Keywords

1 Introduction

Accident and Emergency (A&E) and Emergency Departments (EDs) have been experiencing increasing demands worldwide, with healthcare often facing financial difficulties and departments expanding their range of responsibilities to include, for example, uninsured patients, or arrivals during times and in places where community health and social services are unavailable. A&Es also play a key role in public health surveillance and disaster response; as a result there has been an increasing need for departments to become more efficient as evidenced by various standards and targets. For example, the UK National Health Service (NHS) has had a target of 95 per cent of patients being seen in under 4 h for over a decade, yet the NHS Director (Sir Bruce Keogh) has recently announced that this the problem of long waits in A&E should now be addressed by improving services in the community, evidencing the need for urgent improvement and novel strategies.

In recent years, the use of discrete event simulation (DES) to support healthcare evaluation has gained increasing prominence [1,2,3]. Reasons for A&E departments featuring so prominently may include the relatively short timescales required for treatment and corresponding data collection as well as the comparatively self-contained nature of the department [4, 5]. Moreover, as a showcase of the healthcare system, treating large numbers of patients, these departments attract a lot of interest from the public, commentators and policy makers.

Other techniques have also been used in modelling the healthcare environment. For example, [6] use systems dynamics to demonstrate the interaction between the A&E department and the rest of the hospital. Also, [7] used a stochastic dynamic model that consisted of a noisy measurement and first-order autoregressive (AR) stochastic dynamic process, for modelling the throughput of emergency departments using available time-series data from a London hospital. Such approaches, which link the performance of A&E departments to the arrival mechanism as well as the rest of the hospital system, resonate well with simulation models of A&E which seek to develop new strategies for managing the queues and resource utilization.

Nonetheless, while there is an extensive research literature on simulation and modelling of A&E, little work has been done as yet on the impact of such strategies. In fact, a recent British Medical Journal paper [8] carried out a systematic review of the use of discrete event simulation for patient behavior in UK emergency departments and concluded that while “computer simulation can provide a means to pretest changes to ED care delivery before implementation in a safe and efficient manner” the “evidence base is small and poorly developed” and there are also additional issues which should be addressed.

In this paper, we model the A&E Department of a District General Clinic, motivated initially by a desire to set up a baseline against which a number of streamlining strategies could be assessed. The novelty lies in the application of DES to reduce waiting times in a clinic that is dedicated to people suffering from accidents. In addition, once we have developed the model, improvement strategies can be evaluated. In particular, we will validate the effectiveness of introducing a triage system, a strategy that is not currently adopted by the clinic. We also will endeavor to address issues identified by [8], particularly with regard to establishing a baseline which can then be used to evaluate proposed improvement strategies. The novelty also resides in the fact that this is a unit for accidents only and the results might be thus different.

The remainder of this paper is organized as follows: in Sect. 2, a brief literature review relating to improvement strategies for A&E improvement is presented; Sect. 3 illustrates the proposed methodology; Sect. 4 describes and analyzes the results of a case study from a clinic that deals solely with accidents. Finally, Sect. 5 presents the conclusions and future work emanating from this study.

2 A Recent Literature Review

The use of mathematical models and optimization methods as mechanisms of characterization, analysis, evaluation and selection of alternatives, has an increasingly significant importance in health care decision-making [9], especially in process improvement, customer satisfaction and economic evaluation of services and technologies for diagnosis and health care, where the simulation plays a key role to achieve these goals.

Simulation is defined as the act of representing a real system so that certain key characteristics or behaviors can be effectively described [10]. Considering the above- mentioned definition, the simulation can be carried out from the real or computational perspective. In this regard, an increasingly used alternative to address this problem is DES models. In this respect, DES assists in the development and experimentation of computational models representing complex systems, with the objective of characterizing their behavior [11], as well as analyzing scenarios for the improvement of current systems performance before implementation. In the scientific literature, there are different studies related to the application of DES in different healthcare areas and processes, including its combinations with other modelling techniques. In this sense, we have highlighted scientific studies analyzed the existing literature on the use of the simulation and modeling of processes in health care, from a multidimensional perspective [1]. In this respect, several articles were found to be related to the use of simulation tools for performance improvement in different areas and health processes, such as mammography [12], reduction of planning time and service waiting times in radiation therapy [13], characterization of overall capacity, length of stay, waiting times and service times in physiotherapy [14], and reduction of waiting times in several outpatient specialties [15, 16]. There are also projects carried out in highly complex processes such as gynecology and obstetrics, aiming at improving appointment times, contributing to patient satisfaction and reducing the rate of maternal and infant mortality [17]. Another example of DES application in complex services can be found in [18] where this technique was used to establish strategies for timely planning and care in a stroke unit.

Additionally, DES has been used to analyzing key performance indicators such as resource utilization [19], the design of facilities and healthcare networks [20], reduction of appointment lead-times [17, 21]; reduction of access time to health care services [22, 23], delay minimization in outpatient clinics [24], and improvement in patient waiting times [15, 25]. In the aforementioned works, operational inefficiencies have been identified and significant improvements have been achieved using DES technique.

We also identified that DES can be combined with other techniques e.g. linear programming [19, 21]; systems dynamics [26], Lean methodology [27, 28], queuing theory [29] and agent-based modeling [30]. Regarding the research field of this work, which is oriented to DES applications in A&E and EDs, only a few studies are available. For instance, an analysis of patient flow within emergency departments (ED) was performed in a hospital located in the UK [8]. Another application can be found in [31, 32] where DES was performed to improve the care quality in the emergency department of a community hospital in Lexington and Ireland respectively. On the other hand, in [5], the maximization of expectations (EM) algorithm was used to simulate the performance of EDs. Also, in [7], a study was also carried out in an emergency department located in the United Kingdom via the application of DES to characterize, analyze and improve the length of stay by considering the operational standards demanded by the government. Likewise, in [33] a DES model was developed to analyze the patient flow in an ED in Hong Kong to improve its current performance and evaluate the impact of possible changes in the system. Other interesting work can be found in [34, 35].

However, considering the literature review presented in [35] and the findings derived from this study, little work has been done as yet on the impact of improvement strategies in EDs via using simulation. This is in spite of DES providing a means to evaluate changes to ED care delivery before implementation in an effective manner. Therefore, this work represents a reference source for both ED and A&E managers when assessing possible improvement scenarios reducing patient waiting time. Additionally, related works about the problem of waiting time in accidents and emergency departments are predominantly centered in the UK health care infrastructure and Hong Kong; in this respect the case study presented in this paper was developed in a colombian clinic; thus, new outcomes may be achieved.

3 Methodology

Within our modelling framework, it is necessary to ensure that the simulation model is statistically equivalent to the real-world system. In this respect, data assumptions should be rigorously validated and processes must be effectively characterized. In addition, if the model does not provide a good representation of the A&E department, further analysis cannot be carried out and thus, improvement strategies cannot be properly created and pretested. A methodology comprised of five stages has been developed with the foresight to be applied in other A&E departments (refer to Fig. 1).

Fig. 1.
figure 1

Methodological framework to reduce waiting times in A&E departments

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Our framework starts with the system description (Stage 1) where the healthcare professionals and other medical staff are asked to give information related to the identification of processes, patient flow and stakeholders in order to be described by flow and SIPOC diagrams. Then, in Stage 2, data (process variables and parameters) are identified, collected and analyzed by using intra-variable tests, homogeneity test and tests for goodness-of-fit [36]. This is important to provide more realistic models incorporating variability in accordance with the real-world system. Afterward, the DES model is created with the aid of a simulation software package (Stage 3). The animation provided by the software facilitates engagement with the healthcare managers and underpins the decision-making process in relation to the resource utilization, performance analysis and the identification of bottlenecks [37]. After this, the model should be rigorously validated through statistical tests in order to determine whether it is equivalent (α = 0.05) to the real-world system (Stage 4). Finally, the improvement scenarios should be clearly stated with the support of the healthcare staff and validated via using DES models (Stage 5). This is relevant to pretest the changes to ED care delivery before implementation in a safe and efficient manner as stated in [8].

4 Modeling the A&E Department: A Case Study in a District General Clinic

A case study of an A&E department from a district general clinic has been explored. The model describes the journey of patients from arrival time to discharge. Our simulation model was based on a 3-year prospective dataset extracted from the User Information System (UIS) and consisting of all patients admitted between 1 January 2014 and 31 December 2016. This system operates 24 h per day, 365 days per year. In this department, a discrete distribution was fitted to the arrival process: 92.33% (1 patient/arrival), 6.84% (2 patients/arrival), 0.69% (3 patients/arrival) and 0.14% (4 patients/arrival). Then, an intra-variable independence test was performed to establish whether the variable “time between arrivals” was random. To evaluate this, a run test was carried out with α = 0.05. The results evidenced with p-value = 0.921 that this variable could be modelled with a probability distribution. Afterward, the “time between arrivals” variable was proved to be modelled with an exponential distribution (β = 18.8 min). For the goodness-of-fit of this distribution, the chi-squared test (χ2 = 15.5, d.f. = 4, p < 0.005) provided good support for the exponential assumption.

On the other hand, the department does not currently adopt the triage system. In this regard, patients are classified into two categories: “poor clinical condition” and “minor complications” In the period, there were 33% admitted who had been categorized with a poor clinical condition and 67% with minor complications. Within this system, a homogeneity test (Kruskal-Wallis) was performed to establish whether the distribution of times between arrivals should be modelled separately according to the patient category. In this case, with a p-value = 0.2172 (greater than alpha level = 0.05), the datasets were found to be homogeneous and could be characterized by a single probability distribution.

Medical care is provided by ten doctors who have different schedules. The current schedules of these doctors are described in Table 1. In this regard, there are four types of shifts: Night (N), Mixed 1 (M1), Mixed 2 (M2) and Shared (S).

Table 1. Schedules of doctors attending in the A&E department
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Regarding the length of stay (LOS) in A&E department, a run test was also performed. In this respect, with a p-value = 1.000, this variable was found to be randomly distributed. After this, sub-groups of patients were identified which are not homogeneous (p-value = 0.3630) with respect to the distribution of LOS. These pipelines were stratified based on whether the patient was admitted to A&E with minor complications or poor clinical condition. For the goodness-of-fit of LOS distribution, the Kolmogorov-Smirnov (K-S) test (p-value = 0) provided good support for the uniform assumption in both patient categories: Poor clinical condition (a = 10 min, b = 45 min) and minor complications (a = 10 min, b = 15 min). After staying in this department, five types of destination discharges could occur: Hospitalization, Surgery, Intensive Care Unit (UCI), Home or Death. In this sense, according to the data provided by UIS, the discharge distribution shows that: 15.3% are discharged to UCI, 20% are remitted to Hospitalization Department, and 18.1% to Surgery Unit, 46.4% are discharged to home and 0.2% to the “Dead Room”. The model does not consider the final destination discharges of patients since they depend on the performance of other services.

This service is regulated by the Ministry of Health and Social Protection. In this respect, the upper specification limit (USL) for average waiting time in A&E has been established as 30 min/admission. This information was considered in the simulation model that was designed with the support of Arena 15® software in order to reduce the current waiting time of the A&E department. A Mann–Whitney Test was performed to determine if the simulated model was equivalent to the real-world system. In this regard, a P-value equal to 0.079 (alpha level = 0.05) and W = 4590 demonstrated that the model was statistically equal to the real-world system. Afterward, the current mean waiting time was calculated. On average, a patient has to wait for 34.19 min with a standard deviation of 15.6 min (refer to Fig. 2).

Fig. 2.
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Current performance of the A&E department in terms of patient waiting time

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This means that there is a probability of 96.15% that an admitted patient waits for more than 30 min between the arrival time and the start of medical care. In addition, DPM = 961518 which denotes that 961,518 patients out of 1 million will have to wait for more than 30 min. In an effort to face this problem, three improvement scenarios were designed with the support of the A&E healthcare managers. Each scenario was evaluated via a simulation model before implementation (refer to Fig. 3a–c).

Fig. 3.
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Comparative analysis between current state and Scenario 1 (a), Scenario 2 (b) and Scenario 3 (c)

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After pretesting these scenarios, the results demonstrated that two of the proposals are promising since they provide a reduced waiting time. In this regard, a Mann–Whitney test was carried to compare the current state of the system and each improvement scenario (Table 2). The results have been presented in Table 3.

Table 2. Schedules of practitioners in triage systems
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Table 3. P-values, W statistics and confidence intervals for comparisons between real system and proposed scenarios
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Taking into account the aforementioned results, the improvement scenarios were compared in terms of waiting time via applying box-and-whiskers plots (refer to Fig. 4). It can be appreciated that the proposed scenario 3 provides the best operational performance due to its reduced variation. This is beneficial to increase the customer satisfaction since the main patient complaint is having to wait too long. Furthermore, it reduces the increased suffering for those in pain and the need of more complex healthcare services.

Fig. 4.
figure 4

Box-and-whiskers plots for comparisons between improvement scenarios

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5 Conclusions and Future Work

In this paper, we have validated the effectiveness of discrete-event simulation to improve patient waiting time in an A&E department from a district general clinic. The results demonstrated that considering the current system, 96.15% of the admitted patients in this department will have a waiting time higher than 30 min. Therefore, three proposals were simulated and evaluated with the aid of Arena 15® software, Minitab 16 and knowledge provided by the healthcare managers of the A&E department. In this case, two of the proposals were identified to be operationally effective since they provide a reduced waiting time compared to the real-world system. In particular, the best scenario (Scenario 3) allowed managers to decrease average waiting times from 37.67 min to 30.18 min and the standard deviation from 5.05 min to 3.87 min. This represents an earlier diagnosis and treatment which is beneficial for patients.

On the other hand, healthcare managers can pretest changes to ED care delivery before implementation in an effective manner using DES technique. This is relevant to avoid mistakes, misunderstandings and cost overruns during the implementation process of these changes. Nonetheless, it is necessary to work closely with clinicians and other healthcare professionals to ensure that the models are equivalent to the real-world system. Additionally, collecting suitable and high-quality data is a pivotal aspect when modelling healthcare systems that provide a good representation of the processes variability.

Our case study enriches the existing literature and contributes to the evidence base related to the use of DES techniques when pretesting changes to ED delivery care. However, we plan in future work to develop financial evaluations of each improvement scenario in order to deploy more detailed and informative simulation models. In addition, our work will also consider interactions with other healthcare services (e.g. hospitalization and surgery care) to effectively support integrated planning processes for both hospitals and government.