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The more patients in the morning, the more patience in the afternoon:

An Emergency Department Case Study

July 16, 2017

Author:

C.F. Mulder Student number: S2524279 E-mail: carien.mulder@gmail.com

Supervisors:

Dr. M.J. Land

Prof. Dr. J.T. van der Vaart

Acknowledgement: I thank Ewoud ter Avest, emergency physician at Medical Centre Leeuwarden,

for providing me access to the data of the emergency department and for his help and cooperation

throughout the project.

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Contents

Abstract 2

1 Introduction 3

2 Theoretical background 5

2.1 Emergency departments . . . . 5

2.1.1 Triage . . . . 5

2.2 Performance measures . . . . 5

2.3 What influences lengths of stay? . . . . 6

2.4 Conclusion . . . . 7

3 Methodology 8 3.1 The emergency department of the Medical Centre Leeuwarden . . . . 8

3.2 Data . . . . 9

3.3 Data analysis . . . . 10

3.3.1 Day classification . . . . 10

3.3.2 Analysis . . . . 12

3.4 Conclusion . . . . 13

4 Results 14 4.1 Results of classifications based on total number of patients . . . . 14

4.1.1 Dynamics in arrival and departure rates . . . . 16

4.1.2 Length of stay, number of arrivals and work in progress . . . . 17

4.1.3 Comparison between classifications . . . . 19

4.1.4 Length of stay over 4 hours . . . . 23

4.2 Main specialities - surgery, cardiology, internal medicine . . . . 24

4.2.1 Comparison between classifications . . . . 27

5 Discussion 29 5.1 High Mornings but different afternoons . . . . 29

5.2 High Afternoons but different mornings . . . . 29

5.3 Low Mornings but different afternoons . . . . 29

5.4 Low Afternoons but different mornings . . . . 30

6 Conclusion 31 References 33 Appendix 36 Classification based on entire dataset (all specialities) . . . . 36

Classification based on number of patients for surgery . . . . 43

Classification based on number of patients for cardiology . . . . 45

Classification based on number of patients for internal medicine . . . . 47

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Abstract

A growing problem in emergency care is that of overcrowding, which goes hand in hand with

long stays for patients. A single case study on the emergency department of the Medical Centre

Leeuwarden has been performed in order to analyse how the dynamics in the number of patients

influence the lengths of stay of patients throughout the day. It is known, that an increasing number

of patients in the emergency department causes longer stays. In this study it is found that a busy

emergency department can also increase the number of patients later on in the day, causing the

patients arriving then to be affected as well. The length of stay of patients arriving during the

afternoon is longer when there has been a busy morning compared to a non-busy morning. If the

emergency department is able to increase its productivity during the morning, hereby reducing the

length of stay of patients arriving then, the rest of the day will be less busy. This will then reduce

the average length of stay of patients in the emergency department throughout the entire day. Out

of the three most common specialities, cardiology patients are the least influenced by increases

in the number of patients. The other two specialities, cardiology and internal medicine, can also

benefit from an increased productivity during the morning.

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1 Introduction

With an increasing numbers of patients, overcrowding is a major issue in emergency departments (ED) all over the world. Overcrowding can result in longer waiting times and in extreme cases EDs will no longer accept patients with less severe injuries. The consequences of this are diverse:

patients’ satisfaction decreases as their pain and suffering increases but the injuries might also worsen and medical errors and poor outcomes are more likely, which results in higher mortality rates (Derlet and Richards (2000); Trzeciak and Rivers (2003); Pines and Hollander (2008); Pines and Abualenain (2013)). Countless researchers have investigated this problem and tried to find solutions. This research will focus on the development of the number of visitors in the ED over the day and how this affects the length of stay of patients.

Overcrowding in EDs is an extensively researched problem. Some research has already been performed on the possible sources of extensive throughput times, focusing on the characteristics of the treatment and organisation of the ED. Chan et al. (1997) regressed multiple variables on the throughput time and found significant, but small, impacts for the “main emergency department census (which is the total number of patients in the ED), number of admissions, ambulance arrivals, and paediatric volume”. However, these variables were found to explain only a small part of the variation. Yoon et al. (2003) investigated the length of stay (LOS) for different processes, response times and specialities, where “triage level, investigations and consultations (. . . ) [were found to be] important independent variables that influence ED LOS”. Where Rathlev et al. (2007) have found that the LOS of patients is related to the occupancy of the staffed beds, occupancy has also been considered irrespective of the level of staff (Forster et al. (2003), Dunn (2003). Several studies (Asplin et al. (2003); Derlet and Richards (2000); Bucheli and Martina (2004); Hoot and Aronsky (2008)) have proven that staff levels do positively affect patients’ LOS.

In these studies, the factors have been considered relative to the LOS of the patients arriving in the same period and with those characteristics. As doctors and nurses treat multiple patients at the same time, the lengths of stay of the patients are also affected by the circumstances of the entire ED. Buitelaar (2016) argued that a longer LOS for patients arriving in the morning results in a longer LOS for those arriving in the afternoon because the non-urgent patients that came in during a very busy period will have to wait and thus increase the number of patients in the afternoon. A busy period need not be the only reason for longer lengths of stay. On a quiet day, staff might take more time to treat each patient than when they would if they had more patients to treat. These patients being present in the ED for a longer time might cause larger problems when the arrivals increase later on in the day. The total number of patients then builds up even more and thus might result in a longer LOS then necessary.

The aim of this research is to find out how the development of the number of patients present

in the ED influences the LOS of patients arriving at different times of the day. Patients arriving

during busy mornings or afternoons can be expected to have a longer stay than others due to

increased waiting times. It will be investigated if, in addition to that, the circumstances earlier on

in the day (e.g. in the morning) have an impact on the LOS of patients arriving later on in the day

(e.g. in the afternoon). If this is found to be the case it is worth considering to increase responsive-

ness in certain situations. The reason for this being that Van Achteren (2014) and Koomen (2015)

suggested that a higher responsiveness of staff positively influences the waiting times later in the day.

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This study will focus on a single case, namely that of the ED of the Medical Centre Leeuwarden.

The research question that will be answered in this thesis is:

How do busy mornings and afternoons affect the length of stay of patients arriving throughout the day in the emergency department of the Medical Centre Leeuwarden?

With findings of this research, the Medical Centre Leeuwarden will have more insight into when and how to avoid long lengths of stay and a high work in progress (WIP). Once the WIP has built up, it is more likely that the consequences will have to be suffered. While, if the ED adapts to an upcoming situation at an early stage, it will be easier to avoid the problems all together.

This paper is structured as follows. Section 2 will elaborate on the theoretical background of

the problem and all aspects involved. The proposed method and the results obtained for the ret-

rospective case study will be discussed in Sections 3 and 4, respectively. This thesis will end with

a Discussion (Section 5) and a Conclusion (Section 6).

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2 Theoretical background

2.1 Emergency departments

Emergency departments are open 24 hours a day to treat patients with diverse medical needs. The care delivered by an ED can be divided in emergency care, unscheduled urgent care and safety net care (Asplin et al. (2003)). Patients either arrive in an ambulance or travel there by themselves (Lane et al. (2000)). The latter group of people is either send by the general practitioner or a clinic in the hospital or comes at their own initiative (Thijssen et al. (2012)). The patients of the first group are most often taken to the ED for stabilization, triage and internal diagnostic evaluation.

Patients follow different pathways, mainly depending on their ailment and triage level (Lane et al. (2000)). At arrival, this triage level is determined based on the complications of the patient and their medical history, after that the patient is registered. In order of level of urgency as well as arrival time, the patients are seen by a nurse to take the pulse, blood pressure and other measurements. This nurse also performs the first examination of the patient: draw blood, check the test results and take x-rays (Ganguly et al. (2014)). Physicians of different skill levels and specialities treat the patient, directly and indirectly. These doctors determine when the patient leaves the emergency department, and whether he/she is discharged or is admitted to the hospital (Lane et al. (2000)).

2.1.1 Triage

Around 2008, a national triage system (NTS – Nederlands Triage Systeem) was introduced which is now used by ED nurses, GP’s and control rooms of the ambulatory services all over The Netherlands (http://de-nts.nl/starten-met-nts/wat-is-nts/). The NTS makes use of five urgency levels to rate the complaint (Huibers et al. (2009)):

- U0. One or more vital functions are impaired: Requiring immediate resuscitation;

- U1. Life threatening: Immediate action required;

- U2. Emergent: Take action as soon as possible;

- U3. Urgent: Treat within a few hours;

- U4. Non-urgent: Time should be discussed with the patient;

- U5. Advice: Examination can wait till the next day.

The U0-level is specifically important for EDs and ambulance care. The urgency level is determined by the triage nurse by selecting the options relevant to the patient out of 56 predefined problems and 4950 triage criteria.

2.2 Performance measures

In order to be able to evaluate the performance of the emergency department, performance mea-

sures are needed. The most commonly used performance measure for emergency departments is

the Length of Stay (LOS), measuring the total time a patient spends in the emergency depart-

ment, including the time in the waiting area. This can be divided in multiple time intervals by

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distinguishing different milestones in the process, for instance arrival time, start of treatment, end of treatment, duration of provider contact, time of data-ready, decision and departure time (Welch et al. (2011)). Depending on the number of registration points in the process, the LOS can be separated into more or less intervals.

Other performance measures discussed by Welch et al. (2011) concern the ED diversion and the overcapacity. The latter is an indication that there are more patients than staffed beds available, resulting in patients waiting. ED diversion is a consequence of this, in extreme cases it is communi- cated that only in extreme emergencies patients are accepted into the ED. Both of these measures are related to overcrowding.

Measuring performance in terms of cost or satisfaction is more difficult. Where direct costs such as staff and resources can easily be measured, there are also indirect costs such as delayed ser- vices with all of its consequences (Ganguly et al. (2014)). Patient satisfaction is a more subjective performance measure. This is not only affected by the total length of their stay, the quality of the care and the service has a much bigger influence (Bucheli and Martina (2004)). A more concrete measure for this is the rate of complaints of patients (Welch et al. (2011)).

In this research, the length of stay of patients is used to evaluate the performance of the emer- gency department as this is most directly observed and experienced by the patients. Furthermore, the other measures are related to the LOS and are thus also improved if the LOS is reduced.

2.3 What influences lengths of stay?

The length of stay of emergency department patients is affected by factors concerning the input, output and throughput (Hoot and Aronsky (2008)). A very straightforward relation is that between the total demand, so the number of patients arriving, and the total waiting time, and thus LOS, of patients (Lane et al. (2000)). The more people come in, the more patients the doctors have to treat and the longer patients have to wait for their turn. The number of patients being brought in by an ambulance and the number of young (paediatric) patients also significantly and positively influences the throughput time of patients averaged over the day (Chan et al. (1997)). Moy et al.

(2016) investigated the mean and median LOS for patients with different conditions and found that this also differed between dispositions, so whether the patient was admitted in the hospital, taken to another institution or was discharged.

Furthermore, the length of stay of the patient differs based on the kind of treatment provided,

where the treatment a patient receives is dependent on the ailment of the patient. By regressing

the use of specific processes on the LOS, Yoon et al. (2003) found that ultrasound imaging, labo-

ratory testing and consultation by certain speciality services increase the LOS. The results of Van

Der Vaart et al. (2011) agree with these last two relations; the number of laboratory requests and

the speciality required influence the LOS. Also Koks et al. (2013) found that internists, who treat

the most patients next to the emergency physicians, take more time to do so. Other conclusions

drawn by Van Der Vaart et al. (2011) concerning the staff involved in a treatment is that different

lengths of waiting time and processing time are experienced with different staff members. The

waiting time for doctors was found to be longer than for nurses, and the more experienced the

doctor is, the shorter the processing time.

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Moreover, the LOS of patients is also affected by output factors, such as the disposition. One of these is the number of admissions to the hospital from the ED, which results in a longer LOS (Chan et al. (1997); Lucas et al. (2009); Rathlev et al. (2007)). Patients that will be admitted in the hospital often have to wait for a bed and staff to be available in the respective department, increasing their length of stay in the ED. Following from this is that the availability of hospital beds is a commonly studied factor among researches concerned with the causes of overcrowding (Hoot and Aronsky (2008)). For instance, (Lane et al. (2000)) found that regardless of the number of beds in the hospital, the occupancy is equal, resulting in comparable waiting times. The occupancy of the hospital is flexible in this respect because elective surgeries can be cancelled. Both hospital occupancy (Lane et al. (2000)) and the number of elective surgical admissions are significantly related to the LOS (Rathlev et al. (2007)). It should be noted that Lucas et al. (2009), however, couldn’t confirm these relations.

Furthermore, contradicting statements are made regarding the difference in LOS between triage levels. Data of the ED of a Canadian teaching hospital showed that the most and least urgent pa- tients (triage levels 1 and 5) have the shortest stay, whereas triage level 3 has the longest LOS (Yoon et al. (2003)). The explanation given for this is that patients with the latter triage level, often have the most vague complications which needs intensive investigation. Physicians might then choose to first quickly help a patient with an obvious diagnosis. When assuming that physicians strictly work with the prioritization rule to help patients in order of urgency, the average LOS will be similar for all triage levels (Van Der Vaart et al. (2011)).

2.4 Conclusion

Most of the researches so far have focussed on the relation between the LOS of a patient and the characteristics of the ED at the time of his/her arrival. Based on this, one would expect the stay of patients arriving at a busy moment to be longer than of those arriving at a quiet moment. However, as these longer stays lead to more patients being in the ED later on, the work in progress (WIP) throughout the day can be related. Furthermore, the productivity of staff appears to differ among staff members and time periods, so it can be correlated to the circumstances on different moments of the day.

This study investigates how the number of patients in the ED affects the LOS of all patients

arriving throughout the day, and more specifically, later on in the day. In that way the effect over

time is considered. Of all performance measures discussed, this research solely makes use of the

LOS as explained above.

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3 Methodology

The purpose of this study is to assess the consequences of a high number of visiting patients at certain moments on the length of stay of patients arriving at any time of the day. This is done by means of a case study performed on the emergency department of the Medical Centre Leeuwarden.

In this emergency department, it occurs frequently that ambulances are waiting in line and that doors are closed for patients with an urgency level of two or higher due to overcrowding. Further- more, long lengths of stay are not rare. The first part of this methodology section discusses the ED under investigation, followed by a description of the data that is made use of. After that, the applied method is discussed.

3.1 The emergency department of the Medical Centre Leeuwarden

Medical Centre Leeuwarden (MCL) is a large teaching hospital in the north of The Netherlands.

The current ED of MCL contains 16 treatment rooms and one triage room. A new ED, which will be the largest of northern Netherlands, is being build and scheduled to open in October 2017. A short description of the current situation and procedures follows.

Patients can either present themselves (self-referrals), or be presented after consultation of their primary care physician. Furthermore, patients can be brought in by the emergency medical service, either by ambulance or by helicopter. If a patient comes in on their own initiative, it announces its arrival at the reception desk, where its demographic data is registered. Thereafter, the patient is seen by a triage nurse as soon as possible. Patients sent in by their general practitioner already received a triage level, but this is reassessed by the emergency department triage nurse. Depending on the urgency level assigned by the nurse and the urgency levels of the other patients still wait- ing, the patient is asked to wait for treatment in the waiting room or is immediately placed in a treatment room.

Once it is the patient’s turn, they are moved to a treatment room and seen by a nurse and a doctor. Doctor staffing consists of emergency physicians (in training) and residents of a specific speciality. At all times, at least one emergency physician is present in the ED. Their primary task is to treat patients with unstable vital functions. However, they are educated in all specialities, so they also treat other patients if they are available. During day-time, emergency residents work alongside and are supervised by the ED physicians. Also for many specialities, including inter- nal medicine, geriatrics, cardiology, neurology, surgery, orthopaedic surgery and plastic surgery at least one residents is available to see patients in the ED. These residents are being supervised by a physician of the respective specialities whom they contact, mostly via telephone, for advice and approval. These supervisors are not present in the ED, nor do they treat patients in the ED. For some specialities, the residents are not necessarily present in the emergency department but are called in when they are needed. For the most common specialities, a resident is physically present in the ED at all times. Regardless of whether a resident is in training for a specific speciality (AIOS) or not (ANIOS) they do the same things. It might occur that an extra doctor is called away from their department to the ED when it is extremely busy.

In the treatment of patients, the ED and its staff often rely on staff of other departments. The

ED can make use of multiple types of radiology tests, X-rays, CT-scans and MRI-scans, of which

only the X-rays can be done within the ED itself. Furthermore, blood that is drawn is send to the

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laboratory for testing. The supervisors of the speciality residents work at their own departments and are to be called by the residents. Further, physicians can request a consult of another specialist, who then visits the patient in the ED.

3.2 Data

In order to analyse the processes at the ED of the MCL, data was provided by MCL. In April of 2016, the MCL completed the change to a new software package, called EPIC, which contains all the information regarding the patients and their care. When patients visit the ED, their pres- ence and status are registered. At different moments of their treatment, the system is updated.

Unfortunately, only the arrival time and departure time were found to be reliable. Many data points of events that took place within the ED, such as triage and radiology tests, were found to be incomplete or inconsistent. Therefore, only the total stay of the patients is considered, without any knowledge on the time spend waiting and the time spend being treated. Although the timing or frequency of radiology tests cannot be used, whether the treatment of a specific patient required such a test is considered. Data on the consults is not available and can thus not be considered at all.

The database also includes information on some additional characteristics of the patients, of which the triage level, indicating the urgency of the patient, and the specialities they are signed up for, are used. For a small fraction of the patients, less than 5%, the triage level has not been registered, but this is not expected to affect the results of this study.

The data used spans half a year, from the first of July 2016 till the 31st of December 2016.

To correct for patients that were in the ED at midnight at the beginning or end of this period, a dataset that started one day earlier and ended one day later was requested from and provided by the MCL. To make sure the dataset used is as homogeneous as possible, the patients arriving on weekend days have not been taken into account in this analysis. After all, due to a lower number of visitors in the weekends, staff levels are also lower then.

Table 1: Descriptive statistics of data of the ED of MCL, from 01-07-2016 till 31-12-2016 All Surgery Cardiology Internal Medicine

Number of patients 5330 1490 989 837

Number of patients with radiology request 3196 (60%) 781 (52%) 416 (42%) 457 (55%) Number of patients with triage level 0 15 (0.3%) 1 (0.1%) 7 (0.7%) 0(0.3%) Number of patients with triage level 1 641 (12%) 58 (4%) 245 (25%) 67 (8%) Number of patients with triage level 2 1977 (37%) 359 (24%) 433 (44%) 332 (40%) Number of patients with triage level 3 1655 (31%) 659 (44%) 216 (22%) 288 (34%) Number of patients with triage level 4 202 (4%) 104 (7%) 9 (1%) 23 (3%) Number of patients with triage level 5 568 (11%) 235 (16%) 37 (4%) 86 (10%) Note: The percentages indicate the number relative to the total number of patients with the respective speciality.

As the triage levels of some patients were not registered, these numbers do not add up to 100%.

Source: Data provided by the Medical Centre Leeuwarden

Table 1 displays some descriptive statistics of the dataset. The three main specialities take

up more than 60% of the entire dataset, and are therefore studied more intensively. More than

half of all patients, surgery patients and internal medicine patients undergo a radiology test. For

cardiology patients, this is less than half. Another aspect that makes the cardiology patients stand

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out is the distribution of their triage levels compared to that of the others. Out of the 989 patients, 252 patients are triaged as highly urgent (triage level 0 and 1), which is relatively many. These patients need to be treated as soon as possible and are thus more likely to have a shorter stay in the ED.

Figure 1 shows the distribution of the LOS of all patients, in total and for the three main specialities. On average, patients have a stay close to three hours. Indeed, the average LOS of cardiology patients is shorter than the average of all patients. Apart from the fact that these patients are often more urgent, the range of afflictions that patients have that require a cardiologist is limited and the treatment of the most common is often protocolized which also reduces the LOS (according to an ED-physician of MCL). The average LOS of surgery patients is also shorter than that of the entire dataset, but the distribution is more spread out. The LOS thus differs more among patients. Furthermore, internal medicine patients have an average LOS that is relatively long (which was also found in the research of Koks et al. (2013)) with less deviation.

Figure 1: Distribution of the length of stay of patients arriving in the emergency department of the Medical Centre Leeuwarden between 01-07-2016 and 31-12-2016

3.3 Data analysis

Similar to Buitelaar (2016), all days in the studied semester receive a classification based on the number of visitors in the morning and in the afternoon. The next subsections elaborates on how this is done and how the differences between the classifications are investigated.

3.3.1 Day classification

The days are classified in four categories based on the number of visitors, more commonly referred

to as the WIP, in two distinguished time periods. The number of visitors in the morning and

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afternoon is compared to the median number of visitors in that time period, resulting in the four classifications shown in Table 2. Days where the morning and afternoon are ’busy’, are classified as having a High Morning High Afternoon (HMHA), whereas non-busy days are classified as Low Morning Low Afternoon (LMLA). Days where either the morning or the afternoon are busier than average are named HMLA (High Morning Low Afternoon) and LMHA (Low Morning High Afternoon), respectively.

Table 2: Classification of days

Afternoon

#visitors > median #visitors ≤ median

Morning #visitors > median HMHA HMLA

#visitors ≤ median LMHA LMLA

Notes: HMHA = High Morning High Afternoon, HMLA = High Morning Low Afternoon, LMHA = Low Morning High Afternoon, LMLA = Low Morning Low Afternoon

Note that the number of visitors in an hour is not equal to the number of arrivals, as it is the number of distinct patients that were present in the ED in that hour. Hence, a patient arriving at 10:15 AM and staying for 2 hours, is thus seen as a visitor of the 11th, the 12th as well as the 13th hour of that day. The reason for basing the classification on the number of visitors and not on the number of arrivals is that the WIP has a bigger effect on the LOS of patients than the number of arrivals has. Patients have to wait for any patient that is in the ED at the same time and that is prioritized. Patients that already arrived earlier but are still in the ED can thus also lead to a longer stay for the other patients.

Figure 2: Minimum, average and maximum number of visitors over time, emergency department

of the Medical Centre Leeuwarden from 01-07-2016 till 31-12-2016

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Which hours to be seen as the morning and as the afternoon is determined based on the devel- opment of the number of visitors over the day. Figure 2 shows the minimum, average and maximum number of visitors for each hour of the day. The x-coordinates of the measurements are exactly in the middle of the hour they represent, so between noon and 1 PM the maximum number of visitors has been 24 which is plotted at 12:30. The figure shows that although the number of visitors al- ready starts rising at 7 AM, the increase in maximum number of visitors becomes more significant from 10 AM on. The average number of visitors is almost constant between 1 PM and 6 PM, after which it decreases till 7 AM the next morning.

For easier comparison, time slots of equal length have been chosen. The first time period lasts from 10 AM to 1 PM and is referred to as the ‘morning’. The second time slot, referred to as the

‘afternoon’ lasts the last three hours of the day shift, so from 3 PM to 6 PM. In this way the effect of the transfer from day shift to night shift is included, which is expected to influence the LOS of patients.

The median number of visitors in the morning is 14 and in the afternoon 19. This results in, respectively, 44, 21, 16 and 50 days classified as HMHA, HMLA, LMHA and LMLA. Days where both the morning and the afternoon are either busy (HMHA) or not busy (LMLA) occur more often than days with either a busy morning (HMLA) or busy afternoon (LMLA). Apparently, the morning and afternoon are often alike in terms of number of visitors.

3.3.2 Analysis

Since the goal of this research is to find how the number of patients affects the length of stay of patients, heterogeneity in terms other than the number of visitors should be ruled out within each of the classifications. The classifications are tested in multiple ways. However, it should be noted that there might be other aspects that are not considered and could affect the LOS. First of all, the distribution of specialities within the classifications is tested. This is done because of earlier findings (Figure 1), that the distribution and mean of the LOS differs among specialities. Next, the classifications are compared based on the distribution of urgency levels, radiology requests, the means of arrival, number of paediatric patients, disposition.

Once significant differences have been ruled out, the classifications are investigated by means of throughput diagrams. These diagrams show how the number of arrivals and the number of departures develop over the day for each of the four classifications. The diagrams are created based on the average number of arrivals and departures on days with the respective classification.

Such a diagram also provides insight into the work in progress at each time, which is the vertical distance between the two lines, and the length of stay of the patients, which is the horizontal dis- tance between the two lines. By showing how these four aspects develop over time, it is possible to understand what defines each of the classifications and what causes the morning/afternoon to be more/less heavily visited. A high number of visitors can either be caused by a high number of arrivals in that period, or by a high number of patients still being in the ED at the start of the period. The latter can then be a result of an increased number of arrivals just before the period, or because the patients arriving in the preceding hours are still in the ED due to a long length of stay. If the LOS of patients is found to differ between the classifications, it is important to know what then caused these differences.

After that, the LOS of patients in each of the classifications is studied in more detail, where the

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average LOS is determined using the throughput diagrams. The average LOS of patients is first plotted for each of the classifications. Two versions of this plot are created, one also showing the average number of patients arriving per hour, the other showing the average maximum WIP per hour. Plotting the number of arrivals shows if the LOS responds to increases or decreases in the arrivals. The maximum WIP is plotted to see how many patients were in the ED at the busiest moment of the hour and how this affects the LOS.

First similarities between the trends of all three aspects of the classifications are considered.

Then the differences are highlighted and discussed. The latter is done based on the average LOS of the entire day and specific time periods, on the two types of graphs discussed in the previous paragraph as well as on the number of patients with a stay longer than 4 hours. Based on this information, the relation between the number of visitors, number of arrivals and the maximum WIP, which can all be seen as measures of how busy the ED is, and the LOS of the patients can be studied. Four comparisons are studied:

A. High Morning Low Afternoon versus High Morning High Afternoon B. Low Morning High Afternoon versus High Morning High Afternoon C. Low Morning High Afternoon versus Low Morning Low Afternoon D. High Morning Low Afternoon versus Low Morning Low Afternoon

Comparisons A and C give insight into how similar mornings result in different afternoons. The other two, comparisons B and D, show whether the different mornings have an effect on the after- noon, even though the circumstances in the afternoon are similar.

Finally, the behaviour of LOS within each of the three main specialities is studied. As these specialities each have different staff, urgencies, ailments etcetera, patients of each of these can be expected to be more or less affected by the number of patients in the ED. For instance, having said that cardiology patients are more often highly urgent compared to other specialities, they are often prioritized and thus may be less likely to have a long stay even when it is busy. Hence, the days are again classified based on the number of visitors for each of the specialities. Table 3 displays the median number of visitors which is used to determine three new classifications.

Table 3: Median number of visitors for main specialities

Surgery Cardiology Internal Medicine

Median Morning 4 3 2

Median Afternoon 4 2 3

3.4 Conclusion

With the above described methodology, it is possible to get insight into how the length of stay of patients was affected by the number of patients in the emergency department of the Medical Centre Leeuwarden over the chosen semester. For some findings t-test are performed to test if the conclusions are typical for the studied period or if they are likely to hold at other times as well.

Nevertheless, they cannot be automatically generalized to other time periods as this time period

need not be representative for other time periods.

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4 Results

This section discusses the results of applying the above described method to the dataset provided by the MCL. First, the classifications based on the total number of patients are considered and compared. As there are multiple factors influencing the LOS, it is proven that the classifications only significantly differ in terms of the number of visitors. Then the throughput diagrams are interpreted to see how the number of arrivals and departures result in the specific classifications.

The development of the length of stay, number of arrivals and work in progress (WIP) are compared and related to each other, followed by a comparison of the number of patients having an extremely long stay. Afterwards, the classifications based on the number of patients for a specific speciality are considered.

4.1 Results of classifications based on total number of patients

Before conclusions can be drawn on the differences in LOS between the classifications, first any significant differences between the classifications have to be ruled out. First of all, the days of the week are compared on the number of times they are classified as each of the classifications.

Mondays are more often busy than non-busy (12/44 versus 4/50). Wednesdays and Thursdays receive the least amount of visitors and are thus most often classified as LMLA. The other two days are as likely to be a busy day (HMHA) as to be a non-busy day (LMLA). The classifications where either the morning or the afternoon are busy occur almost equally likely on any of the five working days. Figure 10 in the Appendix shows the exact division. As the staff and resource levels are equal among the five working days, the unequal distribution is not a problem.

Next, the distribution of the specialities over the classifications is considered. Table 11 (see Appendix) shows the proportion of patients that need one of the three main specialities, surgery, cardiology and internal medicine for each classification. The main point of interest in this lies in the differences between classifications, which are displayed in Table 4. For example, the biggest difference between classifications when it comes to the ratio of surgery patients among all patients arriving in the morning is 8%.

Table 4: Maximum difference in speciality ratios between classifications

Surgery Cardiology Internal Medicine

Morning 0.08 (HMHA vs LMHA) 0.03 (HMHA vs LMHA) 0.06 (LMHA vs HMLA) Afternoon 0.05 (LMHA vs HMHA) 0.07 (HMLA vs LMHA) 0.09 (HMLA vs LMHA) Note: This table shows the maximum difference between the entries of Table 11, which shows the ratio of patients for each speciality over the total number of patients in that time period. The first classification between brackets shows the classification with the highest ratio, the second one has the lowest ratio.

The mean LOS of surgery and especially cardiology patients is shorter than average and that

of internal medicine patients is longer (see Figure 1), where this difference in mean LOS between

the specialities is proven to be significant on a 5 percent level by means of a Welch’s t-test. If,

for instance, a classification has significantly more patients of internal medicine than the other

classifications, the average LOS will then also be shorter. The opposite holds for surgery patients

and cardiology patients. Although the differences between classifications are small, the mean LOS

of patients arriving on LMHA-mornings can be affected by this. All mornings having more surgery

and cardiology patients and less internal medicine patients than LMHA-mornings can cause the

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mean LOS of patients arriving in the morning of LMHA-days to be slightly longer than it would have been otherwise.

Secondly, the distribution of urgency levels in both time periods and for each of the classifi- cations is investigated. The differences between the ratios (which can be found in the Appendix, Table 12) are shown in Table 5. The differences are again relatively small. In addition to that, not all differences in LOS between urgency levels can be proven to be statistically significant with Welch’s t-test (as shown in Table 12 in the Appendix). Hence, the classifications are treated as equal in this respect.

Table 5: Maximum difference in urgency ratios between classifications

U0 U1 U2 U3 U4 U5

Morning 0.01 0.03 0.08 0.03 0.05 0.08

Afternoon 0.01 0.02 0.06 0.13 0.03 0.05

Note: This table shows the maximum difference between the entries of Table 12, which shows the ratio of patients for each urgency over the total number of patients in that time period.

Then, patients that have to undergo a radiology test once or more during their stay have a length of stay of 191.37 minutes on average, whereas patients that do not need such a test on average stay for 147.90 minutes. These means are both statistically significantly different on a 1%

level from the average LOS of all patients, which is 173.96 minutes. Hence, radiology tests posi- tively influence the LOS of the patient. As the ratio of patients that undergo a radiology requests for the entire day, morning and afternoon differ between classifications with 0.08, 0.06 and 0.15 respectively, this might slightly affect the LOS. Especially patients arriving on LMHA-days more often need such a test and can thus have longer LOS on average. Table 13 in the Appendix shows the actual ratios.

Paediatric patients, 18 years old or younger, have a statistically significantly (on a 1% level) shorter stay of more than 45 minutes compared to other patients. The number of paediatric pa- tients is limited and takes up a similar proportion of all patients in all the classifications. The maximum difference is 2.2%, 0.9% and 2.6% for respectively the entire day, the morning and the afternoon. The actual ratios and average LOS can be found in Table 14 in the Appendix.

Lastly, the means of arrivals (see Table 15) and the disposition (Table 16) are found to influ- ence the LOS of patients. Whether a patient arrived by ambulance results in a LOS difference of 6 minutes, which is statistically significant on a 1% level. The ratios of ambulance arrivals over all arrivals for the four classifications differ with maximally 11%, which can be expected to have a minor effect on the average LOS. Besides that, a hospital admission results in an average LOS that is 195 minutes, whereas any other disposition results in 145 minutes on average. Since only in the morning the ratios for HMLA and LMHA differ by, slightly, more than 5%, the average LOS on HMLA-mornings can be slightly shorter because of this.

Overall, the different characteristics of the patients within each of the four classifications are

relatively similar. Only the average LOS on LMHA-days can be slightly longer due to the com-

position of the classification. Mainly the distribution of the specialities, a bigger proportion of

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patients requiring radiology tests and more hospital admissions could affect the average LOS of those patients positively. Regardless of this, the findings discussed in the remaining of this section can still be considered valid and reliable.

4.1.1 Dynamics in arrival and departure rates

Figure 3 shows both the throughput diagram of days with a heavily visited morning (HMLA) and that of days which are busy in both the morning and the afternoon (HMHA). All six combinations of the four classifications can be found in the Appendix (Figure 14).

Figure 3: Throughput diagram High Morning Low Afternoon versus High Morning High Afternoon In Figure 3 one can see that the number of arrivals starts rising more quickly from 8 or 9 o’clock onwards for both classifications. The number of departures follows this trend two to three hours later and at a slower pace (the departure lines are less steep than those of the arrivals). This results in an increase in length of stay for the patients on the two types of days. Where the number of arrivals for HMHA-days only starts flattening out at 5 PM, a reduction in the speed of arrivals can be observed on HMLA-days slightly before 1 PM. Since HMLA-days are defined as having few patients visiting the ED in the afternoon, this decreasing number of arrivals is expected. Because of a reducing number of patients in the ED (i.e. a lower level of work in progress), the LOS of the patients arriving after 1 PM decreases as well. On busy days (HMHA) the number of arrivals and departures appear to be fairly constant during the entire day shift, which would result in a stable LOS.

In the afternoon, between 3 PM and 6 PM, the number of arrivals per hour is fairly similar

between HMLA and LMLA, as can be seen in Figure 4. The number of departures, on the other

hand, is higher for HMLA-days compared to non-busy days. This suggests that the work in progress

(WIP) is still decreasing in the afternoon and that the effect of the busy morning has not yet worn

off completely.

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The opposite is true for LMHA-days. Although their morning is classified similar to that of LMLA-days, the number of arrivals already starts increasing faster compared to LMLA-days in the beginning of the morning (11 AM). The mornings of LMHA-days are thus busier than the mornings of non-busy days. The increase in arrivals in the afternoon is approximately the same as for HMHA-days, but the number of departures is lacking. The busy afternoon is thus not caused by a higher number of arrivals but by a higher WIP at the start of the afternoon of LMHA-days compared to LMLA-days.

Figure 4: Throughput diagram Low Morning Low Afternoon versus High Morning Low Afternoon

4.1.2 Length of stay, number of arrivals and work in progress

Next it is analysed how the development of the LOS over time is related to the number of arrivals and the work in progress per hour. Some of the graphs are highlighted and discussed in the coming sections. 1

Figure 5 shows the LOS and number of arrivals for the two extreme classifications, namely the days where both the morning and afternoon are busy, respectively, not busy. The bars show the av- erage number of patients that arrived in an hour, e.g. the bar at x-coordinate 10 shows the number of arrivals between 9 AM and 10 AM. The same holds for the bars that display the maximum work in progress in Figure 6, which is discussed later. The maximum work in progress is the maximum number of patients that have been in the ED, or waiting area, at the same time at some point in the hour. The LOS is calculated as the average LOS of the patients that arrived halfway the hour, e.g. the LOS at x-coordinate 10 portrays the length of stay of patients that arrive in the ED at 9:30.

1

In the Appendix, graphs can be found that compare all classifications, see Figures 15 and 16.

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Figure 5: Average length of stay and number of arrivals: Low Morning Low Afternoon versus High Morning High Afternoon

The pattern in the LOS that is visible in Figure 5 also comes back in the LOS of the other two classifications. Similar to the number of arrivals, the LOS starts increasing around 9 o’clock in the morning and reaches a first peak around 2 PM. Both the LOS and the hourly number of arrivals then decrease until 4 PM, to again rise to a second peak around 7 PM. Hence, for any day, patients that arrive around 2 PM or 7 PM have the longest stay, which reaches up to 200 minutes on average. The trough leading up to the second peak and the peak itself can be caused by the transfer between shifts. Around 4 PM, staff leave the floor for some time to round off their shift, to inform the new shift and in some cases to receive some training. The trough in the LOS is likely caused by staff quickly finishing the treatment of their remaining patients before their shift will finish. Patients that come in during this transfer are more likely to have to wait longer, because of the limited number of staff on the floor, which explains the second peak.

Another factor behind the two peaks lies in the number of arrivals. This number fluctuates in

the same way just before the peaks and trough are seen in the LOS. The most likely way in which

an increased number of arrivals positively influences the length of stay of patients that come into

the ED a few hours later is through an increased work in progress. If at some point there is a

sudden increase in arrivals, patients coming in after that arrive in an ED that is busier and more

likely to have to wait. The opposite would then hold for the trough. However, when considering

the WIP, displayed in Figure 6, one cannot see such an increase followed by a decrease and another

increase. To be exact, the development of the maximum WIP follows a bell shape that has its

maximum at the end of the morning, at the end of the afternoon or in between for respectively

HMLA, LMHA and HMHA. Hence, the total number of patients that is present in the ED at the

same time builds up steadily to a maximum of more than 10 for each of these three classifications,

after which it steadily reduces.

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Figure 6: Average length of stay and maximum work in progress: Low Morning Low Afternoon versus High Morning High Afternoon

The transfer from the night shift to the day shift only appears to influence the LOS for HMLA days. For those days, the LOS reaches a peak around 7 o’clock, so patients that come in during the morning transfer spend a longer time in the ED. For the other days, some fluctuations in the LOS during the night are visible but not a clear peak around 7. The fact that the number of patients that visit the ED during the night is limited makes the average LOS during those hours more vulnerable to outliers and thus less reliable. However, all days experience a decline in LOS somewhere around the beginning of the day shift. With the extra staff that then starts working, patients are treated faster.

4.1.3 Comparison between classifications

Although the LOS of the classifications roughly follow the same pattern, differences can also be distinguished. Table 6 shows the weighted average length of stay for each classification in a specific time period. The average LOS at each hour is weighted by the number of arrivals in that hour.

In that way, a long LOS that is experienced by many patients weighs more heavily on the average LOS than for instance a short LOS during the night when only a few people arrive.

As the aim of this study is to look at the performance of the ED of the MCL in retrospect, the

differences are not statistically tested. However, as is discussed later, the generalizability of the

findings is expected to be limited. Below, the differences between the classifications are discussed

based on the plots made, and the above table.

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Table 6: Average Length of Stay for each classification

All Day 7 AM - 10 AM 10 AM - 1 PM 1 PM - 3 PM 3 PM - 6 PM 6 PM - 9 PM

HMHA 176.40 139.77 180.90 189.35 189.92 188.46

HMLA 176.15 136.64 187.85 197.00 196.04 172.11

LMHA 177.77 157.06 174.91 187.26 185.89 190.16

LMLA 169.20 138.27 174.36 183.25 178.14 185.04

Notes: The values indicate the weighted average of the lengths of stay of patients arriving within the specified time period, on days with the respective classification.

HMHA = High Morning High Afternoon, HMLA = High Morning Low Afternoon, LMHA = Low Morning High Afternoon, LMLA = Low Morning Low Afternoon

For both classifications with a ’high morning’ (see Figure 7), the maximum WIP is similar up until 1 PM and so is the LOS. After that the number of arrivals and the WIP drop for HMLA-days, unlike HMHA. On busy-days (HMHA), the number of arrivals after 1 PM is slightly lower than in the morning, but the WIP rises a little and only starts falling around 5 PM. The fact that the afternoon is classified as busy, is thus not only caused by a higher number of arrivals but also by the fact that the WIP was already high. The difference in both the number of arrivals and WIP between HMLA and HMHA is significant from 1 PM onwards. At the same time, the stay of the patients arriving on HMLA-days is longer until approximately 6 PM, which is slightly after the end of the day shift. This is also visible in Table 6, which shows that for any of the time periods between 10 AM and 6 PM, the average LOS of arriving patients on HMLA-days is longer than for HMHA- days. Only during the night, when there is also less staff available and significantly less patients, the LOS is longer on HMHA-days. Hence, regardless of the fact that it is significantly less busy during the afternoon in the ED, the patients spend more time in it. This is in contradiction with one of our main expectations that the patients arriving at a time when it is busier have a longer stay.

Figure 7: Average length of stay, number of arrivals (left graph) and maximum work in progress

(right graph) of all patients: High Morning Low Afternoon versus High Morning High Afternoon

Next, the days where the morning is not busy and the afternoon is (LMHA) are compared

to those where also the afternoon is busy (HMHA). Patients that come in during the morning

experience a shorter stay if they do so on a LMHA-day than if they come in on a HMHA-morning

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(see Figure 8 and Table 6), which matches our expectation of longer stays on busier moments.

However, although the afternoons of those two types of days are equally busy, the average LOS is still shorter on LMHA-afternoons. The stay of patients on the two types of days is equally long from 6 PM onwards, which is also the moment when the maximum WIP is more or less similar.

This suggests that the WIP is more related to the LOS than the number of arrivals is. Between 7 AM and 10 AM and from 8 PM onwards, the average LOS of patients on LMHA-days is longer than on HMHA-days. This being a relative long period and thus having a higher weight on the average, the average stay of all patients arriving on LMHA-days is slightly longer (176.4 versus 177.8 minutes) than on HMHA-days. Although this difference is negligible, it is odd that on a day with clearly less visitors the average LOS is not shorter. Overall, the main result out of this comparison is that the LOS of patients arriving in the ED on a similar afternoon, is longer when the number of visitors in the morning is higher.

Figure 8: Average length of stay, number of arrivals (left graph) and maximum work in progress

(right graph) of all patients: Low Morning High Afternoon versus High Morning High Afternoon

An expected result is that of the LOS in the morning of LMHA-days being similar to that of

non-busy days (LMLA), which is the case as they are both just below 175 minutes. The plots of

these two classifications are displayed in Figure 9. In the throughput diagrams it was found that

the number of arrivals on LMHA-days increases faster from 11 AM onwards, which is also shown

by the graph below. In addition to that, the WIP starts growing at the same moment. Although

the difference in the number of arrivals and the WIP between LMLA and LMHA start growing at

the 12-th hour, so 11 AM, the LOS is already larger on LMHA-days between 6 AM and noon. This

increased LOS is thus likely to be caused by something else than the number of patients. Patients

arriving in the afternoon of LMHA-days experience a longer LOS on average. This is line with the

fact that the number of arrivals and WIP is also higher for the busy afternoon. Nevertheless, at

some points in the afternoon the LOS is similar for patients arriving on either of those days. Hence,

it appears that at some moments the staff manages to have the same productivity resulting in a

similar LOS but in general they cannot keep up with the higher number of patients.

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Figure 9: Average length of stay, number of arrivals (left graph) and maximum work in progress (right graph) of all patients: Low Morning Low Afternoon versus Low Morning High Afternoon

Finally, the comparison between days with a high number of visitors during the morning (HMLA) and days where the ED is relatively quiet throughout the entire day (LMLA) is made (see Figure 10). Similar to the WIP, the LOS between 10 AM and 7 PM is higher on HMLA-days.

Where this is an expected result for the morning hours, patients arriving in the afternoon would expectedly have had a similar length of stay. Apparently, the slightly higher WIP in the afternoon results in a longer LOS as well. Striking is that the average stay of patients arriving in the after- noon is even longer than that of patients arriving in the morning. Hence, through an increased WIP at the start of the afternoon, patients in the afternoon of HMLA-days are affected by the circumstances in the morning when it comes to their length of stay.

Figure 10: Average length of stay, number of arrivals (left graph) and maximum work in progress

(right graph) of all patients: Low Morning Low Afternoon versus High Morning Low Afternoon

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4.1.4 Length of stay over 4 hours

The occurrence of extremely long lengths of stay is also analysed. For each of the four classifica- tions, Table 7 shows the percentage of patients that had a stay of more than 4 hours (240 minutes). 2 The different columns distinguish the patients based on their arrival time.

As expected, the busier the day, the more patients have such a long LOS. On the busiest days, HMHA, more than 9 patients visiting the ED had a long stay, which is more than 19% of the total number of patients visiting the ED on those days. On a day where either the morning or the after- noon is classified as ’busy’, this percentage lies around 18%, where HMLA has slightly more. This suggests that a high afternoon affects the LOS to a smaller extent than a high morning. Not only is the average LOS shorter, the number of patients with an exceptionally large LOS is also lower. On LMLA-days only slightly more than 15% of the patients have a stay longer than 4 hours. All days classified as either busy (HMHA) or non-busy (LMLA), have the most long-stays in the morning.

This is inconsistent with the development of the average LOS (see Figure 6), which is longer in in the hours after the morning (1 PM to 9 PM). The explanation for this must be that there are also more patients with a relatively short LOS in the morning, making the LOS of patients arriving in that time period differ more amongst each other.

Table 7: Average percentage of patients with a LOS longer than 4 hours per time period 7 AM - 10 AM 10 AM - 1 PM 1 PM - 3 PM 3 PM - 6 PM 6 PM - 9 pm All day

HMHA 18.6% 23.5% 19.3% 20.0% 16.3% 19.1%

HMLA 16.9% 19.7% 28.1% 26.1% 7.3% 18.5%

LMHA 15.6% 20.1% 10.0% 20.1% 26.0% 17.6%

LMLA 18.0% 20.3% 16.8% 16.8% 10.3% 15.4%

Note: The time period from 10 AM to 1 PM is referred to as the morning, the time period from 3 PM to 6 PM is referred to as the afternoon.

Looking at the time period when most patients have a long stay, leads to conclusions that are similar to those described in Section 4.1.3. HMLA and LMHA days have the most long stays in the period after their respective ’busy-period’, so between 1 PM and 3 PM or between 6 PM and 9 PM. Nevertheless, of the patients arriving in the afternoon that have a long LOS, most came in on a HMLA-day and not on a day with a busy afternoon (HMHA or LMHA). Hence, just as the average LOS is longer on HMHA-afternoons than on HMLA-afternoons, so too are there more long stays.

The results found in the comparison of average LOS between LMHA-days and HMHA-days partly holds here. Although the average LOS is shorter in the afternoon of LMHA-days than on HMHA-days, the percentage of patients with a long LOS is similar. Furthermore, it is shown that the average LOS on LMHA days still increases towards the end of the afternoon resulting in the highest average LOS between 6 PM and 9 PM compared to the other classifications. Accordingly, on average 26% of the patients arriving after 6 PM have a long LOS, which is higher than for any other classification. Hence, the average LOS and the number of long stays of patients arriving after 6 PM is even higher when the morning is not busy (LMHA) than on days that have both a busy

2

The average number of patients with a long stay can be found in the Appendix in Table 17. Figure 17 in the

Appendix show how the number of patients with a long stay is distributed for each classification and each time period.

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morning and a busy afternoon (HMHA).

As discussed, and expected, the average LOS of patients that arrive in the afternoon of LMHA- days is longer than on LMLA-days. This also results in a higher number of patients with a stay longer than 4 hours among the patients arriving between 3 PM and 9 PM. The difference, though, is larger in the evening hours. So, the length of stay of patients is clearly affected by a busier afternoon. Also the average LOS of patients arriving in the afternoons of HMLA-days was found to be longer than of those arriving on LMLA-days. Again, Table 7 shows that the same holds for the number of long stays up until 6 PM. Similarly, the average LOS in the evening is shorter for HMLA-days and so is the percentage of patients with a long stay.

Concluding, a period with a longer average LOS does not necessarily have a higher number of patients that have a stay longer than 4 hours. However, busy periods in terms of the number of visitors do result in a higher number of patients with a long stay although this affects those arriving after the busy-period itself most.

4.2 Main specialities - surgery, cardiology, internal medicine

Earlier (Section 4.1) it was found that the three main specialities, surgery, cardiology and internal medicine take up more or less similar proportions of the dataset in the four classifications based on the total number of patients. Now, the results of classifications created based on the number of visitors for each of these three specialities are considered. This is done to see whether similar patterns occur within these classifications, or if some specialities are less or more influenced by higher numbers of patients. All days have now received four classifications, based on the total number of patients, the number of surgery patients, the number of cardiology patients and the number of internal medicine patients in the morning and afternoon. Table 8 displays the number of days that received the same classifications. The total number of weekdays considered being 131, only slightly more than half (67) of the days have received the same classification based on the total number of patients and the number of surgery or cardiology patients. The number of overlapping classifications between the other criteria is even less. Therefore, all criteria result in relative distinct classifications and a busy day for the ED thus need not be busy in terms of any of the three main specialities or the other way around.

Table 8: Number of days with identical classification Surgery Cardiology Internal Medicine

All 67 67 60

Surgery - 44 51

Cardiology - - 43

Note: The numbers in the table indicate the number of days that were high and/or low in terms of the column name and the row name, e.g. 44 days were either busy or not busy in terms of surgery patients and cardiology patients.

For all three specialities and six combinations of classifications plots, like Figure 11, have been

created which can be found in the Appendix (Figures 18 to 23). These classifications have been

created based on the number of visitors for the respective speciality. The lines again show the

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average LOS, where the solid line indicates the LOS of the patients of the speciality and the dashed lines the average LOS of all patients. This time the bars are split up into two parts, the darker part showing the number of arrivals or maximum WIP of patients of the studied speciality and the full bar showing the total number of patients of all specialities.

Figure 11: Average length of stay, number of arrivals (left) and maximum work in progress (right)

of surgery patients: Low Morning Low Afternoon versus High Morning High Afternoon

The general pattern of all classifications based on the number of patients requiring the speciality

surgery is similar to that of the classifications based on the total number of patients, described in

Section 4.1.2. Yet, the differences in LOS between the classifications are more significant. The

distribution of the LOS (Figure 1) shows that the LOS fluctuates the most between patients for

surgery. This is also visible in the plots for the different classifications. The LOS of surgery patients

on a HMHA-day is clearly longer and on a LMLA-day clearly shorter than the average LOS all

patients (dashed lines). Taking into account all four classifications the LOS is more often shorter

than their respective dashed line, which is in accordance with the fact that surgery patients on

average have a shorter stay than other patients, shown in Figure 1.

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Figure 12: Average length of stay, number of arrivals (left) and maximum work in progress (right) of cardiology patients: Low Morning Low Afternoon versus High Morning High Afternoon The LOS of cardiology patients (Figure 12) is more constant over time, when not taking into account the trough in the early morning for HMLA, and shorter than for other patients. In Section 3.2 it has been discussed that relatively low triage levels (which are more urgent) and protocolized care are causes for the shorter LOS for cardiology patients. In the classifications based on the total number of patients, two peaks were visible in the LOS, one around 2 PM and the other around 7 PM. As the LOS of cardiology patients is more stable over time, these two peaks are not present for all the cardiology classifications.

Figure 13: Average length of stay, number of arrivals (left) and maximum work in progress (right) of internal medicine patients: Low Morning Low Afternoon versus High Morning High Afternoon

For internal medicine patients (Figure 13), the two peaks are more clearly noticeable. However,

the first peak rises to four hours, while the second peak is less high. Overall the LOS for these

patients is longer than for other patients, which was also visible in Figure 1. However, from approx-

imately 10 AM onwards, the solid and dashed lines converge and are fairly similar between 1 PM

and 8 PM. Where the LOS rises at the beginning of the day for all classifications and specialities

other than cardiology, the increase in LOS for cardiology patients is much smaller. According to an

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ED physician, an extra physician was employed from 1 PM to the end of the day-shift (5 PM) in the studied period. This physician treated both the specialities internal medicine and cardiology.

As patients of the latter are already often prioritized they are often treated by an ED-physician.

Therefore, the extra physician is likely to treat more internal medicine patients, thus resulting in a less significant increase in LOS. Hence, with the extra doctor, the ED is able to deal better with a higher demand in internal medicine.

4.2.1 Comparison between classifications

To compare the different classifications, Table 9 has been created to display for all classifications the average LOS of patients of the entire day and arriving in any of the five time periods between 7 AM and 9 PM.

Within each of the three specialities, the comparison between the HMLA and HMHA lead to different results. When the classification was based on the total number of patients, the stay of patients arriving in the afternoon on days where only the morning was busy (HMLA) was found to be longer than that of patients arriving at the same time but on days that were busy also in the afternoon (HMHA). This is not the case when the number of patients for any of the three specialities determines the classification. For the three specialities, the LOS of patients arriving between 1 PM and 9 PM is always longer on busy-days (HMHA), although the differences differ.

Patients arriving during the afternoon of HMHA-days experience a stay of 20-30 minutes longer than patients arriving in the afternoon of HMLA-days. For the three main specialities, the expected relation between the number of visitors and the LOS of patients holds. Indeed, the patients arriving during a busy afternoon have a longer stay.

Table 9: Average Length of Stay for each classification

All Day 7 AM - 10 AM 10 AM - 1 PM 1PM - 3 PM 3 PM - 6 PM 6 PM - 9 PM

Surgery

HMHA 184.72 139.29 183.07 198.88 212.39 200.57

HMLA 171.95 157.64 190.64 174.83 180.53 152.99

LMHA 163.72 151.65 169.47 158.87 168.52 177.40

LMLA 153.11 136.71 153.68 155.24 160.24 154.18

Cardiology

HMHA 163.37 137.96 164.02 174.62 176.11 169.32

HMLA 154.68 111.16 172.02 155.07 156.32 166.91

LMHA 613.02 143.04 164.53 173.33 171.49 166.47

LMLA 152.96 141.77 150.50 159.09 160.97 158.14

In ternal

HMHA 200.01 185.49 210.67 203.21 208.06 196.66

HMLA 191.96 181.00 204.38 198.64 180.71 192.41

LMHA 202.73 198.70 227.39 201.99 193.77 193.17

LMLA 186.36 180.99 194.00 182.76 185.78 192.73

Note: The length of stay displayed here is the weighted average of the patients for the respective specialities, which is illustrated with solid lines in the graphs in the Appendix (Figures 18 to 23).

The result of the comparison between HMHA and LMHA days for the total dataset also holds

for the three main specialities. The LOS of patients arriving in the afternoon, is shorter for days

where the morning has not been busy (LMHA). For surgery and internal medicine patients this

can partly be explained by the fact that the WIP is also a little lower on LMHA-days. However,

for cardiology patients this difference is very small, while the difference in LOS is more than half

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an hour. The longer LOS in HMHA-afternoons compared to LMHA-afternoons should thus be ex- plained by other factors than the number of patients present in the ED at the time of arrival. Even so, there is also a discrepancy in the behaviour of the LOS compared to the classifications based on the entire dataset. The LOS of patients arriving in the evening (6 PM to 9 PM) of LMHA-days is still shorter than that of patients arriving in the evening of HMHA-days. The opposite of this was the case for the classifications based on the total number of visitors.

Another similarity between the classifications lies in the average LOS of LMLA-mornings and LMHA-mornings. For all three specialities, the average LOS is longer for patients arriving in the morning of LMHA-days than for patients arriving on non-busy days (LMLA). Regardless that both classifications are classified as having a ’low morning’, the number of arrivals and WIP in the morn- ing of LMHA-days is already higher than for LMLA-days. Again, the busy afternoon is thus more a consequence of a long LOS in the morning than the other way around.

The last comparison made, that between HMLA and LMLA, leads to different results for the different classification criteria. Although the average LOS over the entire day is longer on HMLA- days than on non-busy days (LMLA), for all specialities and the total dataset, this is not the case for all periods during the day. Surgery is most similar to the overall patient. Patients arriving both in the morning, afternoon and the two hours in between have a longer stay when they do so if the day has a busy morning (HMLA). For internal medicine patients this is only the case between 10 AM and 3 PM. The effect of the busy morning on the LOS of cardiology patients is limited, as only patients arriving in the morning itself have a longer stay compared to those arriving in a non-busy morning.

To conclude, similar results have been found within each of the three specialities. The most

significant difference is that the effect of a busy morning in terms of cardiology patients is the most

limited. This suggests that the responsiveness of cardiology staff to busy mornings is the highest

of the three specialities.

Referenties

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