malley,et al.  The analysis of social network data: an exciting frontier for statisticians , 2012, Statistics in medicine.

[55]  Stanley Wasserman,et al.  Statistical Models for Social Networks , 2000 .

[56]  A. James O’Malley,et al.  The analysis of social networks , 2008, Health Services and Outcomes Research Methodology.

[57]  Zoubin Ghahramani,et al.  MCMC for Doubly-intractable Distributions , 2006, UAI.

[58]  Shahadat Uddin,et al.  Mapping and modeling of physician collaboration network , 2013, Statistics in medicine.

[59]  Pavel N Krivitsky,et al.  Computational Statistical Methods for Social Network Models , 2012, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[60]  P. Pattison,et al.  New Specifications for Exponential Random Graph Models , 2006 .

[61]  Erika L. Moen,et al.  An analysis of patient-sharing physician networks and implantable cardioverter defibrillator therapy , 2016, Health Services and Outcomes Research Methodology.

[62]  Alessandro Lomi,et al.  Relational collaboration among spatial multipoint competitors , 2012, Soc. Networks.

[63]  Theodore J Iwashyna,et al.  The incomplete infrastructure for interhospital patient transfer , 2012, Critical care medicine.

[64]  Martina Morris,et al.  A statnet Tutorial. , 2008, Journal of statistical software.

[65]  E. Todeva Networks , 2007 .

[66]  D. Hunter,et al.  Goodness of Fit of Social Network Models , 2008 .

[67]  Julien Brailly,et al.  Exponential Random Graph Models for Social Networks , 2014 .

[68]  P. Holland,et al.  An Exponential Family of Probability Distributions for Directed Graphs , 1981 .

[69]  W. Powell,et al.  Networks, Propinquity, and Innovation in Knowledge-intensive Industries , 2009 .

[70]  M. Schweinberger Instability, Sensitivity, and Degeneracy of Discrete Exponential Families , 2011, Journal of the American Statistical Association.

[71]  Edward O. Laumann,et al.  Microstructural analysis in interorganizational systems , 1982 .

[72]  Alberto Caimo,et al.  Bayesian exponential random graph models with nodal random effects , 2014, Soc. Networks.

[73]  Peng Wang,et al.  Recent developments in exponential random graph (p*) models for social networks , 2007, Soc. Networks.

[74]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: III. Valued relations , 1999 .

[75]  Jeff Gill,et al.  Bayesian Methods : A Social and Behavioral Sciences Approach , 2002 .

[76]  Martina Morris,et al.  Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. , 2008, Journal of statistical software.

[77]  Theodore J Iwashyna,et al.  Guided transfer of critically ill patients: where patients are transferred can be an informed choice , 2011, Current opinion in critical care.