Structure and geography of a hospital patient transfer network

Structure and geography of a hospital patient transfer network Alex Stivala1,2 Maksym Byshkin2Francesca Pallotti3 Alessandro Lomi2,4 1Swinburne University of Technology, Melbourne, Australia 2Universit`a della Svizzera italiana, Lugano, Switzerland 3University of Greenwich, U.K. 4The University of Melbourne, Australia. INSNA Sunbelt XXXVIII, June 26 – July 1, 2018 Utrecht, The Netherlands 1 / 28 The original paper 2 / 28 The data INetwork of transfers of critically ill patients. IData derived from 2005 Medicare claims. I3308 hospitals with 47820 patient transfers. I“nearly all hospitals participated in at least one transfer, and 4.5% of all critical care hospitalizations involved such a transfer.” I“Transfer” from hospital A to B defined as patient in A and then in B on the same or next day. ITransfers are then represented as a directed edge from A to B. 3 / 28 Some general conclusions from the original paper IHospitals transfer patients to several other hospitals in a complex network, not a simple hierarchy. IIt is not like a “hub-and-spoke” model explaining secondary and tertiary care. IPatients seem to move towards better resourced hospitals. While the secondary / tertiary hospital model may have some heuristic value, the implied hierarchy (in which secondary hospitals send but do not receive patients and tertiary hospitals receive but do not send patients) does not appear to be present in our data. Instead, hospitals appear to maintain diverse portfolios of other facilities to which they transfer patients. (Iwashyna et al. 2009) 4 / 28 So the simple model is not right. What can we do? IWe can use network models to try to explain the complex observed network structure. INetwork community detection and stochastic block modeling to try to define classes (more complex than the secondary / tertiary model) of hospitals in the network. IExponential random graph model (ERGM) to try to find the processes that give rise to the observed network. IAnd we will have to account for the effect of geography, as distances between hospitals is clearly likely to be a significant factor. 5 / 28 Community structure and geography INetwork communities are groups of nodes in which the nodes have more connections within the group than to nodes in other groups. IWe can “see” these in the following network plots, Iand there are very many ways to find them algorithmically (we will do some). IBut could the “communities” in this network be mostly be due to geography...? 6 / 28 Network plot by MATLAB “force” (Fruchterman-Reingold) 7 / 28 Network plot by MATLAB “subspace” (Koren) 8 / 28 Network plot in MATLAB according to geography 9 / 28 Blocks found by SBM treating edges as undirected Cluster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 16 / 28 Finding space-independent communities IExpert et al. 2011 “Uncovering space-independent communities in spatial networks” PNAS 108(19):7663–7668 IInstead of using the Newman-Girvan null model (preserve node degrees on average), use instead a null model that preserves weighted average for an edge to exist at a given distance. IThe null model is similar to a “gravity” model: edge probability between two nodes is proportional to the product of the node “masses” (or importances) over function of the distance between them. IFor “importance” we try both node degree (similar to Newman-Girvan null model) or number of discharges (as a proxy for hospital size). IFor the clustering algorithm we use a generalized Louvain method and implement the Expert et al. (2011) null model in the modularity matrix. 17 / 28 Communities found with degree spatial null model (bin size 100 km) Cluster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 18 / 28 SBM (but not Degree-Corrected SBM) and spatial null model communities are less related to geographical regions than network communities are 0.0 0.2 0.4 0.6 0.8 1.0 NMI Community Division SBM Division DCSBM Division Spatial Division Community State SBM State DCSBM State Spatial State Community HRR SBM HRR DCSBM HRR Spatial HRR 19 / 28 ERGM introduction IA way of modeling network ties based on structure and attributes. IGiven an observed network, we estimate parameters for local effects, such as reciprocity, closure (clustering), activity (sending more ties), popularity (receiving more ties), preferential attachment, homophily, etc. IThe sign (positive for the effect occurring more than by chance, negative for less than by chance) and significance tell us about these processes, taking dependency into account. II.e. it tells us about the process occurring significantly more or less than by chance, given all the other effects in the model occurring simultaneously. 20 / 28 Modeling the actual directed network IWe were unable to estimate ERGMs for this directed network with existing methods (statnet, PNet, even with snowball sampling). IWe were only able to estimate a simple model treating the network as undirected with the new IFD sampler (Byshkin et al. 2016 J. Stat. Phys. 165(4):740–754). But ignoring the edge direction is too limiting as transfers are inherently directional. IBut using the new “Equilibrium Expectation” algorithm (Byshkin et al. 2018 Fast Maximum Likelihood estimation via Equilibrium Expectation for Large Network Data. arXiv preprint arXiv:1802.10311.), extended to apply to directed networks, we can estimate ERGM parameters for this network (in less than an hour). 21 / 28 ERGM results (no geography, and with HRR and state) Effect Model 1 Model 2 Arc −6.175 (−6.316,−6.034) −14.914 (−15.058,−14.771) AltInStars 0.371 (0.351,0.391) 0.244 (0.222,0.265) AltOutStars −2.035 (−2.117,−1.954) −2.364 (−2.444,−2.285) Reciprocity 5.257 (5.189,5.326) 6.659 (6.569,6.748) AltKTrianglesT 1.977 (1.955,1.999) 0.937 (0.919,0.956) AltKTrianglesC −0.640 (−0.654,−0.626) −0.383 (−0.395,−0.371) ContinuousSender log discharges −0.142 (−0.149,−0.135) 0.309 (0.297,0.321) ContinuousReceiver log discharges 0.317 (0.312,0.322) 0.837 (0.830,0.843) Diff log discharges −0.287 (−0.300,−0.275) 0.124 (0.104,0.144) Sender teaching hospital −0.293 (−0.351,−0.234) −0.472 (−0.531,−0.413) Receiver teaching hospital 0.506 (0.487,0.526) 0.621 (0.596,0.645) Interaction teaching hospital −0.071 (−0.135,−0.006) −0.150 (−0.223,−0.078) Matching hrr — 2.353 (2.330,2.376) MatchingReciprocity hrr — −1.929 (−1.989,−1.869) Matching state — 3.705 (3.660,3.751) MatchingReciprocity state — −3.767 (−3.857,−3.678) logGeoDistance — — 22 / 28 Model interpretation (1,2) – structural ISome hospitals receive patients from many hospitals, but there tend not to be hospitals that send patients to many hospitals. IThere is a tendency for reciprocity. IThere is a tendency for transitive closure, but against cyclic closure: IIf hospital A sends patients to hospitals B and C, then it is likely that hospital B also sends patients to C (or C to B). IBut if hospital A sends patients to hospital B, and B to C, then it is unlikely that C also sends patients to A: i.e. generalized exchange is unlikely. Path closure AT-T Cyclic closure AT-C 23 / 28 Model interpretation (1,2) — attributes and regions ITeaching hospitals are less likely to send patients and more likely to receive them. And patients are less likely to be transferred between teaching hospitals (than from a teaching to a non-teaching hospital). I(Using number of discharges as proxy for hospital size), larger hospitals are much more likely to receive transferred patients. IWhen geography included, larger hospitals are also more likely to send patients. But this is reversed if geography is not taken into account: it looks like larger hospitals are less likely to send patients! ISimilarly transfers are more likely between hospitals of different sizes, but this is reversed if no geographical information is included. ITransfers are more likely within states and within HRRs. IHowever reciprocity within (rather than between) states or HRRs is less likely. 24 / 28 ERGM results (include geographical distance) Effect Model 3 Model 4 Arc −10.711 (−10.869,−10.554) −6.122 (−6.245,−5.999) AltInStars 0.161 (0.136,0.187) 0.103 (0.083,0.122) AltOutStars −2.918 (−2.989,−2.847) −4.057 (−4.125,−3.989) Reciprocity 5.464 (5.364,5.564) 1.222 (1.183,1.261) AltKTrianglesT 0.715 (0.697,0.732) 0.925 (0.905,0.946) AltKTrianglesC −0.441 (−0.453,−0.429) −0.556 (−0.572,−0.541) ContinuousSender log discharges 0.501 (0.491,0.511) 0.723 (0.719,0.727) ContinuousReceiver log discharges 1.052 (1.047,1.057) 1.039 (1.037,1.041) Diff log discharges 0.296 (0.277,0.315) 0.387 (0.378,0.395) Sender teaching hospital −0.558 (−0.611,−0.505) −0.665 (−0.710,−0.620) Receiver teaching hospital 0.493 (0.465,0.521) 0.316 (0.295,0.337) Interaction teaching hospital −0.439 (−0.505,−0.373) −0.569 (−0.628,−0.511) Matching hrr 1.313 (1.281,1.344) — MatchingReciprocity hrr −1.781 (−1.844,−1.717) — Matching state 2.164 (2.116,2.213) — MatchingReciprocity state −3.435 (−3.536,−3.333) — logGeoDistance −0.982 (−0.993,−0.971) −1.529 (−1.536,−1.521) 25 / 28 Distribution of the number of discharges is consistent with both power law and log-normal distributions 1 10 100 1000 10000 0.0005 0.0050 0.0500 0.5000 US Hospital Discharges Number of discharges CDF Power law α = 5.248 Log−normal µ = 8.602 σ = 0.552 4 / 42 Degree is correlated with number of discharges (inmore so than out-degree) ● ●● ● ●●● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ●●● ● ●● ●●●● ● ●● ● ● ●● ● ●● ●● ● ●● ●● ●● ● ● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ●● ● ●● ●● ● ●●● ● ●● ●● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ●●● ● ● ● ● ●● ● ● ●● ●● ● ●●● ●● ● ●● ●●●● ● ●●● ● ● ● ● ● ●●● ● ●●●● ● ● ●●● ● ● ●● ● ●● ● ●● ●●● ● ●● ● ● ● ●● ●● ● ●● ●● ●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ● ●● ●● ●● ●● ● ● ●●● ●●● ● ●● ● ●● ● ● ● ● ●●● ● ●● ● ● ●●● ●● ● ●●● ● ●● ● ●●● ●●● ● ●● ●● ● ● ● ● ● ●● ●●● ● ● ●● ●● ● ● 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60 90 0 10000 20000 30000 40000 Number of discharges in−degree ● ● ● ●● ● ● ● ●●●● ● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ● ●●● ●● ●● ● ●● ● ●● ●● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●● ●● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ● ●● ●●● ●● ●● ● ●● ● ● ● ●●● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ● ●● ● ● ● ● ● ● ●● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ●● ● ●● ● ●●● ● ● ● ● ●●● ●● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ●●● ● ● ● ●● ●●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●●● ● ●● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ●● ●●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ● ●● ●● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ●● ●●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ●●● ● ●● ● ●●● ● ● ● ●● ● ● ●● ● ● ●●● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●●● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● 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6 / 42 Distribution of the number of discharges is consistent with both power law and log-normal distributions 1 10 100 1000 10000 0.0005 0.0050 0.0500 0.5000 US Hospital Discharges Number of discharges CDF Power law α = 5.248 Log−normal µ = 8.602 σ = 0.552 7 / 42 Distribution of transfer distances and hospital distances 8 / 42 Patient transfer distances are not power law 0.00000000000001 0.00000000010000 0.00000100000000 0.01000000000000 0.0001 0.0010 0.0100 0.1000 1.0000 US Hospital Transfers Distances Distance (km) CDF Power law α = 2.424 Using the statistical tests described by Clauset et al. (2009) this distribution is not consistent with a power law distribution (p<0.01). 9 / 42 The network and all census division subnetworks are small-world Network N LgLrLlC∗ gC∗ rC∗ lSWI USA 3308 5.15 3.74 189.95 0.438 0.003 0.653 0.664 EastSouthCentral 285 3.91 2.68 17.31 0.510 0.029 0.646 0.713 Pacific 428 4.26 3.09 30.15 0.377 0.017 0.627 0.566 Mountain 204 3.93 2.86 15.88 0.440 0.031 0.612 0.646 WestSouthCentral 437 3.69 2.92 27.17 0.462 0.018 0.643 0.687 NewEngland 156 2.80 2.38 9.37 0.516 0.053 0.648 0.733 SouthAtlantic 572 4.03 2.92 32.63 0.492 0.015 0.653 0.719 EastNorthCentral 519 3.98 2.94 30.90 0.464 0.016 0.649 0.681 WestNorthCentral 284 3.82 3.00 21.54 0.402 0.023 0.616 0.611 MidAtlantic 413 3.25 2.62 20.73 0.495 0.024 0.666 0.709 IAll networks are small-world according to the S∆significance test of Humphries & Gurney (2008). ISmall World Index (SWI) (Neal 2017) ranges from 0 to 1. ILgis the average shortest path length of the network IC∗ gis its clustering coefficient. ILrand C∗ rare, respectively, the average shortest path length and clustering coefficient for an Erd˝os-Renyi random graph with same size and mean degree. ILland C∗ lare, respectively, the mean path length and clustering coefficient for a ring lattice graph with the same size and mean degree. 10 / 42 SBM structure examples 11 / 42 Community detection results (nodes with no HRR removed) Method Dir. We. # com. Modularity State NMI Div. NMI HRR NMI Time (m) Louvain N Y 45 0.92 0.82 0.68 0.76 0.00 Fast greedy N Y 46 0.92 0.81 0.65 0.76 0.00 Walktrap N Y 118 0.90 0.79 0.62 0.83 0.01 Edge betweenness N Y 35 0.87 0.79 0.70 0.69 29.16 Louvain N N 31 0.87 0.77 0.69 0.69 0.00 Edge betweenness N N 33 0.86 0.79 0.70 0.69 15.03 Walktrap N N 52 0.85 0.80 0.67 0.73 0.01 Infomap Y Y 197 0.85 0.78 0.58 0.87 0.02 Infomap N Y 251 0.84 0.77 0.56 0.90 0.02 Leading eigenvector N Y 57 0.82 0.72 0.58 0.69 0.03 Fast greedy N N 24 0.80 0.66 0.59 0.56 0.00 Infomap N N 121 0.80 0.81 0.62 0.85 0.03 Label propagation N N 120 0.78 0.80 0.62 0.84 0.00 Infomap Y N 145 0.77 0.79 0.60 0.84 0.02 Label propagation N Y 465 0.71 0.72 0.52 0.88 0.00 Leading eigenvector N N 16 0.40 0.29 0.30 0.26 0.00 Edge betweenness Y N 1629 0.20 0.55 0.39 0.65 4.25 Edge betweenness Y Y 1656 0.19 0.55 0.39 0.65 6.29 12 / 42 Blocks found by SBM with directed arcs Cluster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 13 / 42 Blocks found by Degree-Corrected SBM with k= 32 Cluster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 20 / 42 DCSBM block matrix shows assortative (community) structure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0.01 0.03 0.05 Value 0 200 600 1000 Color Key and Histogram Count 21 / 42 SBM assigns some blocks apparently according to degree heterogeneity 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 0 40 80 Cluster In−degree 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 0 10 20 Cluster Out−degree 22 / 42 DCSBM by construction assigns blocks independent of node degrees 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 0 40 80 Cluster In−degree 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 0 10 20 Cluster Out−degree 23 / 42 Spatial null model generalized Louvain method results Importance Binsize (km) Modularity # communities Size 5 0.63 181 Size 10 0.63 182 Size 50 0.65 159 Size 100 0.66 143 Degree 5 0.70 43 Degree 10 0.70 38 Degree 50 0.71 38 Degree 100 0.72 36 24 / 42 Spatial null model community degree distributions 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 0 40 80 Cluster In−degree 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 0 10 20 Cluster Out−degree 25 / 42 Model configurations — structural Alternating k-stars: useful for capturing degree distribution Popularity spread Alt. in-star AinS Activity spread Alt. out-star AoutS Alternating k-triangles (AT): useful for modeling social circuit dependence Path closure AT-T Cyclic closure AT-C 26 / 42 Model configurations — categorical attributes Matching Matching reciprocity Mismatching Mismatching reciprocity 27 / 42 ERGM results (removing unconverged Interaction teaching) Effect Model 5 Model 6 Arc −10.730 (−10.873,−10.586) −6.147 (−6.282,−6.012) AltInStars 0.167 (0.141,0.192) 0.115 (0.093,0.137) AltOutStars −2.921 (−2.988,−2.854) −4.037 (−4.103,−3.970) Reciprocity 5.499 (5.396,5.601) 1.236 (1.197,1.276) AltKTrianglesT 0.713 (0.696,0.731) 0.919 (0.899,0.938) AltKTrianglesC −0.432 (−0.444,−0.420) −0.543 (−0.558,−0.527) ContinuousSender log discharges 0.499 (0.490,0.509) 0.720 (0.716,0.724) ContinuousReceiver log discharges 1.053 (1.049,1.058) 1.040 (1.038,1.042) Diff log discharges 0.306 (0.287,0.325) 0.401 (0.392,0.409) Sender teaching hospital −0.771 (−0.808,−0.734) −0.961 (−0.997,−0.924) Receiver teaching hospital 0.391 (0.373,0.408) 0.195 (0.170,0.219) Interaction teaching hospital — — Matching hrr 1.306 (1.288,1.325) — MatchingReciprocity hrr −1.762 (−1.816,−1.707) — Matching state 2.175 (2.130,2.221) — MatchingReciprocity state −3.467 (−3.565,−3.370) — logGeoDistance −0.975 (−0.980,−0.971) −1.523 (−1.536,−1.509) 28 / 42 ERGM estimation attempts ICould not estimate network at all using PNet. IAlso could not get estimations to work with snowball samples. IUsing statnet (even new “stepping” algorithm), could not estimate whole network, and only ended up with converged estimations for 4/9 census divisions with MCMC.burnin=1e07 and took between 17 and 78 hours. IThe first successful estimation for whole network was using IFD sampler, but only implemented for undirected networks so limited usefulness. 29 / 42 Comparing results with Lomi & Pallotti 2012 (1) INo significant centralization effects here; unlike our models of US network which find centralization on in-degree and against centralization on out-degree. IBoth find significant positive path closure but negative cyclic closure, just as we did. IBoth also find overall positive reciprocity. 36 / 42 Comparing results with Lomi & Pallotti 2012 (2) IHospital attributes: IBoth show regional homophily effects (HRR and LHU respectively). IWhen geography is included, we find heterophily on size (num. discharges) but Lomi & Pallotti found homophily on size (num. employees). IWe did not have data on organization form, occupancy rate, case mix, complementarity, performance index or patient pool overlap / competition to compare. 37 / 42 Caimo, Pallotti & Lomi (2017) “Bayesian exponential random graph modelling of interhospital patient referral networks” IInterhospital patient transfer network of total 16 557 patients between 110 hospitals in Lazio region (12 Local Health Units [LHUs]) of Italy for 2007. IModel includes: Inumber of beds Ioccupancy rate Iaverage length of stay Icase mix index IOrganizational form (LHU / trust / research / classified / private) IJaccard distance between all hospitals in space of all clinical specialties Igeographical distance between hospitals IEstimation using Bayesian ERGM (Caimo & Friel 2011) 38 / 42 Caimo, Pallotti & Lomi 2017 BERGM results 39 / 42 Comparing results with Caimo, Pallotti & Lomi 2017 (1) IBoth find a limited number of hospitals receive a large number of transfers, but diffuse activity of sending patients. IBoth find tendency for interhospital transfer to be in closed structures of collaborating hospitals: “This tendency towards network closure is consistent with the idea that patient transfer relations require a considerable level of trust and social control between partner hospitals.” (Caimo, Pallotti & Lomi, 2017) IBoth also find overall reciprocity of transfers between hospitals. 40 / 42 Comparing results with Caimo, Pallotti & Lomi 2017 (2) IGeographical: Both show that transfers are less likely as distance increases. IHospital attributes: IBoth show positive sender and receiver effects for hospital size (num. discharges [when geography included] or num. beds). IBoth show regional homophily effects: within HRR, state, division; or within LHU (of course this is also related to geographic distance). IWe did not have data on organization form, occupancy rate, case mix, average length of stay, or clinical specialties to compare. IHowever an interesting difference is that Caimo et al. find no significant effect of organization form, and we use only the binary “teaching hospital”, we actually find heterophily on this attribute: teaching hospitals, while generally more likely to be receivers and less likely to be senders, are also less likely to send patients to each other (although this is only significant in models 1 and 2). 41 / 42 Comparing results with Caimo, Pallotti & Lomi 2017 (3) IThe Bayesian approached used in Caimo et al. allows some more sophisticated analyses than we can do with a non-Bayesian approach, such as incorporating prior information and the greater flexibility and intuitiveness of the posterior distribution, as well as allowing analysis of the posterior correlation matrix. IIt is however, still very computationally expensive: we would not have been able to analyze the 3308 node network with this approach (Caimo et al. use a 110 node network). 42 / 42