Elizabeth West
School of Health and Social Care, University of Greenwich
David N. Barron
Saïd Business School and Jesus College, University of Oxford
Anne Hunt
University of Central Lancashire
NB This is work in progress. Do no cite without permission
In contrast to the hierarchical structure of the past and the market model of the 1980s, the New Labour government's reforms of the NHS were based upon collaboration and partnership working. This model was first developed within cancer services. The Calman-Hine Report (1995) had recommended that care for cancer patients should be based around managed networks of expertise and include the voluntary sector. These networks that moved beyond the informal professional groupings of the past gradually spread across a wide range of specialities.
The most widely accepted definition of a clinical network was first set out by the Scottish Office Department of Health in 1999: Linked groups of professionals and organisations from primary, secondary and tertiary care, working in a co-ordinated manner, unconstrained by existing professional [and organisational] boundaries, to ensure equitable provision of high quality, clinically effective services. Networks increasingly came to be seen as a solution to the co-ordination of services for patients who require care from multi-disciplinary and multi-site teams. Partnership and network based working at all levels of care was a major policy theme in the NHS Plan (2000).
Within paediatric care, Getting it right for children and young people (2010) proposed that the development of successful networks was the best means to manage the complexity of the NHS and enable children to move seamlessly from one service to another. The most effective were considered to be the more formalised and managed networks as already found in newborn, palliative and surgical care. Recommendation 35 states: There should be local networks through which services can share information electronically and protocols should be agreed by the networks to provide for this.
As networks have developed and their impact upon the delivery of health care become more important, researchers have looked to social science theories to examine their strengths and weaknesses and possible implications for the NHS (Ferlie et al. 2013 )
One important element in the success of a clinical care network, then, will be the ability of members of different organizations within the network to communicate effectively with each other and, in particular, to transfer knowledge across organizational boundaries.
The members of the West Midlands Paediatric Palliative Care Network were identified through the chair Claire Thomas and a list of member names and e-mail addresses was made available to the research team at the University of Greenwich. An invitation to participate in the survey was distributed by e-mail to network members, who clicked on the attached link to access the survey. The survey took approximately 15 minutes to complete. At the end of the questionnaire respondents were asked to take part in a semi-structured telephone interview of about 45-60 minutes. Any recipient who did not click the link in the e-mail was sent an electronic reminder after two weeks inviting them to take part in the survey. A second reminder was sent out after four weeks to those who had not yet taken the survey. A paper version of the survey was also handed out at network meetings.
A total of 75 individual members of the network were identified; 22 of them completed network questionnaires. The most important aspects of the questionnaires involved people indicating which of the other 77 network members they
Most of the analysis has to be restricted to the sub-networks of the 22 respondents, as only this enables us to look at a directed network, and thus to explore issues of reciprocity and mutuality in relationships.
We look for evidence of any type of hiearchical structure in the networks of advice and leadership. We begin with relatively simple descriptive statistics of the networks. For example, a high proportion of mutual ties in the advice network (that is, where two people would turn to each other for advice) is an indicator of a lack of a status hierarchy. Such a network would suggest that advice and information can flow freely through the network.
Descriptive statistics, though, suffer from it being difficult to know whether the numbers we obtain are high or low. This can be addressed to some extent by holding constant some characteristics of the network, such as the total number of ties, and generating a large number of random networks with these properties. We can then compare the descriptive statistics from the observed networks with those from the random networks to get a sense of how much they differ from those that would have been expected if network ties were created purely at random.
Finally, we would also like to explore more models that allow us to investigate whether the existence of ties in these networks can be explained by reference to characteristics of individual network members. For example, it is possible that longer-serving members are more likely to be viewed as leaders or approached for advice because they are viewed as having greater expertise. It is also possible that there are 'homophily' effects in tie formation. This well-known characteristic of many networks is often summarised with the saying, 'Birds of a feather flock together'. In these networks, we are particularly interested to see whether professional background helps explain the existence of ties; if it does, then this suggests that professional boundaries could present barriers to effective information flow within the network. This type of study involves the use of exponential random graph models (ergm).
The advice network is plotted, with the seven people who received no nominations omitted. The size of the circles is proportional to the number of times the person was nominated as a source of advice. The degree distribution is shown below.
As is typical, there are a relatively small number of people who have a high degree. Bearing in mind that the maximum possible degree is 22 (as only 22 people participated in the study), it is notable that seven people receive requests for advice from 16 or more people, which is equal to the number of people who are not asked for advice by anyone. This is in itself evidence of a sort of status hierarchy in the network, although we cannot know whether those people who give a lot of advice also frequently seek advice. If they do, then although that would suggest they are in some sense prominent in the network, it would give rather a different picture from one in which there are people who are seen as experts and who do not themselves need to seek advice. However, we can investigate such questions in the sub-network of respondents.
In this sub-network we can again look for evidence of hierarchy. The global reach centrality for this subnetwork is zero, which implies no hiearchy at all. This is because all members of the network are strongly connected to each other. In a traditional hierarchy, where the most senior manager has authority over his or her deputies, who in turn have authority over their subordinates, and so on, are not strongly connected because there are no paths linking subordinates to people above them in the hierarchy. The advice and information network here does not have this quality as some pairs of people ask each other for advice. This reciprocity of advice-giving means that there are directed paths between all members of the network, and hence no hierarchy in the formal sense.
There may nevertheless still be hierarchies in a less formal sense: status hierachies, for example, might exist if some people are more likely to be asked for advice than others, as indeed is the case (see figure x). We can get some sense of the degree of reciprocity by looking at the number of “mutual” dyads. In the sub-network, the number of mutual dyads is 78 while the number of asymmetric dyads is 68 and the number of dyads with no ties in either direction is 85.
To get a sense of the interpretation of these numbers, I generated 1000 random networks with the same in and out degree as the advice sub-network using the degree.sequence.game function in R, and then randomly rewired 100 of the ties in each of these networks. The mean number of mutual, asymmetric and null dyads in these 1000 networks was 43.54 (standard deviation = 4.08), 136.93 (8.16), and 50.54 (4.08), respectively. Notice that there are more than twice as many mutual ties in the observed advice and information sub-network than in the random networks, which suggests that there is a high degree of sharing of information and expertise in this network, implying a very non-hierarchical network structure. On the other hand, there are also twice as many pairs with no connection at all in the observed network than in the random network. One possible explanation for this pattern is that there is some sort of assortative matching, or homophily, taking place; for example, people from the same professional background may be more likely to seek each other out as sources of advice and information. This would be a potential problem for the network if true, as it would be a barrier to a source of learning and integration across professional boundaries.
| V1 | |
|---|---|
| Nurse | 40 |
| Doctor | 13 |
| Allied HP | 3 |
| Social service | 4 |
| Manager | 8 |
| Other | 1 |
| Unknown | 0 |
Professional background of network members
To evaluate any propensity for netowrk members to tend to approach members of their own profession for advice, we need to control for the numbers of each profession in the network. In the table above we can see that there are twice as many nurses as there are doctors. Therefore, even if nurses were choosing people to turn to for advice at random, they would be twice as likely to choose a nurse as a doctor.
The table shows the crosstabulation of ego's and alter's profession in the advice network.
| Nurse | Doctor | Allied HP | Social service | Manager | Other | |
|---|---|---|---|---|---|---|
| Nurse | 164 | 67 | 5 | 14 | 28 | 5 |
| Doctor | 31 | 21 | 3 | 4 | 4 | 1 |
| Allied HP | 0 | 0 | 0 | 0 | 0 | 0 |
| Social service | 26 | 10 | 2 | 3 | 5 | 1 |
| Manager | 52 | 20 | 1 | 5 | 8 | 0 |
| Other | 0 | 0 | 0 | 0 | 0 | 0 |
One way to investigate whether there is evidence of assortative matching controling for the frequency of different professional groups in the network is by means of an exponential random graph model (ERGM). These models provide a method for the statistical analysis of social networks. In these models, the probability of a particular, observed network, \( X=x \) conditional on a vector of parameters, \( \theta \), nodes is given by:
\[ \Pr (X=x | \theta) = \frac{1}{\kappa(\theta)} \exp\{ \theta_1 z_1(x) + \theta_2 z_2(x) + \cdots + \theta_p z_p(x) \}. \]
The functions \( z_k(x) \) are counts of configurations in the network \( x \), the parameters, \( \theta_k \) weight the relative importance of the corresponding network configuration, and the function \( \kappa(\theta) \) is a normalising term (Lusher et al. 2013 ). An intuition behind this method is that we compare the
“observed network to the other possible ways it could be arranged. In all networks there are a finite number of ways that ties can be arranged….Then, for a distribution of [networks], we have to assign a probability to each [network]. Model estimation assigns probabilities so that an observed network is central, not extreme, in terms of the effects being modelled” (Lusher et al. 2013 ).
The table below shows the result sof an estimate that includes main effects of professional background as well as variables that measure the propensity of people in the three main professional groups to select members of their own profession.
| Estimate | Standard error | |
|---|---|---|
| Edges | -1.43* | 0.12 |
| Zero outdegree | 16.55* | NaN |
| Zero indegree | 3* | 0.68 |
| Mutual ties | 2.08* | 0.21 |
| Nurses | 0.42* | 0.17 |
| Doctors | 0.74* | 0.18 |
| Managers | -0.07 | 0.23 |
| Nurse homophily | -0.18 | 0.15 |
| Doctor homophily | 0.84* | 0.39 |
| Manager homophily | 0.34 | 0.44 |
| AIC | 2519.6 |
Note: * = p < .05
The model includes a term for the number of ties (or edges) in the network, a term that is usually said to serve the same function of the intercept in normal regression, representing the baseline propensity for ties to form (that is, for people to name others to whom they turn for advice). This network is, of course, unusual in that there are a large number of nodes with an outdegree of zero—by definition, people who did not participate in the study cannot have nominated any advisors. Therefore, an additional control variable for nodes with a zero outdegree is also included in the model. As we have already noted a tendency for mutual ties to be more common than expected, we also include a term to control for this. We also include main effects to control for the tendancy of nurses, doctors and managers to name advisors; the fact that these are all positive and statistically significant implies that members of these groups have more advisors, on average, than members of the other professions (allied health professions and social service professions).
We can see that there remains a statitically significant tendancy for doctors to prefer other doctors as advisors. The estimated homophily effect for nurses is negative, implying that nurses are less likely to choose other nurses as advisors than would be expected by chance, but this estimate is not statistically significant. Similarly, the postitive estimate for managers suggests that there is some tendancy for managers to disproportionately approach other managers for advice, but again this effect is not statistically significant.
The participants in the survey were also asked to nominate those people that they though occupied leadership roles within the network. The network is displayed in the figure, with the people who received no nominations omitted.
Generally, we would expect to see more evidence of a hierarchical structure in a leadership network. In traditional organizational structures, leadership relationships cannot be reciprocal by definition. However, the situation may be different in this network, lacking as it does any formal authority structure. Survey respondents were asked to identify people who occupied leadership roles in the nextwork, and so it is possible that these ties could be reciprocal as there could be a number of people that are considered to act as leaders in some sense or another.
Indeed, when the network diagram aboove shows that a significant number of people in the network were identified as leaders. In fact 64 people were nominated as leaders by at least one colleague out of the 78 people in the network, a remarkably high proportion.
Turning as before to the subnetwork of those peoplel who were interviewed, the global reach centrality score is 0.05, slightly more than the advice network, but still very low, indicating a low level of hiearchy. In the sub-network, the number of mutual dyads is 65 while the number of asymmetric dyads is 92 and the number of dyads with no ties in either direction is 74. The leadership network is, then, somewhat more hierarchical than the advice network, but for a network on this type of relation there is in fact a very high degree of mutuality in this network, much more than one would expect in a random network.
We can again explore the extent to which mutuality is a reflection of people tending to nominate members of their own profession as leaders, using a similar model to that used for the advice network above. The results are shown below:
| Estimate | Standard error | |
|---|---|---|
| Edges | -1.31* | 0.11 |
| Zero outdegree | 23.09* | NaN |
| Zero indegree | 4.88* | 0.58 |
| Mutual ties | 1.76* | 0.2 |
| Nurses | 0.04 | 0.17 |
| Doctors | 0.76* | 0.17 |
| Managers | 0.07* | 0.22 |
| Nurse homophily | 0.17 | 0.17 |
| Doctor homophily | -0.06 | 0.35 |
| Manager homophily | 0.84 | 0.44 |
| AIC | 2010.62 |
Note: * = p < .05
One possible interpretation of this is that the network is a genuine alternative to a hierarchical structure, and as such is a very different model from that of the managed networks that are becoming a more prominent feature of the NHS.
Turning as before to the subnetwork of those peoplel who were interviewed, the global reach centrality score is 0.05, slightly more than the advice network, but still very low, indicating a low level of hiearchy. In the sub-network, the number of mutual dyads is 49 while the number of asymmetric dyads is 84 and the number of dyads with no ties in either direction is 98. The influence network is, then, somewhat more hierarchical than the advice network, but for a network on this type of relation there is in fact a very high degree of mutuality in this network, much more than one would expect in a random network.
| Estimate | Standard error | |
|---|---|---|
| Edges | -1.56* | 0.14 |
| Zero outdegree | 16.98* | NaN |
| Zero indegree | 3.86* | 0.58 |
| Mutual ties | 1.74* | 0.22 |
| Nurses | -0.13 | 0.19 |
| Doctors | 0.9* | 0.18 |
| Managers | 0.1 | 0.23 |
| Nurse homophily | 0.49* | 0.19 |
| Doctor homophily | -0.21 | 0.39 |
| Manager homophily | 0.32 | 0.5 |
| AIC | 1870.32 |
Note: * = p < .05