Can network science reveal structure in a complex healthcare system? A network analysis using data from emergency surgical services

Abstract

Introduction: Hospitals are complex systems and optimising their function is critical to the provision of high quality, cost effective healthcare. Metrics of performance have to date focused on the performance of individual elements rather than the whole system. Manipulation of individual elements of a complex system without an integrative understanding of its function is undesirable and may lead to counterintuitive outcomes and a holistic metric of hospital function might help design more efficient services.

Objectives: We aimed to use network analysis to characterise the structure of the system of perioperative care for emergency surgical admissions in our tertiary care hospital.

Design: We constructed a weighted directional network representation of the emergency surgical services using patient location data from electronic health records.

Setting: A single-centre tertiary care hospital in the UK.

Participants: We selected data from the retrospective electronic health record data of all unplanned admissions with a surgical intervention during their stay during a 3.5-year period, which resulted in a set of 16 500 individual admissions.

Methods: We then constructed and analysed the structure of this network using established methods from network science such as degree distribution, betweenness centrality and small-world characteristics.

Results: The analysis showed the service to be a complex system with scale-free, small-world network properties. We also identified such potential hubs and bottlenecks in the system.

Conclusions: Our holistic, system-wide description of a hospital service may provide tools to inform service improvement initiatives and gives us insights into the architecture of a complex system of care. The implications for the structure and resilience of the service is that while being robust in general, the system may be vulnerable to outages at specific key nodes.

Keywords: adult anaesthesia; adult intensive & critical care; health informatics; health services administration & management; organisation of health services.

Figure 1

Construction of the network. We show three illustrative patient pathways and how they are combined to construct the network representation using wards as nodes and transfers as edges. Several of the analysis parameters in the text are also explained, for example the degree of a node.

Figure 2

Non-categorised network of emergency surgical admissions. The network of transfers shown grouped by clinical categories of care. The nodes are coloured by betweenness centrality—higher betweenness centrality is shown in deeper colour and sized by overall degree. The nodes were arranged to represent a patient journey from A&E admission (on the left) to discharge (on the right) and the nodes were grouped together to show the different types of locations. Some of the important nodes have been labelled to show the grouping with the medical wards at the bottom left, the surgical wards bottom right, investigations at the top, critical care areas and theatres in the middle and the paediatric services at the top right. Most nodes are left unlabelled for clarity with some indicative labels in each group. The ward abbreviations are explained in the supplementary table. A&E, accident and emergency.

Figure 3

Degree distribution. The degree distribution (as log–log plot) for our network of wards. The distribution shows a power-law behaviour at the right-hand tail of the distribution. The power-law fit (obtained with the package poweRlaw28) is shown in red with a γ of 6.1.

Figure 4

Categorised network. The network of transfers shown grouped by area of care. Here, the nodes are categories rather than physical locations and as in figure 2 coloured by betweenness centrality—higher betweenness centrality is shown in deeper colour and sized by overall degree. The ward abbreviations are contained in the online supplementary table.

Figure 5

Net connectivity of nodes. This shows the unweighted difference in in-degree and out-degree, net connectivity, versus overall degree k for our system of wards. The distribution wards such as A&E are in the lower half of the graph (red labels) and the receiving wards in the upper (blue labels). Most wards have a balanced traffic. The ward abbreviations are explained in the supplementary table. A&E, accident and emergency.

Figure 6

Relation between traffic and connectivity. The figure explores the strength (weighted degree) versus degrees for the categorised system of wards. (A) The overall distribution of strength versus degree, where the labelled nodes are outliers with respect to their degree–strength relation, either significantly higher traffic than expected by their connectivity or significantly lower. The graph also shows in red the relation between strength and degree if the weights were uncorrelated. (B) The inlay shows the log–log distribution of strength versus degree with the uncorrelated distribution (red) and the power-law fit (purple dashed) showing that the strength grows faster than the degree. The ward abbreviations are explained in the online supplementary table.

Figure 7

Assortativity. The weighted nearest neighbour degree k_nn versus degree k for the non-categorised network. It shows the dissociative behaviour of the network where higher degree nodes are connected to lower degree nodes. The best linear fit is overlaid in red.

Figure 8

Betweenness centrality. The distribution of betweenness centrality versus unweighted degree. The relation is fit by a quadratic equation of the degree—as is commonly seen for randomised networks. The ward abbreviations are explained in the online supplementary table.