Patient flow within UK emergency departments: a systematic review of the use of computer simulation modelling methods

Objectives Overcrowding in the emergency department (ED) is common in the UK as in other countries worldwide. Computer simulation is one approach used for understanding the causes of ED overcrowding and assessing the likely impact of changes to the delivery of emergency care. However, little is known about the usefulness of computer simulation for analysis of ED patient flow. We undertook a systematic review to investigate the different computer simulation methods and their contribution for analysis of patient flow within EDs in the UK. Methods We searched eight bibliographic databases (MEDLINE, EMBASE, COCHRANE, WEB OF SCIENCE, CINAHL, INSPEC, MATHSCINET and ACM DIGITAL LIBRARY) from date of inception until 31 March 2016. Studies were included if they used a computer simulation method to capture patient progression within the ED of an established UK National Health Service hospital. Studies were summarised in terms of simulation method, key assumptions, input and output data, conclusions drawn and implementation of results. Results Twenty-one studies met the inclusion criteria. Of these, 19 used discrete event simulation and 2 used system dynamics models. The purpose of many of these studies (n=16; 76%) centred on service redesign. Seven studies (33%) provided no details about the ED being investigated. Most studies (n=18; 86%) used specific hospital models of ED patient flow. Overall, the reporting of underlying modelling assumptions was poor. Nineteen studies (90%) considered patient waiting or throughput times as the key outcome measure. Twelve studies (57%) reported some involvement of stakeholders in the simulation study. However, only three studies (14%) reported on the implementation of changes supported by the simulation. Conclusions We found that computer simulation can provide a means to pretest changes to ED care delivery before implementation in a safe and efficient manner. However, the evidence base is small and poorly developed. There are some methodological, data, stakeholder, implementation and reporting issues, which must be addressed by future studies.


INTRODUCTION
An emergency department (ED), also known as accident & emergency department (A&E), provides acute care for patients who attend hospital without prior appointment. The EDs of most hospitals customarily operate 24 hours a day, 7 days a week. Nevertheless, overcrowding in EDs is an increasing problem in countries around the world, and especially so in the UK. 1 2 ED overcrowding has been shown to have many adverse consequences such as increased medical errors, 3 decreased quality of care and subsequently poor patient outcomes, 4 increased workload, 1 frustration among ED staff, 4 5 ambulance diversions, 6 increased patient dissatisfaction, 5 prolonged patient waiting times 7 and increased cost of care. 8 Furthermore, some less severely ill patients may leave without being seen by a physician, only to return later with a more complicated condition. 8 In the UK, there is an enormous pressure from public and government to alleviate overcrowding and long waiting times experienced in ED. 1 The Department of Health set a target standard for acute hospitals in Patient flow within UK emergency departments: a systematic review of the use of computer simulation modelling methods Syed Mohiuddin, 1,2 John Busby, 3 Jelena Savović, 1,2 Alison Richards, 1,2 Kate Northstone, 1,2 William Hollingworth, 1,2 Jenny L Donovan, 1 Open Access the National Health Service (NHS) that at least 95% of patients attending an A&E department must be seen, treated, admitted or discharged under 4 hours. 7 This 4-hour target standard was initially set at 98% in 2004, but later reduced to 95% in 2010. Beyond target setting, it has been argued that ED overcrowding can be improved by lean healthcare thinking with a focus on improving patient flow. 1 9 Over recent decades, computer simulation and other modelling methods have been used to analyse ED patient flow and resource capacity planning. [10][11][12][13][14] In essence, a computer simulation model is a simplified representation of reality used to aid the understanding of the key relationships and dynamics in the care process, and to evaluate the likely impact of changes before implementation. Typically, a simulation model is based on the notion that each simulated individual is tracked through the care process; the population effect is then estimated from the sum of the individual effects. 15 The precise way in which a simulation model works depends on the type of simulation method used. Generally, simulation models can be categorised as static or dynamic, as stochastic or deterministic, and as discrete time or continuous time. 16 A static simulation represents a process at a particular point in time, whereas a dynamic simulation represents a process as it evolves over time. A simulation model in which at least one input parameter is a random variable is said to be stochastic, whereas a simulation model having no random variables is said to be deterministic. A discrete time model is one in which the state variables change instantaneously at discrete points in time. In contrast, a continuous time model is one in which the state variables change continuously with respect to time. The advancement of computer technology has undoubtedly supported the use of more sophisticated simulation methods for modelling healthcare processes. Today, for example, computer simulation is also capable of providing an insight into the workings of a system through visual animation.
Various types of computer simulation exist, including discrete event simulation (DES), system dynamics (SD) and agent-based simulation (ABS). DES is a widely used method, and can replicate the behaviour of complex healthcare systems over time. A DES model is a network of queues and activities (such as having a blood test, X-ray and treatment). One of the major advantages of using a DES model is its flexibility to model complex scenarios at the individual level. Within a DES model, individuals move from one activity to another in sequential order at a particular point in time. Typically, the individuals enter a system and visit some of the activities (not necessarily only once) before leaving the system. The variables that govern the movement of modelled individuals (such as arrival rate and duration of treatment) can be random and thus readily capture the variation that is inherent in healthcare. As such, a DES model is considered particularly suitable for modelling queuing systems. This simulation method is able to incorporate life histories and complex scenarios at the individual level to influence the care pathway taken and the time between events, but specialist analytical knowledge is required typically to achieve a greater flexibility. 17 Another widely used simulation method is SD, which is used to understand the behaviour of complex healthcare systems over time through capturing aggregate (instead of individual) flows of patients. An SD model is essentially a collection of stocks and flows between them. Stocks are basic stores of quantities over time, for example, number of patients with a disease or in a particular part of a hospital department. Flows define the movement of objects between different stocks over time. Unlike DES, SD does not lend itself readily to including random variables and thus input parameters are given as simple rates in the majority of studies. As such, SD is considered not the ideal method of choice for modelling a closely focused system that involves resource-constrained queuing networks, such as an ED. 10 In a situation like this, DES should rather be the method of choice to model high level of distinct detail. 18 ABS is another method that has more recently been used in modelling the healthcare systems. As a new method in this application area, ABS is often overlooked in favour of using more established methods of DES and SD. The usefulness and practicalities of ABS in modelling patient flow are not well understood. 19 Increasing interest in this area is reflected in the number of computer simulation studies of ED patient flow and resource capacity planning that have been published over recent decades. However, little is known about the usefulness of different computer simulation methods for analysis of any changes to the delivery of emergency care. We, therefore, systematically investigated the peer-reviewed literature on the use of computer simulation modelling of patient flow within EDs in the UK. Our specific objectives were as follows: (1) to investigate the contribution that computer simulation studies make to our understanding of the problem of ED overcrowding; (2) to identify the methodology used to conduct patient flow simulation in terms of key assumptions, systems requirements, and input and output data; (3) to assess the usefulness of each simulation method for service redesign and evaluating the likely impact of changes related to the delivery of emergency care; (4) to report on differences in conclusions about ED performance with different simulation modelling methods; and (5) to identify studies that explicitly aimed to meet the prespecified needs of stakeholders.

METHODS
We conducted a systematic review of the peer-reviewed literature to identify computer simulation studies of patient flow within hospital EDs in the UK. This review complies with the online supplementary PRISMA checklist (www. prisma-statement. org). We produced a review protocol (available from the corresponding author on Open Access request) and set out the process to address our specific objectives.

Search strategy
We retrieved relevant studies from the following bibliographic databases: MEDLINE, EMBASE, COCHRANE, WEB OF SCIENCE, CINAHL, INSPEC, MATHSCINET and ACM DIGITAL LIBRARY. We used a key review paper 20 to select these databases, which were searched from the date of their inception until 31 March 2016. A search strategy was designed to explore three main domains of knowledge associated with the area of our interest: computer simulation, emergency care and patient flow. We included a wide range of search phrases, both keywords and medical subject headings, such as 'computer simulation,' 'emergency department,' 'patient care,' 'patient flow,' 'waiting time,' 'time to treatment' and 'length of stay. ' We first developed the search strategy for MEDLINE since it is known to allow a rich taxonomy of subjects and rubrics. We used a key review paper 20 to inform the MEDLINE search strategy and made further refinements using other relevant studies to improve sensitivity. Online supplementary appendix 1 shows the MEDLINE search strategy and results from 1946 to end of March 2016. We adapted the MEDLINE strategy to search the other databases (available from the corresponding author on request). We also conducted backward and forward citation searches of all included studies using Google Scholar.

Inclusion criteria
We identified studies as being eligible for inclusion if they: (1) were published in peer-reviewed journals or conference proceedings as full papers; (2) were conducted within the ED of an established UK NHS hospital responsible for assessing and treating civilians in need of emergency care; (3) captured the progress of patients through at least two activities of an ED care process; and (4) used a computer simulation method such as DES, SD, ABS, hybrid simulation, Monte Carlo simulation, distributed simulation or stochastic modelling.
We excluded editorials, letters, commentaries, conference abstracts, notes and books. We also excluded studies that used methods such as regression analysis, likelihood ratio test, time series analysis, generalised linear model, mathematical programming, optimisation methods, queuing theory, structural equation modelling, process mapping, problem structuring method or risk analysis without combining it with a computer simulation method.

Selection of studies for full-text review
To identify the studies suitable for full-text review, two authors (SM and JB) independently screened the titles and abstracts of all the initially retrieved studies. The individual responses from each reviewer were stored in a common database. At this stage, a study was excluded if it was clearly irrelevant based on our inclusion criteria. In cases of discrepancy, we selected the studies for full-text review by consensus.

Appraisal of studies for inclusion
An electronic questionnaire was designed to appraise the studies selected for full-text review. The questionnaire included four key questions: (1) Is the study a full paper published in a peer-reviewed journal or conference proceedings? (2) Is the study set within the UK NHS? (3) Is the study conducted within the ED of an established hospital? (4) Does the study use a computer simulation model of emergency patient flow? A study with positive responses on these four questions was then included in the final review. SM and JB completed this process independently and resolved any discrepancies that arose by consensus. Further to the electronic search, SM and JB reviewed the backward and forward citations of all studies included in the electronic search to identify other potentially relevant studies.

Data extraction
An electronic data extraction form was created to retrieve information about a number of key aspects, including simulation methods, data sources, key assumptions, input and output data, conclusions drawn and benefits of simulation outputs in practice. SM and JB independently recorded, collated and extracted the necessary information. Any discrepancies were resolved by consensus.

RESULTS
We retrieved a total of 2436 references from the 8 databases: 437 from MEDLINE; 460 from EMBASE; 14 from COCHRANE; 253 from WEB OF SCIENCE; 65 from CINAHL; 1103 from INSPEC; 4 from MATHSCINET; and 100 from ACM DIGITAL LIBRARY. We removed 440 duplicate references, and then assessed the remaining 1996 unique references by title and abstract screening. At this stage, we selected 159 of the 1996 studies for fulltext review. Nineteen of the 159 studies were included following full-text review. Two more studies were included from the backward and forward citation searching of the 19 studies. A total of 21 studies 10-14 21-36 were included in the final review. Four studies [37][38][39][40] were excluded from the final review because the models used by these studies are identical to the models reported in other already included studies. 13 30 33 36 Figure 1 shows a summary of the study selection process. Table 1 summarises the included studies, outlining publication type, simulation purpose, ED details and patient flow description. The first study 33  More than two-thirds of the studies (n=16; 76%) did not provide the name of the hospital studied. All 21 studies described the underlying purpose of simulation; and in many cases (n=16; 76%), this centred on service redesign. Surprisingly, seven studies 12 13 21 25 31 34 36 (33%) did not provide any details about the ED being investigated, while five studies 10 21 23 26 30 (24%) did not provide patient flow diagram. Table 2 provides summary of simulation methods, including simulation type, key assumptions and use of software. The types of simulation varied only between two methods (DES and SD). DES modelling was used in 19 studies (90%), while SD was used in 2 studies (10%). All but one study 25 either explicitly or implicitly justified the choice of underlying modelling method used. The majority of studies (n=18; 86%) used specific hospital models of ED patient flow. The reporting of modelling assumptions was poor overall. For example, as many as 12 studies 10 12 13 21 23-25 29 31 32 34 35 (57%) did not provide any details about simulation duration, warm-up period and run number. Only five studies 11 22 27 30 33 (24%) specified the number of simulation runs and three studies 27 30 36 (14%) specified the simulation warm-up period. Simulation duration ranged from 24 hours 27 33 to 52 weeks. 26 30 Almost 50% (n=10) of the studies used Simul8 software (www. simul8. com) for running the model. Two studies 24 34 (10%) did not provide any details about the use of software. Table 3 provides detail of simulation inputs and outputs. The identified models were populated from three sources of data: primary (ie, collected within the hospital being studied), secondary (ie, collected in another setting) and expert opinion. One study 21 did not describe the source of data for any of the model inputs. Three studies 13 26 31 described the source of patient arrival rates, but not the sources of activity duration, activity progression and use of resources. Eight studies (38%) stated explicitly that they used expert opinion to populate some of the model inputs. The proportion of studies that used primary data was reasonably high (table 3). In particular, 95% (n=20) of the studies used primary data for patient arrival rates, 67% (n=14) for activity duration, 62% (n=13) for activity progression and 52% (n=11) for resource inputs.
The most common changes considered in the simulation studies were ED patient flow (eg, changes in the triage system for arriving patients 30 ) and resource capacity planning (eg, changes in the number of cubicles 30 ). However, one-third of the studies 11 13 21 24 26 27 31 (n=7) did not provide any details about the changes considered by the simulation. The majority of studies (n=19; 81%) considered patient waiting times (ie, time from arrival to discharge, admission or transfer) as the key outcome measure. In particular, 11 studies 10 11 13 21 22 25 27 29-31 34 considered patient waiting times alone, 7 studies 12 23 24 28 32 35 36 considered patient waiting times and resources used, and the other study 33 considered patient waiting times, resources used and elective cancellations. Two other outcome measures considered were resources used 26 and bed occupancy. 14 Only 12 studies (57%) reported some involvement of stakeholders in the simulation study, mainly when deciding the study questions or specifying the model structure. However, in the study conducted by Mould Open Access  Table 4 describes simulation results, summarising conclusions in terms of whether the changes considered (eg, increase in staffing numbers) were supported by the simulation, whether the changes supported were implemented in practice (eg, staffing increased), and barriers to conducting the simulation (eg, data issues) and implementing the changes supported (eg, poor clinician buy-in and credibility). Two-thirds of the studies (n=14; 67%) provided some discussion on the usefulness of simulation for analysis of changes to the delivery of emergency care (table 4): six studies supported the proposed changes, one study opposed the proposed changes and seven studies recommended differential changes. Only a small number of studies 12  We identified a broad range of challenges, including oversimplified assumptions 22 25 33 35 and model structure, 14 25 system complexity, 11 14 30 31 34 poor data quality, 12 25 29 34 36 high expectations, 24 short-timescale, 33 poor stakeholder engagement, 12 limited specialist analytical skills, 36 model runtime, 11 24 generalisability 14 28 and impact of simulation 36 ; six studies 10 21 23 26 27 32 (29%) did not describe any emergent issues.

DISCUSSION
This review has shown that computer simulation has been used to analyse ED patient flow and resource capacity planning to the delivery of emergency care. The most common types of computer simulation used were DES (n=19; 90%) and SD (n=2; 10%). All but one study 25 provided either explicit or implicit justification for the choice of modelling method used. However, the use of computer simulation of patient flow within EDs in the UK does not appear to have increased in recent years as may have been expected. This could be a reflection of the relatively limited availability of funding for research in this area compared with funding for health technology

hours
Not reported Simul8 *The authors used an agent-based simulation approach to model the ambulance service, but modelled the ED through a DES. These two individual models were then linked together to form a hybrid emergency services model. †The authors used a Markovian queuing network, but computed the moments and densities of patient treatment time through a DES. ‡The authors used an SD model as part of a bigger picture, but modelled the ED through a DES. §The authors used their ED model elsewhere 37 to form a whole hospital DES model consisting of two other departments: inpatient and outpatient clinics. ¶The authors used their ED model elsewhere 38 to form a whole hospital DES model consisting of three other components: inpatient bed management, waiting list management and outpatient clinics.
**The authors used their ED model elsewhere 39 to explore the issues that arise when involving healthcare professionals in the process of model building. † †The authors constructed the ED as a separate submodel which was not detailed in the paper. However, we believe this ED submodel 14 is identical to the ED model reported in another included study. 10 ‡ ‡The authors used their ED model elsewhere 40 to illustrate the role of care pathways to the redesign of healthcare systems.
DES, discrete event simulation; ED, emergency department; SD, system dyamics. Open Access assessment. There is also a limited number of research groups with the analytical skills required to develop technically complex simulation models for the analysis of service redesign. Identified studies varied in the style and quality of reporting; but assumptions used in the analyses were not always transparently reported. The opaque reporting of key assumptions prevents decision makers from appraising the quality of evidence from simulation experiments. Although there is a set of guidelines for researchers of DES to follow when building models, 43 this has not been widely adopted yet. Most of the studies (n=19; 90%) considered patient waiting or throughput times as the main outcome measure. This is perhaps unsurprising since waiting time has been shown to be a key determinant of patient satisfaction and has been strongly prioritised through the 4-hour targets. 2 Some studies 13 21 26 31 did not provide enough information on how input parameters were selected and synthesised. A handful of studies used expert opinion to populate some of the model inputs, but none explicitly justified the reason for using expert opinion. It is important to have transparent criteria for using expert opinion since it can overestimate or underestimate the model inputs. There are several methods for eliciting expert opinion as discussed by Grigore et al. 44 Most models were intended to capture specific aspects of the emergency care process, but some authors have argued that understanding of patient flow requires study of the entire care process. 45 Conversely, others argue that it is sufficient to focus on the specific needs of the care process rather than modelling a large and complicated care process. 27 Most of the studies (n=18; 86%) used specific hospital models of ED patient flow. Interestingly, there seemed to be no standard hospital model of patient flow of emergency care process. One generic model was developed by the Department of Health in 2007 for use across all EDs. 12 This generic approach allows hospitals to benefit from simulation methodology with minimal costs and technical expertise, but there are challenges of using a generic national model for specific local use due to the local context of each NHS hospital including differences in physical space, the demographics of local patient populations, and so on.
Just over half of the studies in our review reported some involvement of stakeholders in the simulation study. Involving stakeholders is important since it helps to understand the problem better, 8 46 assess the simulation outputs fully 47 and translate simulation outputs into policy. 15 Very few studies reported clear summaries of whether the changes considered were supported by the simulation and of whether the changes supported were implemented. Some studies drew attention to a number of challenges particularly associated with simulation conduct and implementation. Brailsford 48 provided a helpful discussion on how to overcome the barriers such as methodological suitability, data crisis and stakeholder issues.

Open Access
Only three studies 12 34 36 (14%) reported on the implementation of the changes supported by the simulation outputs. This may show that the impact of computer simulation modelling within the field of UK's emergency care has been limited, though we do not know if any changes were implemented at a later date. We also do not know if any changes implemented led to any improvements in the process or outcomes of ED care. The systematic use of simulation modelling is not yet part of healthcare, whereas its use in other sectors like in manufacturing or airline industry is an integral part of the actual decision-making process. 49 Why is simulation yet to make the same impact in healthcare as in other industries? Lack of stakeholders' engagement has been argued as one of the main reasons for this. 8 46 48 49 To this end, Harper and Pitt 46 discussed the basic components of successful implementation of simulation methods in healthcare. Absence of lucid guidelines about how to use simulation methods effectively in healthcare has been argued as another reason. 50 However, more recently in 2012, the ISPOR-SMDM Modeling Good Research Practices Task Force-4 laid out a set of guidelines about how to use DES method effectively in healthcare. 43 In line with a few others, 8 46 48 49 we also argue that if simulation is to make sustained impact in healthcare, the clinicians and decision makers must cooperate across physical and organisational boundaries and come to understand how seemingly small changes in design of processes can improve patient care.
We systematically searched eight bibliographic databases to identify the included studies; however, our study has some limitations. First, we focused on the use of computer simulation methods in the context of patient flow within EDs under the jurisdiction of UK NHS only. Improving emergency care is a research priority for UK NHS. 1 In this review, we examined the current literature that analysed ED patient flow within the context of UK, and discussed how simulation can be better used as a tool to address this problem. It would be interesting to compare the identified methods with other jurisdictions across Europe, in the USA and Australasia, but this was beyond the scope of this study. Besides, comparing studies from different jurisdictions and reaching consensus would be challenging since healthcare delivery is different in the UK. Nevertheless, computer simulation has been used to analyse and design ED overcrowding in other countries. In particular, DES models have been used to identify optimal ED flow patterns, 51 forecast ED overcrowding 52 53 and evaluate staffing levels and changes in ED bed capacity. 54 Fletcher et al 12 cited a number of other international ED models which have different designs to English ED.
Second, we were not aware of any formal assessment checklist to estimate quality scores of the identified studies. The set of guidelines reported by the ISPOR-SMDM is not a quality assessment checklist for reviewers. 43 It is rather a set of recommended best practices for modelling teams to consider and embrace when building DES models. Furthermore, there is a good rationale for a component-based approach, instead of using a quality score. For example, in the field of randomised controlled trials (RCTs), there is evidence that the use of quality scores and scales, especially of those with a numerical summary, is problematic and meaningless. 55 The current best practice for assessment of validity of RCTs requires assessing individual components of trial design, conduct and analysis (eg, Cochrane risk of bias tool). We adopted a similar approach, whereby assessing the key methodological components of all included studies.
Third, we neither verified whether any of the hospitals implemented the findings found from simulation experiments, nor do we know if any changes implemented led to any improvements. Typically, there is little opportunity to assess the impact of the simulation since publication emerges before the work is fully implemented in many healthcare studies. 56 Finally, we did not include Google Scholar in the database search list since it has a number of issues with its indexing and citation algorithm, although it is known to provide increased access to non peer-reviewed publications. 57 Anecdotal evidence suggests that NHS hospitals have used simulation modelling (and other methods) to improve patient flow through the ED. However, our review will not capture all of this work as it is not all reported in peer-reviewed academic publications. We used a key review paper 20 to select a wide range of databases covering the comprehensive sources of literature in computer science, operations management and healthcare fields.

CONCLUSIONS
We found that computer simulation can provide a means to pretest the likely impact of changes to the delivery of emergency care before implementation in a safe and efficient manner. In particular, it is used to identify the key relationships and bottlenecks in the process of ED care, test 'what-if' scenarios for service redesign, determine levels of uncertainty, provide visualisations and forecast future performance. However, the evidence base is small and poorly developed, with many methodological and practical issues, including lack of awareness regarding system complexity, lack of good quality data, lack of persistent engagement of stakeholders in the modelling process, lack of in-house analytical skills and lack of an implementation plan. Furthermore, the level of detail of reporting of the computer simulation methods differed in the style and quality of reporting; and in some instances, key aspects of the assumptions underpinning the analyses were not always reported explicitly and transparently.
This review is a useful source providing direction on why simulation needs to be better used as a tool for analysis of ED patient flow. Future studies should justify the choice of simulation modelling method explicitly, avoid making selective use of the available data, engage stakeholders in the modelling process and keep them on board continually, be transparent in the reporting of simulation inputs and outputs, and report on the implementation of changes supported by the findings of Open Access simulation experiments. We recommend the adoption of reporting guidelines 43 by academic journals and conference proceedings, and more persistent exploitation of innovative models of engagement and knowledge mobilisation between academics and healthcare professionals such as the Researchers in Residence. 58 Further research is necessary to assess the quality of computer simulation models of ED patient flow across different countries and to establish the extent to which the simulation outputs have been translated into policy.
Contributors SM and JB independently screened and appraised the relevant studies, and extracted the data from the included studies. CV, SM, JS, KN, JB and AR designed the search strategy. AR, an information specialist, conducted the electronic search. SM drafted the manuscript in conjunction with CV. JD, WH and CV revised the draft critically for intellectual content, while the other authors commented on the draft. All authors read and approved the submitted manuscript. Competing interests None declared.
Provenance and peer review Not commissioned; externally peer reviewed.

Data sharing statement No additional data available.
Open Access This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http:// creativecommons. org/ licenses/ by/ 4. 0/