“Plan the unexpected and remain flexible” Acute Medical Unit offers capacity during crowding at the Emergency Department

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UNIVERSITY OF GRONINGEN & NEWCASTLE UNIVERSITY

Double Degree Master Thesis

“Plan the unexpected and remain flexible”

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Acknowledgement

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Abstract

Background: Crowding at emergency departments is known to challenge the acute healthcare chain

and is a real burden for the hospitals. Acute medical units are instigated in many hospitals with literature reporting several benefits. However, no set guidelines or uniform standard are present for these units. Aim: This study aims to examine a flexible AMU by supporting the ED with additional capacity during crowding. We aimed to contribute to the reduction of crowding by determining the support offered by a flexible AMU. Methods: A single case study at the University Medical Center Groningen was conducted over a timeframe of two years. Patient flow analysis is evaluated by inflow, outflow, and throughput of all 50247 patients visiting the ED. In depth analysis of potential AMU patients is conducted by a simulation of a flexible AMU. All the quantitative data is extracted from the electronic patient’s information chart of the case studied hospital. Results: From all the admitted patients after an ED visits 17%, 31% and 42% are eligible for admittance to the AMU for discharge times of respectively <24 hours, <48 hours and <72 hours. For these discharge timeframes and a blocked patient rate of maximum 6% the flexible AMU can support the ED during crowding in 97%, 92% and 88% of the cases without additional resources. Conclusion: In order to improve the current strain on the acute healthcare system a flexible AMU could potentially provide extended capacity without additional resources. However, further research is needed to generalize this across other hospitals.

Keywords: Acute Medical Unit, Emergency Department, crowding, short hospital admissions,

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List of figures

Figure 1 patient flow traditional and including AMU ... 12

Figure 2 Dataset cleaning for 2-year period ... 19

Figure 3 Average patient arrival pattern per hour (days of the week) ... 25

Figure 4 Frequency of occurrence number of patients arriving on one day (24 hours) ... 25

Figure 5 Number of patients arriving per day (24 hours) represented by days of the week ... 26

Figure 6 Representation of 8-16 patients arriving in an hour represented over time ... 27

Figure 7 Average patient arrival rate based on triage colors ... 27

Figure 8 Average departure rate patients for each day of the week ... 28

Figure 9 Average patients admitted per hour to hospital nursing wards from the ED ... 29

Figure 10 Average patient departure rate based on triage colors ... 29

Figure 11 Input- output diagram patients including desired output ... 30

Figure 12 Length of stay patients grouped in half hour timeslots ... 31

Figure 13 Work in progress count and cumulative percentage ... 32

Figure 14 Combination graph LOS and WIP ... 32

Figure 16 Average LOS of ED-rooms (vertical axis in h:mm:ss) ... 33

Figure 15 Utilization of ED-rooms ... 33

Figure 17 Number of times ED-room changes ... 34

Figure 18 Cumulative chart of patients discharged from nursing ward ... 35

Figure 19 Specialisms discharge time within 48 hours ... 36

Figure 22 Specialisms all admitted patients ... 36

Figure 23 Percentage of patients in age groups according to discharge 24, 48, 72 hours ... 37

Figure 24 triage colors based on admitted patients from the ED ... 37

Figure 25 Boxplot of time durations for WIP greater or equal to 25 and 30 beds ... 40

Figure 26 Boxplot of actual duration WIP and adjusted duration WIP ... 41

Figure 27 Actual WIP (orange) and adjusted WIP (blue) number of times occurrence ... 42

Figure 28 Frequency of WIP>22 over time ... 44

List of tables

Table 1 Number of beds according to discharge rate and blocked patients ... 38

Table 2 Erlang-B and actual number of blocked patients ... 39

Table 3 Erlang-B and actual occupancy rate ... 39

Table 4 Boarding time and LOS regarding the time in nursing wards ... 41

Table 5 Number of beds occupied at the AMU during a WIP at the ED >22 ... 43

Table 6 Occupancy rate, blocked patient rate and available beds with an AMU of 20 beds... 45

Table 7 Discharge rule of 48 hours and 17, 18, 19, 20 beds ... 45

List of abbreviations

AMU Acute Medical Unit

ED Emergency department

EPIC Electronic patient information chart

LOS Lenght of stay

MTS Manchester triage system

UMCG University Medical Center Groningen

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1. Introduction

"Waiting is good. It means you’re not going to die. The person you need to feel sorry for is the one who gets rushed into the Emergency Department and treated first." —Joan Somes, RN

This quote gives a positive perspective on the waiting and capacity issues within the Emergency Department (ED) faced by the patients. However, the hospitals have been increasingly under pressure, caused by the steady rise in emergency admissions due to the aging population with multiple diseases and the raised expectations of care (Delia & Cantor, 2009). From an analysis on older patients visiting the ED in the Netherlands it became clear that 75% of older patients tend to spend longer in the ED than young adults (Samaras et al., 2010). Moreover in 2016 for the first time in years, the adjusted mean hospital length of stay for the ED has increased by 8.5% (van Galen et al., 2017). Not only the rise in admissions resulted in these negative effects but also bed shortage and non-effective bed use contributed. Therefore, hospitals need to consider structural reforms for the acute care chain to improve efficiency.

Solutions are not universal, but one of the possible solutions to the current overburden on the acute health system could be an Acute Medical Unit, further referred to as AMU. This concept is gaining popularity in many counties in the world and is already widely implemented in the UK and Australia (Scott et al., 2009). The AMU or units with similar names such as medical assessment units (MAU), early assessment medical units (EMU), acute planning units (APU), or acute assessment unit (AAU) can be defined as a hospital ward that is designated to receive patients with acute illness from mainly the emergency department and in certain countries from outpatient clinics. In this ward medical specialist assessment, care and treatment can be provided for a designated period which is typically 24 to 72 hours after which patients are discharged or transferred to another ward (Bokhorst & van der Vaart, 2018).

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8 An AMU can have a fixed or flexible capacity, but currently all AMU’s reported in literature operate as fixed AMU’s. The idea of a flexible acute medical unit in the UMCG is that it can provide extended capacity for the ED in addition to the original AMU functions. So, in more detail, the flexible AMU will remain having the already proven positive effects of a fixed AMU but can play a role in extra buffer capacity at the ED during peak hours. Bed capacity shortage is mentioned as cause of crowding at the ED (Moskop et al., 2009). Khare et al (2009) and Han et al. (2007) both mentioned that adding beds directly to the ED does not reduce the overall ED length of stay without addressing other bottlenecks in the hospital (Han et al., 2007; Khare et al., 2009). Therefore, the beds that are already available at the AMU will be used during peak moments by the ED. This way the AMU acts as a buffer for ED and patients can be assigned to beds even during crowded moments at the ED. This will also increase the ability to respond quickly to mass casualty events and the safety net is higher (Schneider et al., 2003). The ideas around this flexible AMU are still in a conceptual phase and therefore the research question for this research is defined as:

To what extent can the flexible AMU concept contribute to the ED crowding given the ED patient flow characteristics?

A successful implementation of the flexible AMU depends on the current issues of the emergency department such as the inflow, outflow, and processes within the system. Hence, this study identifies bottlenecks and process-related factors that contribute to emergency department capacity problems, with a focus on identifying factors that could potentially be improved by the initiation of a flexible Acute Medical Unit (AMU) to provide extended capacity of the ED. To be able to answer the above question it is important to understand the capacity issues of the ED in detail such as the frequency of extra capacity needs, the type of extra capacity, the duration of extra capacity needs, the distribution of acute patient intake, the type of specialism and urgency of care. This will all be discussed in this work.

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2. Theory

In this section, the current capacity issues at the ED are discussed and the basic principles of the existing acute medical units will be provided. Various results of previous literature on the AMU are explored to determine how the flexible AMU can elaborate on the gaps in literature.

2.1 Crowding at the emergency department

A patient that requires acute care will go into the ED where time delays should be minimal since this might result in harm to the patient. The arrival in an ED can be through referral by a general practitioner, ambulance, or self-referral. Mostly a triage is performed to determine the priorities among patients which is usually according to Manchester Triage System (MTS) (Mackway-Jones et al., 2014). After triage, a diagnosis and treatment policy follow, and the patient will be discharged from the ED and is either sent home or admitted to a hospital ward.

When the need for emergency services matches the available resources, the system is in balance, but various studies have shown that ED crowding is a long-term challenge in many countries (Pines et al., 2011). There is no consensus on the exact definition of tools for correct measurement of crowding. According to Moskop et al (2009) it is defined as a state where care demand exceeds available resources, resulting in long waits for tests and treatments. Indirectly this suggest that crowding is the result of capacity shortages, while Ter Avest et al. (2018) showed that inadequate synchronization of available capacity can also be a cause of crowding. Although the Netherlands is not considered as a country with major issues regarding ED crowding, there is still a mismatch between supply and demand in the healthcare system, which can result in long waiting times and delays in critical treatments (Anneveld et al., 2013). Moreover, according to Van der Linden et al. 68% of Dutch hospitals experienced crowding problems once a week or even daily in 2013 (van der Linden, 2015).

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10 workforce shortages, lack of educated health professionals, (5) health care financing, lack of insurance coverage and relying on market forces brings down the healthcare system (Schafermeyer & Asplin, 2003). Derlet et al. (2001) mentioned similar causes of overcrowding with a main focus on the patient inflow variability and shortages of various staff members (Derlet et al., 2001). Lastly, Ter Avest et al. (2018) emphasizes that improved timing of internal efforts within the ED should be an integral part of a system approach to prevent crowding at the ED. While most of the other researchers are focused on the external causes Ter Avest et al. (2018) center crowding around the operational processes in the ED. Due to the various causes of overcrowding the solutions are not universal either. Multiple options to this prolonged challenge of the healthcare system have been explored in literature and these are discussed in the next paragraph.

2.2 Reduction of crowding

Crowding in the ED is an ongoing issue with extensive literature about the harms of emergency department crowding but relatively limited studies show effective solutions to reduce the crowding issues (Boyle et al., 2012). The minimization of crowding can aim at solving input, throughput or output related causes of crowding, where the output factor is acknowledged to be the main cause (Morris et al., 2012).

Demand management plays an important role to reduce crowding during the input phase. Due to the high variation within the healthcare operations a mismatch between demand and supply can easily occur. Variations at an ED can happen due to the number of patients in the system, the degree of illness or the difference in response to particular treatment and the different capabilities of medical professionals (Litvak & Long, 2000). Research on demand management focusses on methods to redistribute patients or encourage appropriate utilization such as nonurgent referrals. These are referrals where ED visits could be replaced for a primary care appointment which is as high as 38% according to Grumbach, Keane and Bindman (1993). Furthermore ambulance diversion avoids arrivals at crowded moments which decreases the number of ambulance arrivals at peak capacity and increases the number of ambulances at quiet moments (Grumbach, Keane and Bindman, (1993) and Lagoe et al., (2009)). Moreover, destination control could reduce ambulance diversion which uses an internet accessible operating information system to redistribute ambulances (Shah et al., 2006).

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11 the right people to the right places. Most research has been done on crowding measures and indicators; Emergency Department Work Index (EDWIN) and National Emergency Department Overcrowding Scale (NEDOCS) (Weiss et al., 2004).

Lastly the output factor is, according to Morris et al. (2012), the main cause of crowding due to the lack of resources available (further) in the system. The easiest solution is to add resources such as additional personal, observation units and hospital bed access. However this is a costly option and is contradicting with the trend of a decrease in emergency departments (Hoot & Aronsky, 2008; Schafermeyer & Asplin, 2003). Therefore, Khare et al (2009) investigated the effect of an improved outflow process for admitted patients using rapid inpatient bed transfers. As a result, a decrease in LOS and number of boarders were observed so improving outflow processes is likely to reduce ED crowding.

The acute medical unit (AMU) contributes mainly to the last two themes, throughput, and output, to reduce crowding at the ED. It is an extra resource in terms of observational units where patients enter for expedited multidisciplinary and medical specialist assessment, care, and treatment for up to a designated period prior to transfer or discharge. Besides the additional capacity the AMU concept regulates the demand for beds in nursing wards. The nursing wards work according to predetermined schedules with mostly elective patients. Admissions from the ED are unexpected and therefore interrupt their timetable. The AMU becomes specialized in quick patient admission and discharge. They can handover patients at predetermined times to nursing wards. Furthermore, in this research an additional function will be added to the AMU which is the flexibility to support the ED during peak moment where they run out of capacity. In the next section the AMU is described to get a better understanding on the current effect of the AMU and how the ED can possibly benefit from the flexible AMU.

2.3 AMU and its potential as crowding solution

The acute medical unit first emerged in the 1990s because of the strict target that 95% of the patients should not spend more than 4 hours in the ED in the United Kingdom (Bokhorst & van der Vaart, 2018). This triggered the establishment to admit patients in a specialized ward for a designated period for assessment, care, and treatment (Reid et al., 2016).

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12 of acute patients and increase the stay length. All this led to the development of a specialized ward named the acute medical unit (AMU).

To be able to achieve the maximum 4-hour target for a stay at ED that was set in the United Kingdom, the AMU emerged and became a solution for outflow problems. One of the aims of the AMU is to improve quality of care of acute patients and provide the organization with a novel way to improve the efficiency of the acute care chain without disturbing the planned medical care. Although AMUs have local and national differences in organization, they all share similar objectives (Scott et al., 2009). The first objective is a smooth and multidisciplinary assessment of acutely ill medical patients when more clinical investigation is needed such that they can be referred to the correct specialized team if appropriate. The second objective is a faster turnaround time in various clinical investigative services due to improved access. The third objective is the elimination of frequent acute patient admittance and discharge in nursing wards. Although Scott et al (2009) focus mainly on the benefits for the nursing wards and the patients, the after-hour admissions also affect the waiting times at the ED negatively. A simplified patient flow model, based on previous models, can be found in figure 1 where the traditional flow is black, and the green lines represent the additional AMU (Scott et al., 2009; van Galen et al., 2017).

Figure 1 patient flow traditional and including AMU

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2.4 Success factors and problematic issues of AMU

From the previous section it became clear that the AMU does not have a specified layout, but literature emphasized several factors that are critical for the success of an AMU. The critical factors in major lines are: structure that includes medical, nursing and allied health disciplines; business rules around patient entry and a clearly defined process of admission and discharge; supportive hospital management; dedicated staff to work in multidisciplinary teams and good cooperation with the other wards that accept or refer patients form AMU (Scott et al., 2009). Furthermore, the main issues with the AMU’s are based on the staff, function of AMU and cooperation between the departments (van Galen et al., 2017). The recruitment of staff that fit the required level of acute assessment skills can be challenging as well as the high nurse patient ratios leading to high workload. When the function of AMU is not clear for other departments the AMU can become a receiving and holding area for beds to become available and the reluctance of other wards to admit patients from the AMU can increase. Therefore, a solid cooperation between the ED, nursing wards and the AMU needs to be in place for the AMU but even more for the flexible AMU. When the departments combine effort, the AMU can become a buffer for the ED during peak moments and act as a flexible force within the system.

2.5 Performance of AMUs

The most examined factor to determine the effectiveness of AMU is the hospital length of stay, where AMU groups were compared to non-AMU groups. The reduction in LOS ranged from 0.3 up to 2.62 days where 75% found a statistically significant difference (Reid et al., 2016). Bokhorst and Van der Vaart (2018) reported that LOS should be reduced by more than 10% to compensate for the other performance deterioration such as percentage of elective patients that needed to be rescheduled due to the AMU. Over 10% reductions have been reported in previous studies and therefore it could suggest that the negative logistical effects could be compensated (Downing et al., 2008; Lo et al., 2014; E. Moloney et al., 2005; Scott et al., 2009).

Another aspect is the mortality rate which is linked to the performance level. The absolute change between the AMU and the non AMU ranged from +0.1 to -8.8% (Reid et al., 2016), although the significance levels of these mortality rates are less than 50%. Furthermore, there are differences in the exact definition of mortality rate and whether it is calculated according to the entire hospital or specific medical wards.

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14 expected that reduced length of stay results in higher readmission it is concluded that the AMU’s are not associated with increasing rates.

The patient and staff satisfaction concerning implementation of AMU’s are diverse and varies from positive experience to more concerning effects. The positivity is mainly from the patients and indicate an improvement after implementation of AMU (McErlain-Burns et al., 1997) whereas staff are more concerned about bed occupations and stress at the work floor (Hanlon et al., 1997).

Lastly the AMU studies showed that it can reduce pressure on emergency departments and that they are an effective, efficient and safe way to assist in the increasing number of medical patients at the emergency department (Queensland Helath, 2017). However, it is important to note that the performance factors are hard to measure and compare. Introducing AMUs are complex interventions and numerous interacting components are in place (Mason et al., 2014). Therefore, it cannot be concluded that for every hospital similar positive outcome will result from implementation of an AMU. Furthermore, the flexible AMU will become even more complex due to the extra function in terms of capacity buffer for the ED.

2.6 Flexible AMU

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15 flexible AMU. Lastly, most of the literature compares before and after AMU implementation but with this research the goal is to analyze a flexible AMU before implementation based on historical data (Scott et al., 2009).

2.7 Summary

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3. Methodology

The goal of the study is to investigate the effects and added value for the ED by adding a flexible AMU. This chapter explains the approach taken in this case study, which is conducted at the emergency department of the University Medical Center Groningen.

3.1 Study design

A single case study is conducted to determine to which extent a flexible AMU could serve the emergency department during overcrowding. This case study is done at the University Medical Center Groningen (UMCG) which is a large tertiary university hospital without an AMU in the Netherlands. A case study enables the researcher to study a phenomenon in real life setting (Winterton, 2008), in this case to get a good understanding of capacity issues within the ED. With this exploratory case study an extensive examination of the disposition process in the rich content of the ED enables for a more specific research to the design of the AMUs. Both quantitative as well as qualitative data is used in this study such that the qualitative results can support the quantitative data (Modell, 2005). Although the quantitative data is the main guidance using a combination of quantitative and qualitative data results in a greater understanding of the complex situation. Quantitative data is obtained from the electronic database from the UMCG and the qualitative data is gathered by meetings during the process to evaluate and explain the outcomes of the results. Furthermore, an emergency physician from the UMCG was closely involved to validate the data.

3.2 Hospital case description

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3.3 Research sub questions

To answer the main research question to what extend the flexible acute medical unit can provide extended capacity for the Emergency department a thorough understanding of the current ED is needed. This is done according to the four sub-questions based on inflow, process and outflow which will then be connected to the flexible AMU.

1. How is the inflow at the ED of the patients distributed?

According to the emergency physician involved it is important to recognize the peak inflow moments because this can result in capacity issues at the ED. According to literature inflow is one of the phases where crowding can be detected. When the inflow shows a regular pattern, it is easier to determine when the flexibility of the AMU is needed by the ED. Furthermore, the type of incoming patients’ needs to be determined since the difference between the treatment of a trauma patient and a patient with a broken leg is completely different. Multiple trauma patients arriving at the same moment influence the rest of the department drastically since more specialists and nurses are needed for this type of patient. Moreover, these patients need to be directed towards specific rooms that are designed for the specialized care that is needed. All these inflow characteristics determine the needs of the ED and with this information the required flexibility of the AMU can be determined.

2. How is the bed capacity during the ED process and which type of beds are in use?

The number of available beds is one of the main bottlenecks according to the ED physicians at UMCG and therefore the utilization of the different type of beds are monitored. There are various rooms available at UMCG such as the observation room, trauma room and KNO room (Full list in appendix A.9). When all the 22 regular beds are in use the hospital has some emergency beds in the hallway which can be used when maximum bed capacity is reached. Moreover, patients can temporarily be sent back to the waiting room or moved to different departments for further treatment such as plaster room and x-ray facility. When crowding at the ED occurs and the flexible AMU is asked for assistance, they should have the required equipment for patients. Especially the beds that have high utilization at the ED could be useful to duplicate in the flexible AMU. Furthermore, the length of stay (LOS) and the work in progress (WIP) is assessed and evaluated. The WIP is used to determine the number of times the flexible AMU could offer additional capacity to the ED.

3. What is the ED’s outflow pattern and how many patients get discharged within 24, 48 and 72 hours after getting hospitalized?

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18 of interest to determine the doctors needed on the AMU and which nursing wards benefit most from the AMU and can relinquish beds.

4. How many beds are needed for the regular AMU function to account for the patients that are discharged within 24, 48 and 72 hours after hospitalization?

Before determining if the AMU can be used in a flexible way, the number of beds required according to a regular AMU is needed. The patients that are of interest are the ones that are discharged within 24, 48 and 72 hours. Furthermore, the occupancy rate is calculated as well as the blocked patient rate to investigate the possibility of using the AMU as extra capacity.

5. How many beds in the AMU are available to act as a buffer for the ED during peak capacity? For a flexible AMU beds need to be available during peak capacity moments at the ED. It is known that the beds will not be fully utilized. Therefore, the number of beds available after accounting for regular AMU patients is determined. These beds can directly be used when the ED is suffering from crowding without any additional equipment required.

6. How many additional beds are required to change the regular AMU into a flexible AMU? It is important to know the probability that the WIP in the ED is at its peak and the AMU is full as well because then additional capacity cannot be offered by the AMU. Furthermore, this determines whether there is a need of additional beds to account for the flexibility of the AMU or whether this can be achieved without any additional resources. In case the regular AMU does not have enough resources to become flexible the effect of an addition bed is evaluated.

3.4 Data collection

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19 Qualitative data is used to validate the results such that a good understanding can be formed on observed phenomena. The results were discussed with health professionals to examine their view on the patient flows and outcomes in terms of inflow, outflow, throughput, and flexible AMU. The quantitative results were presented to health professionals during an online meeting and afterwards their opinions were evaluated. In this meeting physicians, nurses, and managers from UMCG were represented. Furthermore, more in-depth discussion of observed phenomena took place with an ED physician (Ewoud ter Avest).

3.5 Data cleaning

The dataset is obtained from the electronic patient information chart which is filled in by doctors, nurses, and assistants. A thorough data cleaning was required such that inaccurate records are identified and removed from the dataset. During this process, the unfinished, unreliable, inaccurate, or non-relevant parts of the data were removed such that the dataset represents reality.

In figure 2 the cleaning of the entire dataset is summarized; the total dataset consists of

60.361 observations. All patients that arrived after 1-3-2020 are removed such that the analysis will not be influenced by the covid-19 outbreak. 50513 observations remain and from these observations all patients with a length of stay (LOS) of longer than 18 hours are removed because this is the absolute maximum for patients to stay at the ED according to the involved emergency physician. Some of the observations even showed a length of stay of a few months which clearly indicates an administrative error. Furthermore, the patients that had an arrival time after departure time are excluded from the dataset which reduces the total observations to 50.249. Lastly two patients with unrealistic ages of 168 and 178 are not included which leads to a final dataset of 50247 patients. Besides the removed patients the triage times will not be taken into account since these are sensitive to administrative errors due to nurses that first see multiple patients and then insert them to the system. All in all, 266 patients are removed due to administrative inaccuracy and 9.848 due to the removal of the COVID-19 timeframe. The dataset was checked by the emergency physician for accurateness. Nevertheless, it should be kept in mind that there might still be some minor administrative errors present.

•Reason of removal Number of patients remaining in dataset 60361 •Patients after 1-3-2020 due to covid-19 50513

• LOS longer than 18 hours

50335

• Arrival after departure

50249

•Incorrect age

50247

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3.6 Data analysis

Based on quantitative results, a relatively full understanding of the complexity and nature of the phenomenon can be obtained. The goal is to find possible patterns at the ED and to use these in understanding the possibilities of a flexible AMU. To gain insight on the data, the distribution of some general characteristics are examined. Such as the age and gender of patients. The patients that arrive at the ED are coded with a timestamp in the following format: 01-03-2018 12:56:55 AM. Patients that arrive between half hours are assigned to the closest full hour, for example between 14:30:01 and 15:30:00 are assigned to 15:00. The data analysis will be discussed according to the sub questions in section 3.3: inflow, outflow, throughput, AMU and flexible AMU.

3.6.1 Inflow

To be able to investigate the main research question some general characteristics of the ED need to be evaluated before going into detail for the flexible AMU. One of these characteristics is the arrival rate of patients at the ED, which is important for the flexible AMU since an altered inflow pattern and distribution is known as a cause of crowding. The average arrival rate diagram is made to show the average number of patients arriving per hour of the day to detect (remarkable) arrival patterns. These patterns are based on averages but to investigate high patient arrival within short intervals additional graphs are presented. Patient arrival of more than 8 patients within a 1-hour timeframe is investigated since this constrains the temporarily availability of capacity and resources according to the involved physician. Lastly a diagram with the total number of patients arriving daily is presented.

3.6.2 outflow

Besides the inflow, the outflow is analyzed for patterns. Outflow factors are acknowledged as the main contributor to crowding and influences the throughput in the system (Morris et al., 2012). The outflow factors are described by analyzing the patients discharged immediately and the patients admitted to nursing wards in the hospital. The patients that are immediately discharged after an ED visit, are less interesting for a flexible AMU, but the admitted patients are potential users. The average departure rates per hour are depicted for both groups in figures regarding the weekdays to discover outflow patterns.

3.6.3 throughput

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21 from the departure time of a particular patient which gives the length of stay (LOS). The goal of the hospital is to discharge a patient from the ED within the national norm of 4 hours. Furthermore, the work in progress (WIP) is defined as the number of patients present at the ED when a particular patient arrives. This is determined by the difference between the summation of patients arriving before the particular patient arrives and the summation of patients that are discharged before the particular patient arrives. To see whether the LOS increases when there are more patients at the ED (WIP increases) a combined diagram and scatterplot with trendline are plotted.

Lastly, the average length of stay in various treatment rooms and the utilization of the rooms are determined to give an indication of the ED’s needs in rooms. Furthermore, the number of times a patient is changed from room is included to evaluate the efficiency.

3.6.4 Acute Medical Unit

The case study hospital does not have an AMU yet, but with previous analysis an indication of the needs for this AMU are established. The patients that are currently admitted to a nursing ward in the hospital after a visit to the ED are grouped according to the nursing ward discharge timeframes of 24, 48 and 72 hours, since they are the potential users of the AMU according to literature (Bokhorst & van der Vaart, 2018; Reid et al., 2016). The analysis in this section is based on all patients admitted to a nursing ward and patients discharged within 24, 48 or 72 hours. From all groups the specialisms that the patients are assigned to are determined to analyze the care needed in the AMU.

Historical data is used to determine the potential users of the AMU. However, it can be challenging for physicians to determine if a patient meets the requirements of the AMU. Therefore, analysis based on triage color and age are executed to find patterns to predict whether the patient is suitable for admittance to the AMU.

To get an approximation of the number of beds required at the AMU without flexibility an Erlang-B queuing model (or M/G/c/c) is used. This model proofed to be accurate to determine the number of beds required for hospital wards according to De bruin et al. (2007). With this model a first indication of the number of beds in the acute medical unit can be determined, based on the probability of refusal and the resulting occupancy rate (De Bruin et al., 2010, 2007; Laheij et al., 2019; Van Zanten, 2007). Some other studies use M/M/s queuing models, however this ignores blocking, which should be incorporated in the AMU-model because acute patients can usually not wait and will therefore be moved to another bed instead of waiting in a queue.

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22 independent, negative exponential and can be calculated by subtracting the arrival time of the patient by the arrival time of the previous patient. The length of stay is independent and identically distributed with expectation µ for each arriving patient. The number of beds in operation are defined by c, and no waiting area is assumed such that the fraction of patients blocked can be calculated with the following formula (De Bruin et al., 2007; Koole & Bekker, 2013; Van Zanten, 2007).

𝑃𝑐 =

(λμ)𝑐_/𝑐!

∑𝑐 (λμ)𝑘_/𝑘! 𝑘=0

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The occupancy rate is related to the fraction of patients blocked (Pc), arrival rate (λ) and the length of

stay (µ) and can be calculated with the following formula.

𝑂𝑐𝑐𝑢𝑝𝑎𝑛𝑐𝑦 𝑟𝑎𝑡𝑒 =(1 − 𝑃𝑐)λ ∙ μ 𝑐

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The Erlang-B model gives an indication of the approximate number of beds needed. Nevertheless, the arrival rate (λ) is assumed to be constant and does not incorporate the patterns of the ED found in the previous sections. Therefore, additional analysis is performed to validate the outcomes of the Erlang-B model. Historical data is used to determine the actual blocking rate and actual occupancy rate of the AMU. A simulation is made according to historical data which determines the number of patients present at the AMU at every moment a new patient enters the ED. Three simulations of AMU’s are generated for the various discharge times within 24, 48 and 72 hours. A patient that has a length of stay in the nursing ward of 47 hours will be included in the AMU simulation of 48 and 72 hours but not in the simulation of 24 hours. When this analysis shows similar occupancy and blocked patient rates as the Erlang-B model, we can say that the model is a good indication to determine the number of beds with respect to an AMU.

3.6.5 Flexible AMU

After the analysis of the regular AMU the additional function for this AMU are evaluated. The flexibility of the AMU will be used when the ED is suffering crowding. Therefore, it is important to determine the time duration the ED requires additional capacity. According to the involved emergency physician the peak moments at the ED are usually felt, when there are more than 25 patients in the system. When there are more than 30 patients it is considered to be extremely challenging to assign patients to beds.

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23 According to literature the boarding time of patients decreases for patients admitted to an AMU because the process in the AMU will cooperate closely with the ED. The current boarding time is calculated by the time difference between the moment a request is made for admittance to a nursing ward to actually leaving the ED. A projection of an adjusted WIP is created by a reduced boarding time of 10 minutes to detect the effect on the time duration of crowding (WIP>25 and 30).

With the number of patients present at the AMU when a new patient enters the ED from previous analysis it can be determined how often there is need for additional bed capacity by the ED and the number of beds available by the flexible AMU. Depending on the timeframes of 24, 48 and 72 hours it is determined how often the AMU is able act as a buffer for the ED for different number of beds. According to the studies of Scott et al. (2009) and Reid (2016) the LOS decreased with approximately 25% after implementing an AMU. This reduction of LOS in the ED is incorporated in the simulation for the patients that get admitted to the AMU. When the number of patients present at the ED exceeds the number of beds available in the ED (22), the number of beds that are occupied by AMU patients is determined. With the number of beds occupied at the AMU the probability of having a bed available for a patient from the ED during a crowded period can be determined. Furthermore, with this analysis it can be seen whether additional AMU beds are required to switch form a regular AMU to a flexible AMU.

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4. Results

In this section the results from the case study on flexible AMU’s from an ED perspective in the University Medical Center Groningen are presented. The general characteristics of the dataset are evaluated, and no abnormalities were found regarding these analyses (Appendix A.1). To be able to determine in which way a flexible AMU can be beneficial for the ED the patterns of the ED are evaluated first. The results section will start with analyses of the inflow, outflow, and throughput patterns to provide the inputs for the AMU analysis. Lastly the flexible AMU is investigated with the help of the information from the previous sections.

4.1 Inflow

In this section the patient inflow patterns are presented, mainly focused on the arrival patterns which can be used for the requirement of the flexible AMU. Patients can arrive at the ED in 4 ways: ambulance, helicopter, police or other. From the total dataset 1347 patients (2.7%) are not assigned to any way of arrival and is considered unknown (NULL) and therefore excluded in this specific analysis. Most patients arrive by ambulance and other, the arrivals by helicopter and police are almost negligible (Appendix A.2)

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Figure 3 Average patient arrival pattern per hour (days of the week)

In figure 3 the weekend days show a slightly different pattern. Therefore, the weekend and weekdays days are separated to verify the effect of these days (Appendix A.3). During the weekend, a lower arrival pattern is visible. Nevertheless, the effect of the weekend days on the average of all days is minimal. The pattern remains the same when the weekends are eliminated but the peak lowers with an absolute maximum of 0.5 patient at 17:00. Thus, the weekend and weekdays are not split up for the remaining analysis.

The previous figures are based on averages of the two years but, the variation in reality is rather large which is revealed in the next graphs (figure 4, 5 and 6). The number of patients arriving on one day is on average 68.7 but can vary from 39 (December 28th_{, 2019) to 107 (March 12}th_{, 2018) patients.}

Especially the days with high inflow are of interest for a flexible AMU since it is more likely that the ED is suffering with crowding and the flexible AMU can act as a buffer.

Figure 4 Frequency of occurrence number of patients arriving on one day (24 hours)

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f p at ie n ts Time in hours

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

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26 To get a further understanding of this variability, the number of patients arriving at the emergency department the inflow is split in days of the week (Figure 5) and months (Appendix A.4). All the boxplots in this report show the mean as a ‘x’ and the whiskers extend up from the top of the box (75th

percentile) to the largest data element that is equal or less than 1.5 times the interquartile range. Similarly, down from the bottom of the box (25th_{percentile) to the smallest data element that is}

smaller than 1.5 times the interquartile range. The values that do not fall within these ranges are represented by dots and are considered outliers. The medians (middle line of the box) of the weekdays are relatively similar, the highest median is on Tuesday (76 patients/day) and the lowest median is on Thursday (62 patients/day). Looking at the monthly representation there is a bit more variation however it should be kept in mind that it is only a representation of two years so conclusions on monthly patterns are debatable (Appendix A.4).

Figure 5 Number of patients arriving per day (24 hours) represented by days of the week

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Figure 6 Representation of 8-16 patients arriving in an hour represented over time

In healthcare not only the number of arriving patients is of importance but also the required care that patients need. When the urgency is high more staff and specific equipment is required for these patients which implies less capacity for the other patients. Although from previous literature the triage color did not determine the exact required care, it can give a good prediction of the proportion of patients admitted to the hospital (Martins et al., 2009; Van Der Wulp et al., 2009). In figure 7 the average number of patient arrivals over time is presented with respect to the triage colors. The patients that received triage color NULL did not get any color assigned which is against the hospital policy but are shown in the figure for full representation. It can be concluded that triage color yellow determines the arrival patterns which can be explained by the high number of patients within this triage group.

Figure 7 Average patient arrival rate based on triage colors

0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Fre q u en cy o f o ccura n ce Time in hours 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f p at ie n ts Time in hours

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28 In conclusion, the inflow patterns on average show similar trends with respect to the days of the week. The peak arrival is between 10:00 and 17:00 with approximately 5 patients per hour while the average is 2.68 patients per hour. The averages do not raise concerns regarding crowding however the total number of patients arriving per day vary from 39 to 107 patients. Moreover, the arrivals within a 1-hour timeframe showed that this only occurred between 9:00 and 20:00. This indicates that the likelihood of crowding will be lower outside these timeframes and the flexible AMU might only be needed during the day.

4.2 Outflow

All the patients that entered the system must leave the emergency department as well. In this section a more in-depth representation is given regarding the departure of patients from the ED.

In figure 8 the average departure patterns are plotted per hour of the day for each day of the week. The average departure rate is 2.86 patients per hour which is logically equal to the average arrival rate per hour. The peak of all days is between 14:00 and 23:00 which indicates a delay of 4 hours since the peak arrival is between 10:00 and 17:00. The highest average departure rate is 6.09 patients on Monday around 18:00.

Figure 8 Average departure rate patients for each day of the week

Departure from the ED does not directly imply that the patient can go home, in 40% of the cases the patient is admitted to the nursing wards in the hospital (Appendix A.6). On average 1.12 patients per hour are admitted to the nursing ward in the hospital following the pattern represented in figure 9. The patients admitted to the hospital could be potential users of the flexible AMU when they are

0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f p at ie n ts Time in hours

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29 discharged within 24, 48 or 72 hours from the nursing ward. The peak of patients getting admitted to the nursing wards in the hospital is at 19:00 which is in line with the general peak in departure at the ED between 14:00 and 23:00.

Figure 9 Average patients admitted per hour to hospital nursing wards from the ED

In figure 10 the average number of patient departure over time is presented with respect to the triage colors. The patients that received triage color NULL did not get any color assigned which is against the case study hospital policy but are shown in the figure for full representation. Similar as in the arrival pattern according to triage colors the yellow line represents the biggest group and influences the overall departure pattern most.

Figure 10 Average patient departure rate based on triage colors

0 0.5 1 1.5 2 2.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f p at ie n ts Time in hours 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f p at ie n ts Axis Title

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30 All in all, the output pattern follows approximately the same flow as the inflow patterns with a delay of 4 hours. Forty percent of the patients are admitted to a nursing ward in the hospital after a visit to the ED. This is on average 1.12 patient per hour with a peak similar to the average departure rate of the ED. From this it can be concluded that the outflow pattern from all patients is close to the patients admitted to a nursing ward. For the flexible AMU the patterns of outflow are valuable since this contributes strongly to the throughput of the system.

4.3 Throughput

So far, the arrivals and departure of patients are evaluated. In this section, a closer look is given on what is going on within the system. The input-output diagram is discussed first and then the length of stay (LOS), work in progress (WIP) and room occupancy are evaluated.

In figure 11 the input-output diagram for the ED of the UMCG can be found, including a line for the ‘desired output’. This is the output rate that would occur if the ED is able to keep up with the arrival rate. The desired output is the arrival rate plus the average length of stay which is 198 minutes, roughly 3 hours. From this figure it can be concluded that at the start of the day the ED can keep up with arriving patients. However later in the day the difference between the ideal output rate and the actual output rate increases. Between 12:00 and 18:00 the actual output speed is slower than the ideal speed which causes an increase the length of stay and work in progress, which can result in crowding.

Figure 11 Input- output diagram patients including desired output

The average length of stay of all patients at the ED is 3 hours and 18 minutes. The goal of the case study hospital is to discharge or admit patients to the hospital within a target timeframe of 4 hours. Splitting up the LOS according to triage colors the average length of stay remains between 1:09 and

0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f p at ie n ts Time in hours

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31 3:52 (Appendix A.7). Nevertheless, figure 12 shows that only 69% of all patients leave the ED within the target of 4 hours which is caused by the variation in the system. The patients in this figure are all grouped in length of stay timeslots of 30 minutes, so discharge between 0-30 minutes, 30 minutes-1 hour and 1 hour- 1 hour 30 min etc. A cumulative line chart is depicted on the secondary axis which indicates the percentage of patients discharged within the time indicated. According to literature the LOS for the ED decreases with an AMU which should be examined for the flexible AMU as well.

Figure 12 Length of stay patients grouped in half hour timeslots

The work in progress (WIP) at the ED is determined when a new patient enters the system. It shows the number of patients present in the system. From figure 13 it can be concluded that when a new patient arrives the chance is 50% that there are 13 or less patients are in the system. Furthermore, it is visible that twice (which was on the 12th_{of March 2018) 39 beds were occupied. Although there are}

officially only 22 beds at the emergency department, it is possible that there are more patients in the system since patients leave the ED for extra tests or must go back to the waiting room, while they are still counted as being in the system. During these moments the flexible AMU could be of great potential such that patients do not have to be sent back due to lack of capacity.

0% 20% 40% 60% 80% 100% 120% 0 1000 2000 3000 4000 5000 6000 Cou n t o f p at ie n ts Time in ED

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Figure 13 Work in progress count and cumulative percentage

When the WIP is higher a logical reasoning is that the LOS increases as well and therefore a combined graphical representation is displayed over time in figure 14. On the primary vertical axis, the length of stay is shown and fluctuates between 167 and 212 minutes. The work in progress differs more over time 3.45 to 18.84 patients. Noteworthy is that the LOS line does not increase when the WIP increases. With a scatterplot the trend line shows an increase in LOS of 1 minute and 35 seconds for each added patient, but the correlation is minimal and therefore a more thorough analysis is needed to determine the reliability of this trend (Appendix A.8).

Figure 14 Combination graph LOS and WIP

0% 20% 40% 60% 80% 100% 120% 0 500 1000 1500 2000 2500 3000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Cou n t o f o ccura n ce

Number of beds occupied

0 2 4 6 8 10 12 14 16 18 20 0 50 100 150 200 250 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Av era ge # o f b ed s o ccup ie d LOS in min u tes Time in hours

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33 Not all the rooms in the hospital are similar. Some rooms have specific equipment. An overview with all the different rooms and translations from Dutch to English can be found in appendix A.9. In figure 15 the utilization of each room is displayed where rooms K1-K4 are all occupied for more than 60% of the time which can partly be explained due to the average LOS in these rooms. The time that a patient spends in rooms K1-K4 is approximately 2 hours and 45 minutes and slightly higher than all the other rooms (figure 16). The flexible AMU could offer optimal buffer capacity by having the right type of rooms that are needed by the ED during crowding.

0% 10% 20% 30% 40% 50% 60% 70% K2 K1 K3 BUIT EN S EH K4 K5 _K12 K6 W A CH T O P KA ME R _K7 K10 K11 K8 REA _OBS1 O B S5 O B S4 O B S2 O B S3 K9 IS O LA TI E1 TR IA G E _S1 K9A CT G A N G 1 _S2 G A N G 2 PO LI GIPS KA ME R KIN DE R W A CH TKA ME R G A N G 3 FA MIL IE G A N G 4 W A CH TKA ME R K14 R A MP G A N G 5 G A N G 6 0:00:00 0:28:48 0:57:36 1:26:24 1:55:12 2:24:00 2:52:48 3:21:36 K2 K1 K3 BUIT EN S EH K4 K5 _K12 K6 W A CH T O P KA ME R _K7 K10 K11 K8 REA O B S1 O B S5 O B S4 O B S2 O B S3 K9 IS O LA TI E1 TR IA G E _S1 K9A CT G A N G 1 _S2 G A N G 2 PO LI GIPS KA ME R KIN DE R W A CH TKA ME R G A N G 3 FA MIL IE G A N G 4 W A CH TKA ME R K14 R A MP G A N G 5 G A N G 6

Figure 16 Utilization of ED-rooms

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34 Changing a patient from one room to another is time consuming. In healthcare some transportations are essential due to the patients’ needs but more in-depth analysis is needed to detect ineffective changes. Most patients are changed 0-4 times when they visit the ED but in rare cases it can occur that a patient is changed up to 11 times (figure 17). Examples of these frequent changes can be found in appendix A.10. Some of these are logical and explainable while others are more remarkable. ‘Waiting for room’ is noticeable for both patient example 1 and 3 while patient 2 is a patient that is changing rooms due to his needs.

Figure 17 Number of times ED-room changes

In conclusion, the inflow-outflow indicated that the outflow cannot keep up with the inflow later in the day. This results in more patients in the system so an increased WIP, however the LOS is not influenced by the WIP. The flexible AMU can be of advantage when there is a high WIP since extra capacity is needed. The type of rooms in a flexible AMU need to be determined in collaboration with the ED such that the right rooms are available during crowding. Lastly the number of room changes could decrease with a flexible AMU since it will be less likely to be sent back to the waiting room due to additional capacity during crowding.

4.4 Acute Medical Unit

In this section the historical data is used approximate the number of beds required and to simulate an acute medical unit for the academic hospital UMCG. The focus is on the bed capacity in the AMU by potential patients with discharge times within 24, 48 or 72 hours.

In total 20.025 patients are admitted to the nursing wards in the hospital after a visit to the ED. With an average length of stay of 7.5 days an AMU with a maximum stay of 24, 48 or 72 hours might not sound beneficial. However, the distribution of the length of stay in the nursing wards is highly dispersed

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 0 1 2 3 4 5 6 7 8 9 10 11 12 cou n t o f o ccura n ce

Number of room changes

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35 and 3.449 patients are discharged within a timeframe of 24 hours which accounts for 17% of all admitted patients. Another 2799 patients are discharged from the nursing ward after admittance through the ED in 24 to 48 hours. Lastly, 42% of the patients (8377) are discharged within 72 hours after admittance by the ED (figure 18). These patient groups are potential users of the AMU and will therefore be further evaluated.

Figure 18 Cumulative chart of patients discharged from nursing ward

Currently all patients are admitted to specific nursing wards for the required care. Similar care should be offered at an AMU therefore the specialisms for the various potential user groups are explored. Looking at the type of specialism cardiology and neurology clearly prevail over the other specialisms (see appendix A.1 for list of specialisms). Some specialisms such as abdominal (CHI-A) are present in the top 10 for all admitted patients but not in the discharge timeframes of 24/48/72 hours (figure 19-22). A top 10 is constructed because for 70% of the patients the specialism is included in one of these groups. For an acute medical unit, it is important to have support from the departments that deal with the specialisms where most patients would be admitted to. From the total patients discharged within 24 hours 74% is linked to this top 10. For 48 hours this is 72% and 71% for discharged within 72 hours. In appendix A.11 a combination graph is included to see the differences between the various discharge times. Depending on the discharge time that is set by the hospital for the AMU the specialisms can be determined but for all discharge time the cardiology and neurology are far outreaching.

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36 The historical data is used to determine whether the patient would be admitted to the AMU however the physicians need to decide this based on predictions if the patient will be discharged within the given timeframe. According to literature older patients tend to visit the ED more often than younger patients (Samaras et al., 2010).To determine if this hold for the AMU as well, the ages of patients are depicted on the horizontal axis and the percentage with this age in the specific groups on the vertical axis in figure 23. The age of patients that are admitted and discharged within 24, 48 or 72 hours follow approximately the same pattern. The biggest peak starts around 50 years and ends around 80 years. There is one remarkable peak in figure 23 which is the peak of all patients and all admitted patients for the age group 18 to 27. From this it can be concluded that there are more patients in this age group that are admitted to the nursing wards for a longer duration and are therefore less likely to be of interest for the AMU.

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00%

Figure 20 Specialisms all admitted patients Figure 21 Specialisms discharge time within 24 hours

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Figure 23 Percentage of patients in age groups according to discharge 24, 48, 72 hours

From the input and output section the triage color yellow was mainly determining the daily patterns. Therefore, the triage color and the groups of admittance are evaluated to indicate which group is most likely to be present in the AMU. Figure 24 shows the percentages of each triage color according to the discharge time of the nursing ward. The potential users of the AMU (discharge times within 24, 48 and 72 hours) show almost similar percentages. However, the percentages of green and blue triage colors are lower for potential AMU patients compared to all admitted patients. From this it can be concluded that patients triaged with green or blue and admitted to the hospital are more likely to have a LOS in the nursing ward of more than 72 hours. Whereas for the orange triage color it is more likely to have a LOS shorter than 72 hours. Nevertheless, it cannot be concluded that there is one particular triage group more important for the AMU than the other.

Figure 24 triage colors based on admitted patients from the ED

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 0 3 6 9 ₁₂ ₁₅ ₁₈ ₂₁ ₂₄ ₂₇ ₃₀ ₃₃ ₃₆ ₃₉ ₄₂ ₄₅ ₄₈ ₅₁ ₅₄ ₅₇ ₆₀ ₆₃ ₆₆ ₆₉ ₇₂ ₇₅ ₇₈ ₈₁ ₈₄ ₈₇ ₉₀ ₉₃ ₉₆ ₉₉

24 hours 48 hours 72 hours all patients all admitted patients

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38 The first indication of the number of beds required in the AMU is calculated with the help of the Erlang loss (or M/G/c/c) model. To be able to execute this analysis the dataset is split up in patients admitted to a nursing ward and discharged within 24, 48 and 72 hours. The patients that fall into the group within 24 hours will also fall in the groups discharge within 48 and 72. For these three groups the interarrival times are determined by subtracting the arrival time of a patient from the time of arrival of the successive patient. From the figures in appendix A.11 it can be concluded that the interarrival times are approximately negatively exponential distributed. According to the patients in the groups the average LOS is calculated which is respectively 831/1467/2038 minutes (13/24/33 hours). The average demand is calculated per month over the timeframe of 2 years. The average demand for each timeframe is respectively: 144, 260 and 350 patients per month. Table 1 represents the required number of beds and occupancy rate with input parameters: average LOS, average demand and the fraction of patients blocked for each group. The number of beds is rounded to a full number which gives the first value of a patient blocked being lower or equal to the blocking rate. The Erlang-B calculator by Koole and Bekker (2013) has been used after performing part of the analysis in Excel to check the accuracy of the automatic calculator and to be sure of the correct understanding the calculations. From table 1 it can be concluded that the number of beds increases more than proportionally with a reduction of the rejection rate.

Table 1 Number of beds according to discharge rate and blocked patients

Discharged <24 hours Discharged<48 hours Discharged <72hours Patients blocked Beds Occupancy rate Beds Occupancy rate Beds Occupancy rate 1% 8 34% 16 54% 26 62% 5% 6 44% 13 64% 22 71% 10% 5 50% 12 67% 19 78% 15% 5 50% 11 71% 17 81% 20% 4 56% 10 74% 16 83%

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39 the model gives limited insight in the number of beds required for the AMU. This can be a result of the patterns that are presented earlier in this result section, the Erlang-B model cannot account for peaks in the arrivals.

Table 2 Erlang-B and actual number of blocked patients

Discharged <24 hours Discharged <48 hours Discharged <72 hours

Beds Patients blocked Erlang-B Patients blocked actual Beds Patients blocked Erlang-B Patients blocked actual Beds Patients blocked Erlang-B Patients blocked actual 8 1% 2% 16 1% 4% 26 1% 6% 6 4% 10% 13 5% 15% 22 4% 16% 5 9% 18% 12 7% 20% 19 9% 27% 5 9% 18% 11 11% 26% 17 15% 35% 4 18% 30% 10 16% 33% 16 18% 39%

Besides the blocked patients the actual occupancy rate for the number of beds proposed according the Erlang-B model are calculated with historical data (table 3). The occupancy rate is calculated by summing the LOS of all patients that are admitted to the simulated AMU and divided by the total hours available. The total hours available depends on the number of beds in use. For example, if there are 8 beds in the AMU the total available hours is 8 times the total duration of the dataset (17520 hours/2 years). The blocked patients are not considered in the occupancy rate because they did not enter the simulated AMU. The actual occupancy rate is for all the discharge times lower than predicted with the Erlang-B model. For the lower discharge times the occupancy rate is still relatively similar. However, for the higher discharge time of 72 hours the Erlang-B model did not give a good indication for the occupancy rate. The discharge timeframe within 48 hours gives the highest occupancy rate for the AMU according to historical data while the Erlang-B model gives higher occupancy rates for discharge within 72 hours. The lower occupancy rates can partly be explained by the higher number of blocked patients. The patients that are blocked do not enter the AMU system and are therefore not counted in the occupancy rate either. Therefore, higher blocking rate lower occupancy rate.

Table 3 Erlang-B and actual occupancy rate

Discharged <24 hours Discharged <48 hours Discharged <72 hours

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40 All in all, the acute medical unit is of interest for patients admitted to the nursing ward and discharged within 24, 48 or 72 hours. Respectively for the UMCG this is 17%, 31%, 42% of all patients admitted to a nursing ward. In all these groups the specialisms cardiology and neurology were prevailing which are the specialism that must be present in an AMU. Historical data is used to regulate the patients however the physicians need to decide this based on predictions. Although literature mentioned that the age and triage colors can assist in forecasting the length of stay this could not be confirmed according to this historical dataset. Lastly the Erlang-B model cannot be used for the exact number of beds since it does not account for the flow patterns and outliers present.

4.5 Flexible Acute Medical Unit

In this section all previous mentioned results are combined to see in which way a flexible acute medical unit could assist the ED during crowding. The focus will be on the previous simulated AMU and the timeframes additional capacity is needed by the ED.

The flexibility of the AMU is most likely needed when the bed capacity at the ED is at its peaks. Therefore, analysis is done when the WIP of the ED is higher than 25 and 30 beds, since this is when additional capacity is needed according to the emergency physician involved. From the previous sections it became clear that there are days that 107 patients arrive, and on these days the WIP was also at its maximum (39). These specific days can influence the WIP plots due to continuously high WIP. Therefore, the duration of the high WIP levels is analyzed. Furthermore, for the flexible AMU it is useful to know how long additional capacity is requested by the ED. The average duration of 30 or more patients in the system is 38 minutes which occurs 72 times while the number of times 30 or more patients are

in the system is 372. This indicates that when the WIP is above 30 this holds for 5 patients before it is below the 30 patients again. Similarly, for 25 or more patients the average is 51 minutes which occurs 409 times while the number of times the WIP is higher than 25 is 2524. From this it can be concluded that at times of crowding it can take time before the system is below the level of 30 or 25 again. A closer look at the boxplot, in figure 25, shows a maximum duration of a work in progress above 30 is 4 hours and 37 minutes and for 25 or more beds it is 7 hours and 14 minutes, but these are the outliers.

“Plan the unexpected and remain flexible” Acute Medical Unit offers capacity during crowding at the Emergency Department

UNIVERSITY OF GRONINGEN & NEWCASTLE UNIVERSITY