Applications of Social Network Construction and Analysis in the Medical Referral Process

Wadhah Almansoori▼ Omar Zarour+ Tamer N. Jarada+ Panagiotis Karampales* Jon Rokne+ Reda Alhajj+* #

▼EMS, Alberta Health Services1632 14 Avenue NW

Calgary Alberta, Canada

+Dept of Computer Science University of Calgary

Calgary, Alberta, Canada

*Hellenic American University 156 Hanover Street

Manchester, NH, USA

#Dept of Computer ScienceGlobal University Beirut, Lebanon

Abstract The application of social network analysis (SNA) and mining in health care domains has recently received a considerable attention for its key role in understanding how doctors form communities, and how they are socially connected with each other. This understanding helps enhance organizational structures and process flows. In this paper, we show how SNA techniques can solve issues in the medical referral system by analyzing the social network of general practitioners (GPs) and specialists (SPs) associated with a medical referral system in the Canadian healthcare system and the like. Various SNA and mining procedures are proposed backed by experimental results.

Keywords: SNA, referral system, communities, healthcare

1 Introduction In this paper, we apply Social network analysis (SNA) and data mining techniques to solve some issues occurring in the medical referral process. Three social networks of GPs and SPs are developed and then analyzed to discover doctors’ communities and hidden patterns that will be useful to solve the issues related to the medical referral process. SNA could benefit from data mining techniques as a pre-processing step to prepare the social network data. The main data mining technique to be used is clustering which is the assignment of a set of observations into subsets (called clusters) so that all the observations in the same cluster are similar in some sense. SNA and mining have received a good attention by researchers in the health care domain. For example, Anderson & Jay [1] applied SNA and mining techniques to study the relationship between physician networks and the utilization of computer based hospital information system (HIS); they concluded that physicians were influenced to use the new HIS because of the strong social relationship between the physicians.

One of the important processes in the health care domain in countries like Canada is the medical referral process. It is the process of referring patients to doctors with special practice specialty. We have studied the referral process being used by Alberta Health Services (AHS) in Calgary. When a patient has a health problem, he/she visits a General Practitioner (GP); a GP may decide that the illness problem of the patient requires special expertise. Accordingly, the

GP will refer the patient to a specialist (SP), who is specializing in the patient’s illness type.

The larger and more complex the integrated health care system is the more complicated and, hence, important the problem of finding an appropriate specialist it becomes [22]. The reason behind the unacceptable delay in the referral process comes from the long time spent in finding the appropriate specialist. We have met some GPs from AHS in Calgary and they have told us that the way used in Calgary to find the appropriate specialists, if the GP is not familiar with the right SP, is either by: contacting different specialists, searching in previous referrals records and try to match the symptoms, or consulting with any other GPs who might be knowledgeable about some specialists. This way, indeed, causes the following problems: (1) A delay in the referral process if the GPs are just new and spend a long time trying to consult with other GPs to find the right specialist. (2) GPs do not refer patients to specialists with the right skills. (3) Patients are referred to the right specialists, but the waiting time is too long where there are other available SP with the right skills who can serve the patients in a shorter time.

In this paper, our motivation is to solve the problems mentioned above related to the referral system and to speed up the referral process specifically in the consultations stage between physicians when needed for a referral. Since GPs face problems in finding the right doctors to consult with for a referral, we have introduced a model to discover the doctors’ communities who can be recognized as the significant consultation group. In other words, using a referral dataset, we discover which doctors should be targeted by other GPs for referral consultations. In addition, we analyze the social network of SPs to discover hidden patterns that are hard to discover by looking at the raw data. These patterns relate to disease discovery. We then, analyze the bipartite graph that contains nodes as GPs and SPs. We analyze this graph in two different models: 1-mode and 2-mode network models. The outcome of this analysis is to predict future relations between GPs with other GPs and SPs with other SPs.

Contributions of the research described in this paper are summarized below: 1. We incorporate SNA measures with data mining

techniques and apply them to a very important domain (health care domain) to help the society to have a better medical referral process.

2011 Ninth IEEE International Conference on Dependable, Autonomic and Secure Computing

978-0-7695-4612-4/11 $26.00 © 2011 IEEE

DOI 10.1109/DASC.2011.140

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2011 Ninth IEEE International Conference on Dependable, Autonomic and Secure Computing

978-0-7695-4612-4/11 $26.00 © 2011 IEEE

DOI 10.1109/DASC.2011.140

817

2011 IEEE Ninth International Conference on Dependable, Autonomic and Secure Computing

978-0-7695-4612-4/11 $26.00 © 2011 IEEE

DOI 10.1109/DASC.2011.140

817

2011 IEEE Ninth International Conference on Dependable, Autonomic and Secure Computing

978-0-7695-4612-4/11 $26.00 © 2011 IEEE

DOI 10.1109/DASC.2011.140

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2. We use SNA measures to find hidden referral patterns such as future associations (consultations) between GPs. This enhancement will increase the density of the network at some point in the future.

3. We use SNA measures to work as a disease discovery. For example, knowing specialists who appear in the center of the network in a given time and region can help the health care people to make disease awareness. The rest of this paper is organized as follows. Section 2

discusses related works. Section 3 presents the proposed solution and methodology to analyze social networks of doctors association with the medical referral system. Section 4 reports and discusses experimental results. Section 5 is summary and conclusions.

2 Related Work In this section we present basics of the background necessary for the reader to understand details of our proposed solution. We first discuss the medical referral process. Then, we cover the related work.

2.1 Medical Referral Process Calgary has one of Canada’s largest integrated health care systems serving 1.2 million people. More than 25000 staff members and 2200 physicians provide services over 100 locations.

The referral process is defined by Shortell & Anderson [20] as the permanent or temporary transfer (including sharing) of responsibility for a patients care from one physician to another. The reason of the referral is because the receiving physician is more experienced and specializing in the patient’s illness. Patients are referred by a general practitioner to a specialist or by a specialist to another specialist.

When a patient is sick, he/she visits a GP. Then, the GP diagnoses the patient to see if he/she can solve the problem of the patient. In some cases, the GPs know the problem of the patient, but they cannot solve the problem themselves. Therefore, they have to send the patient to a specialist with the right skills to solve the patient’s problem. Due to the large number of GPs and specialists in town, it is hard for GPs to know every other doctor in town especially for new GPs so they have to consult with other GPs who have been practicing for a longer time. In the consultation stage, GPs seek recommendations from other GPs who might have some knowledge about to whom a particular patient should be referred to. Other factors that may dictate and shape the referral process include how urgent is the case and average wait time of the available specialists, how far is the specialist from the residence of the patient and whether the patient is willing to travel far to get faster handling of his/her case.

2.2 Related Work Recent work in SNA area examines the association of the SNA quantitative measures with organizational performance outcomes. For example, Cummings & Cross [9] found that

degree of hierarchy, core-periphery structure, and structural holes of leaders correlated negatively with performance in 182 work groups in a large telecomm company. Aydin, et al. [2] found that increased network communication density was associated with higher use of an electronic medical record system by nurse practitioners and physician’s assistants. In addition, there are studies showing how network parameters change with time. For example, Shah (2000) showed that network centrality decreased after downsizing in a consumer electronics firm, whereas Burkhardt & Brass [6] documented increased network centrality after introduction of a new computer system in a federal agency.

Fattore et al. [12] have used SNA as a tool to analyze the patterns of decision making and discuss how these measures can be used to facilitate the design and measure the outcomes of interventions to improve the organizational behaviour structure in primary care practices. They conducted their study based on two primary practices. Each member of the primary practices makes decision about new regulations or policies or any decision that relates to their practice from time to another. Some members consult with other members before they make the decision. The main focus of this work is to study the decision making patterns for individuals with their relationships with other practice members’ and compare these patterns with the patterns of the other practice. As a first step, they collected data from members of each practice by making interviews and surveys. They asked everyone to indicate which other member he/she consults with when making a decision. Then, they visualized the network of each practice and they used SNA quantitative measures: network density, clustering coefficient, hierarchy, and centralization. Based on the calculations of these measures, Marin et. al. [16] concluded that decision-making patterns differ widely in the two practices. For example, practice 2 has a much more collaborative in decision-making process than practice 1. A shortcoming of this approach is that their study was to compare the power of an individual with another individual. And their centrality measures do not detail how important a node is among the whole structure of the network. Another gap in this approach is that it does not identify cohesion subgroups that have a density of 1. Instead, they only calculated the density for the whole network.

Anderson & Jay [1] introduced a block model analysis and multidimensional scaling to analyze the network of 24 physicians in a private practice. The main focus of the analysis is to study the relationship between the physicians’ network and the utilization of computer based HIS. They collected data from physicians to create four different matrices: referrals, consultations, discussions, on-call coverage. They clustered the physicians into subgroups and each subgroup consists of physicians with similar patterns. Then, they calculated densities indices and the image matrices that reflect every matrix to indicate the arrows directions of the networks. The results of this study indicated that the network location has a significant effect on the time at which physicians adopt an innovation.

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Moreover, they concluded that the adoption of a new hospital information system highly depends on the peer influences. A shortcoming of this approach is that it discovers the doctors communities based on one time period. In fact, the social network structure changes from one time period to another which may affect the findings of the previous time period. For example, if a group appears in the center at some point of time, it may no longer be in the center in another future point.

The shortcomings of the existing approaches have motivated our work described in this paper, which is intended to be more comprehensive. Our proposed approach focuses to solve existing issues in the health care domain as well as to discover useful patterns and predictions that will serve the health care regions. We introduce various analysis strategies of social networks of general practitioners and specialists. First, we analyze the social network of GPs network over different periods to discover significant communities of doctors who can be recognized for referral consultations. Second, we analyze the social network of SPs in different periods to discover hidden patterns as potential for disease discovery. Third, we analyze the bipartite graph of GPs and SPs network to find cliques/communities with similar interests and predict future collaboration between the members of the communities.

3 Proposed Solution and Methodology In this section, we introduce our proposed solution which consists of three main components: (1) Social network analysis of General Practitioners; (2) Social network analysis of Specialists; (3) Social network analysis of General Practitioners and Specialists combined together

3.1 Social Network Analysis of General Practitioners New GPs face difficulties in finding the right doctor to consult with for an appropriate specialist. In this section, we solve this problem by designing a social network for general practitioners to study the relationship between the general practitioners in terms of making consultations with each other about a referral. Analyzing this social network later on will allow us to identify the most powerful general practitioners group that has been sought for referral consultations. In other words, this group will be considered as the most knowledgeable group of specialists in the community since most of the other GPs seek their consultations. In addition, this identified group can be targeted by new GPs for any further consultations. This will save a lot of time because the GPs will not have to keep consulting with random GPs who are not familiar with the right specialists.

We use the following steps, as shown in Figure 3.1, to visualize and then analyze the social network of general practitioners: Step 1. The physicians’ relationship is represented in an incidence matrix where rows represent GPs and columns represent SPs, and the matrix data is either zero or one

which represent whether a GP made a referral to a particular specialist or not, respectively.Step 2. We define a threshold Θ= 6 and consider only those GPs who made referrals >= Θ. The reason behind this threshold is because after looking at the overall data, we realized that those GPs who made referrals less than six (average) will not play a good role in the network because they might be just newly hired and it is unlikely to consider them for consultations. Thus, we consider them as noises. We have chosen the threshold value after studying the distribution of the referrals. Step 3. We then apply k-means clustering algorithm using MATLAB on the incidence matrix to find five sub-groups of GPs who have similar referrals patterns. The number of clusters was chosen after trying different numbers and since the k-means does not always give the correct output, we had to check the clustering assignment manually to make sure every cluster has the correct GPs members based on the referral patterns similarity. Step 4. For each sub-group, we find the consultation relations among each pair of GPs in the internal sub-group as well as with the external sub-groups. In other words, we explore the consultation patters of which GP has consulted with whom. This means members of group1 may consult with group2 or members of group1 may consult with members of the same group. Step 5. Since our study is based on the previous year to make our analysis stronger, we extract twelve consultation matrices where each matrix corresponds to a previous month. We repeat Step 4 to each one of these matrices.

Based on this step, we visualize the social network for each month where nodes represent the groups resulted from the clustering process in step 3 and edges connect two nodes if any member of a group consulted with another member from the other group. Step 6. Finally, we calculate the indegree centrality measure for each SN and then find the average of these indegree centrality measures of the twelve matrices to identify which group is the central based on the average.

To validate our result and analysis about which group is the most significant based on the whole network structure, we define four consultation indices as following:

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These calculations will allow us to know which group is the most powerful in receiving consultation requests; this will validate our findings using the indegree measure. Consultation index1: shows the interaction behaviour in seeking consultations from other groups among the whole nodes in the network. For each group, we calculate the value of the consultation index1 by dividing the number of

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consultations this group sought by the number of the overall sought consultations of the whole groups in the network. Consultation index2: is similar to the previous index, but here we consider the consultations coming to the group. This index shows the status of receiving consultations of each group comparing to the overall network. Consultation index3: In this index, we want to see the interaction between the groups based on the comparison of the consultations coming to the group to the sum of the total consultations coming to the group and the total consultations made by the group. With this index, we can know the big picture of how active the group is in terms of receiving and making consultations. Consultation index4: studies the interaction between the group members themselves when they seek consultations from members inside the group. We divide the internal consultations by total internal consultations of all groups.

3.2 Social Network Analysis of Specialists In this section, we aim to identify and analyze the social network of specialists. This step will help to find some hidden patterns that will be helpful for the medical referral system. The nodes in this network are specialists. And the edges are connected between two nodes if they have common GPs received referrals from. This way, if a specialist say ‘A’ has common GPs with all the nodes (specialists) in the network, it means that specialist ‘A’ will have connections with every other node in the network which will make this node to appear in the center. The more connections a specialist has, the busier he/she becomes. Knowing that a specialist is busy only in a specific time period gives us a hint that patients suffered from a particular disease in that period. A more detailed explanation about the disease discovery is provided in the next section.

For the specialists’ social network, we use adjacency matrix, i.e., each specialist is assigned to both a column and a row in the matrix. In this case, the matrix will have two cells representing the intersection of any 2 nodes, 1 above and 1 below the diagonal and the intersection between them will be the relation type patterns among them, which is the number of common GPs in this particular work.

To visualize and analyze the social network of specialists, the following steps are used: Step 1. We extract the adjacency matrix of the specialists based on the referral patterns of three different recent periods. Step 2. We define a threshold Θ1= 7 and consider those SPs who only received at least a Θ1 number of referrals. The reason behind this is because specialists who received less than Θ1 would not be very socially effective in the network. The value Θ1 was chosen after studying how referrals are distributed among the SPs. Step 3. To construct the SN of specialists, we calculate the number of the GPs who made referrals to each SP. A node represents a SP and a link is associated between two nodes if they have some GPs in common. The benefit of this analysis comes from the fact that if a SP has links with many SPs in the network, it means that this SP receives

referrals from many different GPs and, hence, will be identified as a popular specialist in receiving referrals in the health region. The most popular specialist will always appear in the center of the network. Step 4. We analyze the social networks in two different views: Visualization and Calculation views.

- Disease Discovery: We can use SNA to discover new diseases in the community for awareness purposes. We first construct the social network of specialists for different recent periods (every month). The method used here is similar to the one discussed in “SN of Specialist” section except that the data set contains the referral patterns for those successful referrals. In other words, we consider only the data for patients who have been seen by specialists. We analyze the different networks for the different extracted periods by finding the center specialist in every network. If a specialist of the same area appears in the center in a particular month, this means, there is a significant need for each one of these specialists in different periods; this tells us that the community experiences specific diseases in each of the three different periods which makes some specialists too busy. This analysis is helpful for the health care system as it could be used a disease discovery tool. For instance, given that a cardiology specialist is the busiest specialist in terms of receiving referrals in a specific period, it indicates that many people have heart problems in that period and this will encourage the health care region to issue awareness to people to decrease the possibility of getting the diseases in that period.

3.3 General Practitioners and Specialists Social Network In the previous sections, we have talked about the general practitioners social network and specialist social network individually. Now, we are combining both networks together in one network and analyze it to find some hidden information that will be helpful for the medical referral system. The hidden information could be predicting the consultation patterns. For this section, we use the following steps: Step 1: When we draw the SN of the referral matrix, all what we get is a bipartite graph that doesn’t give us so much information that might be helpful in analyzing the consultation relationship. Instead, as the first step, we transpose (rotate) the original referral matrix by switching columns and rows. Step 2: We multiply the original matrix by the transposed matrix. We get a new matrix that has both GPs as rows and columns. The weights of this new matrix represent the common specialists that the GPs referred patients to. Step 3: We multiply the transposed matrix from Step 1 by the original matrix. The result of this multiplication will give us a matrix of specialists that have GPs in common. Step 4: We draw the network of the matrices generated in Steps2-3 and then find the cliques in each of these networks. With the help of the cliques, we can study the interaction behaviour between nodes that do not currently have any links between them.

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4 Experimental Analysis In this section, we conduct experiments to demonstrate the applicability and effectiveness of the four approaches of our study presented in Section 3.

4.1 The Testing Environment Datasets: We succeeded in only finding one real dataset that was used in a previous similar study. In fact medical referral data is not publicly available because of privacy concerns; hence we have mainly used synthetic data to run the experiments in order to demonstrate the applicability and effectiveness of our methodology. The synthetic data we have used was based on the nature of the real data.

We have found a previous work in the social network analysis area; the authors made the matrices which have been used in the study unidentified and public. We have used these matrices in our study in addition to the synthetic dataset. These matrices represent referral and consultation patterns that were collected by Anderson & Jay [1] based on a survey that was conducted among physicians who participated in a private group practice that includes a number of subspecialties of internal medicine. They collected the data using an interview with each physician, which he/she was asked to indicate how many times he/she had (related to each of the other physicians in the group): (1) Referred a patient to; (2) Consulted about a patient with; (3) Discussed professional matters with; and (4) Taken calls for. Each type of relationship is represented by a 24 x 24 matrix as shown in Table 4.1 which reflects the relationship due to the first item listed above (referral). For our experiment, we have used the referral patterns and the consultation patterns matrices. Software/tools: For clustering purposes, we have used MATLAB. For classification we have used WEKA. In addition, we have used NetMiner, Visone, and Netdraw [4] for social network visualization and measures calculations. Computer:All the experiments have been conducted on a laptop with the following specifications: Processor: 2.0 GHz, Main memory: 4.0 GB, Operating system: 64-bit Vista operating system.

4.2 General Practitioners Social Network In a referral matrix each row represents a general practitioner (denoted by small-case letter) and each column represents a specialist (denoted by upper-case letter); entries in the table are used to reflect the relationship; 1 means that a GP made a referral to a specialist and blank stands for 0 to mean that there has not been any referral transaction between the two doctors.After performing Step1-2 as described in the previous section, we find five groups of GPs using clustering who have similar referral patterns as in Step3. Then, we examine the consultation patterns of these groups over twelve-month period using the consultations matrices.

For the general practitioners groups’ social network, (12 figures, one per month, have been omitted for space limitations). Nodes represent different groups as resulted

from the clustering process. An arrow leading from one group to another indicates that the first group consults with the second group when making a referral. Some groups have self-referencing arrow meaning that these groups consult with themselves. Weights of the links represent the number of consultations from one group to other groups’ members.

Figure 4.1: SN of the GPs consultation average

Figure 4.2: Consultation index1

Figure 4.3: Consultation index2

Figure 4.4: Consultation index3

Figure 4.5: Consultation index4

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Figure 4.6: Average of the consultation indices

Table 4.1:Indegree centrality measure

4.2.1 SNA Quantitative Measures Degree centrality: Centralization is the degree to which a network forms the shape of a “star” network. In analyzing the GP network, we consider the indegree centrality which is the number of ties entering the node. We calculate the indegree centrality measures of each of the twelve matrices and we show the average in Table 4.1.

We noticed that the central node changes from time to time. Therefore, we take the average of the consultation patterns of the twelve matrices and we visualize the network in Figure 4.1. It is obvious in Figure 4.1 that G1 is located in the center of the network meaning that it is the most powerful group and hence it may be considered as the most knowledgeable group of the SPs in town since all the other groups consult with this group G1 regarding finding the appropriate specialist. Moreover, Table 4.2 shows the indegree centrality percentage as 32.16, 19.75, 19.33, 15.09, and 13.65 for G1, G5, G4, G3, and G2, respectively. G1 has the highest indegree centrality indicating that it receives the highest number of referral consultations.

This will help the health care practices to target G1 as the first group members to consult with by any new GP who is not familiar with specialists in town and hence this solves the consultations issues.

We validate our findings, about the most important group in referral consultations, by defining consultation indices and calculate the values of each index based on the consultation patterns we have in the twelve matrices. For the five groups in every month, Figures 4.2-4.5 show the consultation indexes-1-4, respectively. The charts show how the highest indices values change from month to another which shows the dynamic changes of seeking consultations during the year. Similar to the indegree centrality calculations, it is better to take the average of these four indices and conclude based on the highest average.

Figure 4.6 shows the average of the four consultations indices values of the five groups. It is clear from the chart that G1 has the highest value in all the indices. This supports and validates our finding in the indegree centrality that G1 is concluded to be targeted as the most important

group in consulting with and can be targeted by the new doctors for any referral consultations.

4.3 Specialists Social Network In this section, we identify the social network of the specialists for three different periods as shown in Figures 4.7-4.9. Circular nodes represent the active specialists that satisfy Θ1 condition and square nodes represent the inactive specialists who do not satisfy Θ1 condition.

Using NetDraw, we draw the SN of the specialists of three different periods as shown in Figures 4.7-4.9. A node represents a SP and two nodes will be connected with each other if they received referrals from the same GPs. The links are undirected because the flow of the information does not matter in this network.

We used some of the developed quantitative measures for use in SNA and these measures as follows: Network Density: The density of a network is the number of actual connections between members divided by the number of the maximum possible connections. The following formula is used:

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Density values range from 0 to 1; a closer density value to 1 indicates a greater degree of interactions between the network actors in the process of making consultations.

Table 4.3 shows the density of the GPs network which is 0.9 meaning that almost every group makes consultations for the referral decision with every other group. Table 4.2 also shows the network density of the three specialists’ networks. We can analyze these networks in two levels: visualization and calculation. From the visualization view, we notice that specialists’ distribution in the network changed from one period to another. For instance, in Period1 network, specialists F, A, P, M, I, X, W, S, K, H, Q, and G have highly interacted with each other in the network which made them all appear in one section of the network. In addition, we notice that three specialists did not have any ties with anyone else and those ones are already considered as noises since they did not satisfy the Θ1 requirement mentioned earlier.

On the other hand, in Period2 network, we see the specialists as in Period1 highly interacted with each other and the difference is in Period2 where all specialists have ties with at least one other specialist. However, some specialists are still considered as noises since they did not satisfy Θ1 requirement. In Period3, specialists seem to be less interacted with others and specialists did not have more ties with other specialists. From the calculation view, as shown in Table 4.3, we notice that SP ‘F’ is the central in Period 1 and ‘H’ in Period2, and SP ‘X’ in Period3. This means, there is a significant need for each one of these specialists in different periods which tells us that the community experiences specific diseases in each of the three different periods which makes some specialists too busy.

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Figure 4.7: Period1- SN of specialists. Node F with the highest degree centrality Figure 4.8: Period2- SN of specialists.

Node H with the highest degree centralityFigure 4.9: Period3- SN of specialists. Node

X with the highest degree centrality

Another benefit of this analysis is to provide recommendations of alternative specialists in case any of the needed specialists cannot accept referrals or will be on vacation during the busy periods. For example if SP ‘X’ is known to be busy in a specific period and it happens that he will be on vacation on the same next period, then we may consult with SP ‘X’ to recommend alternative doctors for the future referrals.

On the other hand, the network density is different among the three Periods. For instance, Period1 has the maximum density (0.59) meaning that specialists have a greater degree of interaction (receiving referrals from common GPs) than in Period2 and Period3.

Table 4.2 -Social Network Analysis Quantitative MeasuresMeasure Period 1 Period 2 Period 3

Network density 0.59 0.52 0.35 Highest DC node F H X

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Figure 4.10: GPs network resulted from the bipartite graph

Figure 4.11: SPs network resulted from the bipartite graph

4.3 General Practitioners and Specialists Social Network In this section, we show how social network analysis techniques can find hidden information of the social

network of the GPs combined with the social network of the SPs. A GP is connected to a SP if there is a referral made between them. Looking at the graph directly won’t give us so much information except the interaction between the nodes. In fact, this social network has some other hidden information that is useful for the referral patterns. Figure 4.10 shows the social network resulted from multiplying the transpose matrix by the original matrix. The nodes of this network represent GPs. Two GPs are connected together if they send referrals to the same specialist. Similarly, Figure 4.11 shows the social network where nodes represent specialists and two nodes are connected together if they have received referrals from the same GPs. We then calculate the cliques of each one of these networks to find some hidden relationships between the nodes. Tables 4.3-4.4 show a summary of the cliques’ values of the networks shown in Figures 4.10-4.11, respectively. Next, we provide a discussion on how these cliques’ values can be helpful in the medical referral system. Finding cliques in a network is to find smaller groups (three or more nodes) within a larger group who all choose each other. The benefits of finding cliques is to see how smaller groups within the social network share common interests and this may lead to predict future connections between nodes. Tables 4.3-4.4 show the clique names, clique members, and the size of the clique which is basically the number of nodes in a clique sorted in a descending order.

The social network of GPs presented in Figure 4.10 contains 11 cliques with a maximum size as 18 and a minimum size of 9 nodes. We analyze the cliques by comparing the members of each clique with the other cliques’ members. For instance, if we compare clique1 and clique2 in Tables 4.3, we find that the cliques have the same 16 members except GPs o, a, and i. If we look at the other cliques, we don’t find the GPs o, a, and i appear in any clique meaning that these three GPs do not have links to each other at all. However, in clique1 and clique2 they share a large number of other GPs meaning that they referred patients to the same specialists. In the health care domain, this can predict connections between o, a, and i in the future through the common 16 GPs.

Similarly, clique 4 and clique 5 in Table 4.3 share the same nodes except s and d. With this information, we can predict that these two nodes will have a link together sometime in the future since they have common interest by sharing the same other members of the clique. Knowing this hidden information can support the interactions between GPs and increase the density of the network. Moreover, the

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nodes that are unlinked together must have something in common since all of them have links to the same nodes. The common interest may be that all of them receive some patients with similar diseases; therefore, it is better to discuss their experience with each other about the type of diseases to increase their knowledge. Moreover, analyzing these cliques discovers hidden sub-communities which have a density of 1.

Table 4.3: Cliques summary of Figure.4.10

Table 4.4: Cliques summary of Figure 4.11

5 Summary and Conclusions In this paper, we discussed current issues that exist in the medical referral system and showed how SNA and mining techniques can design models to address these issues.

By analyzing the GPs social network, we identified significant consultations communities to be targeted for future consultations. We discovered the most significant communities among the discovered communities and proved their centrality against the ego and the whole network. Therefore, new GPs can save time and target the significant community for future referral consultations.

Analyzing the SPs social network was helpful to observe which SP was needed the most in different periods. This analysis plays a good role in terms of disease awareness. We plan to extend this work in a number of directions. We want to consider patients data in our analysis to make it more valuable for the patients’ side. For example, some patients have specific individual preferences to which SP they should be referred to such as language, time, or gender.

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