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JT has received investigator-initiated research grants and Honoria from Bristol-Meyers- Squibb / Pfizer Alliance, and CS has received funding from NHS England via the 100k Genome Project. This does not alter our adherence to PLOS ONE policies on sharing data and materials. DMB, NB and RJBD declare no potential conflict of interest.

The topology of the patient flow network in a hospital is complex, comprising hundreds of overlapping patient journeys, and is a determinant of operational efficiency. To understand the network architecture of patient flow, we performed a data-driven network analysis of patient flow through two acute hospital sites of King’s College Hospital NHS Foundation Trust. Administration databases were queried for all intra-hospital patient transfers in an 18-month period and modelled as a dynamic weighted directed graph. A ‘core’ subnetwork containing only 13–17% of all edges channelled 83–90% of the patient flow, while an ‘ephemeral’ network constituted the remainder. Unsupervised cluster analysis and differential network analysis identified sub-networks where traffic is most associated with A&E performance. Increased flow to clinical decision units was associated with the best A&E performance in both sites. The component analysis also detected a weekend effect on patient transfers which was not associated with performance. We have performed the first data-driven hypothesis-free analysis of patient flow which can enhance understanding of whole healthcare systems. Such analysis can drive transformation in healthcare as it has in industries such as manufacturing.

Patient flow through a hospital is a key determinant of efficient hospital functioning. Previous studies have focused on linear flow processes, queuing and single patient pathways [

A hospital can be considered as a network of wards that are connected when patients are transferred between them. By modelling it this way, we sought to understand both the spatial and temporal nature of network activity to help determine where and how bottlenecks form during periods of high activity. Due the complexity of the network, it was difficult to visualise network dynamics changing over time and so we took a network science approach to achieve a global, high-level perspective on hospital network dynamics.

The National Health Service (NHS) England's Five Year Forward View proposed that IT will be an essential tool for transforming the NHS [

Green nodes are in Denmark Hill (DH), turquoise nodes are in Princess Royal University Hospital (PRUH), purple nodes are External to King’s, red nodes are Orpington Hospital. Edge thickness represents the relative flow of the patients (see

Accident and Emergency department (A&E) performance against the UK’s 4-hour waiting time target is a key metric used to assess hospitals, and patient flow through the hospital has been attributed to be a contributing factor [

Data was derived from the patient administration system (PAS) and the electronic patient record at both acute sites of King’s College Hospital NHS Foundation Trust (King’s College Hospital, Denmark Hill, London [DH] and Princess Royal University Hospital [PRUH]). The PRUH-site deployed the iSoft i.PM software system (Computer Sciences Corporation, CSC) in November 2014 thereby introducing a single unified PAS across both acute sites. Identifiable information on patients was not accessed by any authors. The patient transfer data analysed in this study was exported without any identifiable information from the PAS at Kings College Hospital. There is no potentially identifiable information in the transferred dataset, and identification of individuals would only be possible by linking the data with the original PAS dataset or an external dataset. The dataset cannot be made available without specific information governance approval on a case-by-case basis.

A database query was performed to extract all A&E attendances and patient ward transfers between the period of 01/12/2014 and 01/07/2016. Only transfers for non-elective patients admitted via an A&E department at DH or PRUH were included.

The project was reviewed by the King’s College Hospital Information Governance committee chaired by the Caldicott Guardian (UK statutory individual responsible for protecting the confidentiality of health and care information) and approval was granted in June 2016 with continued oversight. The basis of secondary use was analysis for service improvement, operational performance and clinical audit.

Patient transfers were modelled as a weighted directed graph [

The edge weight variability score is a local property of a node that measures the observed deviation from a perfectly balanced distribution of its input or output edge weights as a proportion of the maximum possible deviation. If edge weights are perfectly balanced then every edge has the mean weight, so for a node n with k input edges _{1},_{2},…,_{k} with edge weights _{1},_{2},…,_{k}, the edge weights are perfectly balanced if

The least balanced distribution possible is the case where edges _{1},_{2},…,_{k−1} have weight 1, and the remaining edge _{k} has weight

The weight variability score is now calculated by Eq (

A score close to zero means the weights are balanced, a score close to 1 means the weights are unevenly distributed. This score is only defined when there are at least two (input or output) edges.

Unsupervised clustering with principal component analysis was performed in R version 3.2.4 [

Weekly aggregated transfer data are available in

The patient transfers dataset contains 194,410 transfers for 78,400 hospital admissions (38,561 in PRUH, 38,115 in DH and 1,724 involving both sites) over 578 days. The weighted, directed network of all transfers analysed for the DH site contains of 78 nodes (wards) and 1531 edges, and the PRUH site has 72 nodes and 921 edges. The total number of transfers through each edge range from 1 to 11,775 in DH and 1 to 9,353 in PRUH.

From the transfer data, it is possible to reconstruct the specific path from admission to exit for each individual patient in the flow network. Many commonly used network statistics are based on the calculation of shortest paths through the network, however in this case shortest paths are not meaningful as the path a patient takes through the network is determined by the requirements of their treatment. We therefore considered the unique observed sequences of wards. Considering only those patients whose entire visit was spent in a single hospital site, there were more unique sequences of wards visited by patients in the DH site (3253) than the PRUH (2263) and the distribution of patient flow over these paths is highly uneven in both sites. Only the top 11 (DH) or 12 (PRUH) most common sequences are required to reach 50% of all visits, corresponding to 0.34% (DH) and 0.53% (PRUH) of all observed sequences of wards. In both sites the single most frequent path was an equivalent sequence from the emergency ward to a clinical decision unit and finally to exit, accounting for 21% of all visits in each case.

Transfer data was integrated per calendar month for each of the 19 months included in this study to capture medium-term stability of the network. The average monthly network size for DH is 919 edges (SD 60.4) and 63 nodes (SD 2.08). The PRUH networks have 592 (SD 45.4) edges and 46 (SD 2.50) nodes.

In the flow network node in-degree represents the number of other wards sending patients into a ward and out-degree represents the number of other wards patients are sent to. The difference between the in- and out-degree of a node was used as an indication of the structural role that a ward plays in the distribution of flow throughout the network and whether this changes over time (

(a) and (b) Each line represents a single ward over time. Black lines represent “balanced” wards, with similar in- and out-degree. Other colours represent individual wards with either much greater in-degree than out-degree, or vice versa. Corresponding ward names for these wards are shown to the right. (c) and (d) In-degree vs. out-degree, each point is one node in one month. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

From the degree difference alone, there is no way to know whether these are high or low degree nodes.

The patient flow network is a weighted network. We defined a weight variability score for a node (see ^{th} (PRUH) and 6^{th} (DH) lowest output variabilities.

The input and output weight variability scores were calculated for every node each month. Counts are over all nodes and months. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

Edges that are consistently present over time are likely to be important to the overall functioning of a hospital, in addition to just those edges with the greatest weight. These “core” edges were defined as any edges present in all the monthly transfer networks for each site. For PRUH this leaves a subnetwork with an average of only 16.8% (SD 1.38%) of all edges per month, which accounts for 89.7% (SD 1.37%) of monthly transfers. A similar result was found for DH, where the core edges are 12.6% (SD 0.89%) of the full network on average, but support 83.4% (SD 1.54%) of all transfers. This is consistent with the above finding that that the input and output edge weights of all nodes are unevenly distributed. Therefore, although the monthly networks for both sites are quite large, a small and consistent portion of the network is sustaining the bulk of the transfer activity and is likely to be critical to maintaining patient flow.

For the period considered in this study, the average A&E performance against the 4-hour waiting time was higher for DH than PRUH (87% vs 74.5%,

“High” and “Low” groups are the top and bottom 10% of best- and worst-performing days respectively for each site, “Mid” is the remaining 80%. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

The upper row shows the density of number of arrivals at A&E in each group for the points in the corresponding scatter plots in the lower row. There is no correlation between the number A&E performance against the 4-hour target and the number of arrivals at A&E (linear regression R-squared = 0.14 for DH and 0.09 for PRUH). “High” and “Low” groups are the top and bottom 10% of best- and worst-performing days respectively for each site, “Mid” is the remaining 80%. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

Performance |
Arrivals |
|||||||
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Overall (n = 578) | High (n = 57) | Mid (n = 464) | Low (n = 57) | Overall (n = 578) | High (n = 57) | Mid (n = 464) | Low (n = 57) | |

DH | 87.0 (6.63) | 95.5 (0.84) | 87.7 (4.50) | 73.3 (3.33) | 385 (33.2) | 366 (34.9) | 385 (32.2) | 411 (22.6) |

PRUH | 74.5 (14.3) | 96.3 (1.56) | 74.9 (10.7) | 49.5 (5.91) | 177 (18.6) | 168 (15.6) | 177 (18.5) | 186 (17.8) |

All values are the mean daily value with the standard deviation in brackets. “High” and “Low” groups are the top and bottom 10% of best- and worst-performing days respectively for each site, “Mid” is the remaining 80%. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

We looked for network changes that correlate with extreme (good or bad) A&E performance with a differential network analysis approach [

Edge weights in the differential network were calculated by subtracting the weight in the worst network from the weight in the best network. An edge with a negative weight in the differential network accounts for a greater proportion of transfers in low-performing days. Weight differences between the best and worst networks were normally distributed with a mean of zero in both sites, with standard deviations on the same day of 2.19 x 10^{−3} in PRUH and 2.6 x 10^{−3} in DH, and with the 1-day lag of 1.32 x 10^{−3} in PRUH 2.13 x 10^{−3} in DH (

Only edges for which the difference in proportional flow between the best and worst networks is more than two standard deviations from the mean difference (zero) are shown in the differential networks. Red edges account for a greater proportion of transfers in the lowest-performing network, green edges account for a greater proportion of transfers in the highest-performing network. Edge direction indicates the direction of the transfer and thickness represents the magnitude of the difference in weight between the best and worst networks. Wards are named according to their role, and multiple wards with the same role are numbered consistently between rows for each site. Top row = flow on days with extreme A&E performance. Bottom row = flow on the days before days with extreme A&E performance. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

Given these differences in network flow between the best and worst days, we asked whether unsupervised clustering of daily patient flow networks using principal component analysis would separate the best and worst days as defined earlier (top 10%, bottom 10%, middle 80%). Edge weights were normalised to represent the proportion of all transfers each day to allow for comparisons between daily flow networks with different numbers of admissions. As shown in

Principal component analysis of daily transfer networks separates the best- and worst-performing days in each site and weekdays from weekends. (a) DH performance (b) PRUH performance (c) DH weekday vs. weekend (d) PRUH weekday vs. weekend. “High” and “Low” groups are the top and bottom 10% of best- and worst-performing days respectively for each site, “Mid” is the remaining 80%. Red = Low, blue = Mid, green = High. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

The differential network analysis focused on the largest changes in edge weight, however in the PCA the weights are centred and scaled so there is no effect of magnitude. Therefore, the fact that the same edges are identified in both analyses increases our confidence that these edges are indeed related to A&E performance. For the PRUH, the separation of the best and worst days was less clear than for DH, but is still largely achieved by a combination of the 2^{nd} and 4^{th} components (

In both sites, the third component (0.83% of variance in DH, 1.24% in PRUH) is correlated with whether the day is a weekday or weekend (

In the PCA analysis for PRUH, the first component (1.89% of variance) did not separate A&E performance or weekday vs weekend. There is insufficient information from our dataset to understand what this PC1-PRUH component reflects but the loadings on surgical wards raises the possibility that it relates to clinical activities specific to surgical wards (e.g. elective surgery pathways interacting with non-elective surgery pathways).

We have performed a completely data-driven analysis of patient flow using modern graph theory analysis, which we believe to be the first to be done in a UK healthcare system. Our analysis shows that on a monthly basis the local network structure around wards remains constant (

Most of the edges in the flow network lie outside the core sub-network and account for 10–16% of all transfers. These edges may constitute the pathways which have been least optimised. As this residual flow does not travel down the same set of edges every month, these ‘ephemeral’ sub-networks will be much harder to study. One hypothesis is that this flow constitutes less common clinical events that necessitate transfer between clinical areas made up of low-frequency ‘freak’ events (e.g. a patient having myocardial infarction after an unrelated procedure) and ‘patient safety’ events (e.g. missed opportunity to detect a deteriorating patient to prevent admission to critical care). More complex modelling will be needed to study this ephemeral sub-network.

Our analysis confirmed prior data showing that A&E attendance rate is poorly correlated with hospital performance statistics [

It is worth mentioning that caution must be taken when forming general hypotheses around these key pathways, as they may be specific to the local health economy for each site. One possibility is that they relate to the surrounding network of social care and community facilities that is not captured in our dataset. However, the importance of the Clinical Decision Unit to performance was clear in both sites for all network metrics used. The Clinical Decision Units in PRUH and DH are analogous units–they act as units for observation and triage of patients from A&E which may not require admission into hospital but no definite decision had been made yet. This result emphasises the value of dedicated observation and triage units to efficient A&E function, possibly by reducing unnecessary admissions or reducing misallocation of patients to the wrong specialties. One conclusion is that for both sites, well-functioning Clinical Decision Units should be studied in greater detail to understand how they optimise support for A&E.

Unsupervised clustering showed a weekday-weekend effect (PC3) at both hospital sites, indicating a difference in how the hospital flow network functions between weekday and weekends. This finding fits with

However a large scale study showed that while changing the working patterns of senior healthcare staff (hospital consultants) did increase weekend discharges from most general medical wards, it did not have any effect on elderly medicine or geriatrics wards [

It is important to be mindful that this weekend-weekday effect looks specifically at the question of patient flow and operational efficiency rather than on patient outcomes, and while the question of weekend effect on patient safety and 30-day mortality has been a topical issue in 2016 [

In conclusion, this approach validated

(a, b) Mean monthly A&E performance over time for each site, as measured by the percent of patient meeting the 4 hour A&E waiting time target. (c-f) Centrality of wards over time. Here centrality is defined as the proportion of all observed paths each node lies on per month. This measure was chosen as shortest paths do not reflect actual patient trajectories. (e) this general medical ward was re-organised during Dec 2015 to try to cope with winter pressures. R-squared values are shown for the correlation between the monthly centrality of each ward and the monthly performance of the corresponding hospital A&E department. DH = Denmark Hill, PRUH = Princess Royal University Hospital, CDU = Clinical Decision Unit.

(PDF)

(a, b) A series of differential patient flow networks (comparing the High (top 10%) and Low (bottom 10%) performance groups) was created for each site by applying an increasingly large lag to the flow data e.g. using the patient flow observed 3 days prior to the days in each performance group. A lag of 0 indicates the same day, a lag of 7 is one week earlier. Networks were generated for all lag values from 0 to 14 days and the standard deviation over all edges in each network is shown. PRUH = Princess Royal University Hospital, DH = Denmark Hill.

(PDF)

This file contains the total number of patients sent between each pair of wards for every week of the data analysed in this study after applying the pre-processing steps described in the Methods section. Only edges with weight > 0 per month are included. All transfers were aggregated per week, with weeks starting on Mondays. DH = Denmark Hill, PRUH = Princess Royal University Hospital.

(CSV)

We would like to thank Jack Barker for his insightful comments on the analysis, and to express thanks to the King’s College Hospital ICT department and Electronic Health Record team for their support in this project.