Health Care Manag Sci DOI 10.1007/s10729-014-9311-1

Dynamic patient grouping and prioritization: a new approach to emergency department flow improvement Omar M. Ashour & Gül E. Okudan Kremer

Received: 30 June 2014 / Accepted: 25 November 2014 # Springer Science+Business Media New York 2014

Abstract The demand on emergency departments (ED) is variable and ever increasing, often leaving them overcrowded. Many hospitals are utilizing triage algorithms to rapidly sort and classify patients based on the severity of their injury or illness, however, most current triage methods are prone to over- or under-triage. In this paper, the group technology (GT) concept is applied to the triage process to develop a dynamic grouping and prioritization (DGP) algorithm. This algorithm identifies most appropriate patient groups and prioritizes them according to patient- and system-related information. Discrete event simulation (DES) has been implemented to investigate the impact of the DGP algorithm on the performance measures of the ED system. The impact was studied in comparison with the currently used triage algorithm, i.e., emergency severity index (ESI). The DGP algorithm outperforms the ESI algorithm by shortening patients’ average length of stay (LOS), average time to bed (TTB), time in emergency room, and lowering the percentage of tardy patients and their associated risk in the system.

Keywords Group technology (GT) . Emergency severity index (ESI) . Triage . Discrete event simulation (DES) . Emergency department (ED)

O. M. Ashour (*) Industrial Engineering Department, Pennsylvania State University, The Behrend College, Erie, PA 16506, USA e-mail: [email protected] G. E. Okudan Kremer Industrial and Manufacturing Engineering, and School of Engineering Design, Pennsylvania State University, University Park, PA 16802, USA e-mail: [email protected]

1 Introduction At the turn of the millennium, the World Health Organization (WHO) ranked the U.S. health system’s performance at 37th out of 191 countries [1]. Six years later, the U.S. was number one in terms of health care spending per capita, but it ranked 43rd for adult female mortality and 42nd for adult male mortality [2]. In general, the performance of healthcare service can be assessed by overall responsiveness, measured in terms of patient waiting time and the quality of service. The longer the waiting time for medical intervention, the poorer the service is—the most critical issue for EDs as they are considered to be vital components of the nation’s health care safety net [3–5], and are responsible for 45–65 % of all hospital admissions [6]. Crowding is considered a global problem, adversely affecting the quality of provided health care [7–10]. Bernstein et al. [11] found that crowding is correlated to the increased risk of in-hospital mortality, spawned by conditions such as longer waiting times (time-to-treatment) for patients with pneumonia or acute pain. Moreover, crowding is also correlated with a higher probability of patients who leave the ED without being seen or leave against medical advice. Hoot and Aronsky [8] found that crowding commonly affects mortality, transport delays, treatment delays, ambulance diversion, patient elopement, and financial effects. Therefore, we conclude that crowding is correlated with two important domains concerning quality: safety and timeliness. Any typical ED setting is unique and complex, as patients arrive without a planned appointment, with various injuries or illnesses, and with various health insurance plans or even without insurance. Some patients come with a lifethreatening status requiring immediate treatment, while others come with non-urgent status and can wait to be treated. Therefore, upon their arrival to the ED, patients undergo a triage interview. Triage has been in place, formally or

O.M. Ashour, G.E. Okudan Kremer

informally, since the first ED opened [6]. In the U.S., EDs started using triage as early as the 1960s [12]. The purpose of the triage interview is to quickly sort incoming patients to the ED by severity of their illness or injury [12, 13], and the projected resources and operational needs [14, 15]. Each patient is placed in one of several queues, having an associated maximum time until the patient sees a physician [16]. It is a critical and necessary element to assign scarce resources to limitless medical needs [17], therefore, effective triage acts as a patient flow regulator [18] where crowding is prevalent. The contemporary emergency severity index (ESI) triage system sorts patients into five clinically distinct levels. The most acutely-ill patients are assigned to ESI level 1 (the highest acuity level) or level 2. ESI levels 3, 4, and 5 (the lowest acuity level) are assigned based on the number of resources needed by the patient [19]. For example, a patient in ESI level 1 or 2 may be taken immediately to the treatment area, while patients assigned to level 4 or 5 can wait for treatment [14]. During the triage process, the nurse checks the patient’s vital signs, temperature, pulse, respiration rate, and blood pressure. The nurse also discusses the present illness, past medical history, and other pertinent information such as allergies and immunization status with the patient. The nurse then determines how quickly the patient must be treated [20]. Myriad attempts have been made to improve ED care services. Examples include minimizing waiting time intervals and improving patient satisfaction [21], developing reliable decision support systems to improve patient waiting times and service quality problems [6], and developing expert systems to aid the triage nurse in assigning a patient’s category [22, 23]. Most U.S. hospitals use a three-level triage evaluation (emergent-urgent-nonurgent), which sorts patients based on the question: “How long can this patient wait to be seen?” [12, 24]. On the other hand, the five-level triage instrument (e.g., ESI, Australian triage scale (ATS), and Canadian triage and acuity scale (CTAS)) has been developed and validated based not only on “Who should be seen first?” but also “What will this patient need?” [19, 24]. Despite the fact that the five-level system sorts patients and prioritizes them based on the severity of their illness or injury [19], the waiting period or the order of treatment, especially for patients at the same acuity level, is rarely investigated [20]. Tanabe et al. [25] stated that physicians and nurses face a serious limitation when using the ESI triage algorithm: they could not determine how acutely ill the level 2 patients in the waiting room were when faced with the scenario of multiple level 2 patients in the waiting room. Moreover, two categories of ESI level 2 patients can be identified: those who can safely wait for physician evaluation for at least 10 min without clinical deterioration, and those who cannot wait [25]. In sum, the challenge for triage nurses is the prioritization and ranking of non-urgent patients and recognizing who is most in need of care [12].

The prioritization of time-to-be-seen is essential to the patient and is directly related to patient safety, especially when ED crowding delays evaluation [26]. Recent research investigated the use of the utility theory to prioritize ED patients assigned to the same acuity level [20]. In this study, Claudio and Okudan [20] demonstrated the use of the multi-attribute utility theory (MAUT) in patient prioritization using a hypothetical example. They explained the choice of MAUT due to the inherent uncertainty in ED settings, and that MAUT accounts for uncertainty. Ashour and Okudan [27] also presented a solution for ED patient prioritization using MAUT, by which patients were ranked with different acuity levels using patient age, gender, pain level, and the assigned ESI. While vital signs (temperature, pulse, respiration rate and blood pressure) were considered for patient ranking in Claudio and Okudan [20], patient age, gender and pain level information were neglected. Further, these variables were not considered explicitly in the ESI algorithm. Argon and Ziya [28] delivered insights about prioritizing customers in the case of imperfect information about customer identity; they mentioned triage as an example. They are assuming that each customer arrives with a signal that can be used as an indicator for his/her identity. For example, customers with a signal that falls within a specific interval (i), they are assigned type (i). Then they compared different prioritization policies, i.e., highest-signal-first (HSF) policy, two-class policy, first-come-first-served (FCFS) policy, and the generalized cμ (GE-cμ) policy. The comparison was based on the average long-run waiting cost. They took into consideration two cases: linear and non-linear waiting cost functions of time. Their analysis showed that when the waiting cost is linear with time, HSF policy outperformed any finite class priority policy. On the other hand, when the waiting cost is convex with time, the two-class policy and the FCFS policy performed better than the HSF policy. Nevertheless, GE-cμ policy outperformed all the other policies when the waiting cost is convex and is a quadratic function of time. This policy reduces to the HSF policy when the waiting cost is a linear function of time [28]. Even though Argon and Ziya [28] have described techniques to choose the better signal, they did not develop a signal for patients who visit the ED. The dynamic grouping and prioritization (DGP) triage algorithm is intended to close this gap. It is easy to state triage’s purpose, but it is difficult to achieve it due to the complexity of the ED setting. Additionally, it is difficult to compare different triage systems because there are no standard criteria to measure the outcomes of the process and its impact on patients [26]. Measured outcomes will not be the same as clinical outcomes. Therefore, a proxy measure should be considered [26]. For example, no single outcome measure captures the stated purpose of triage; in its place, Cooper [26] suggested using patient flow and system level utilization metrics. Waiting times and throughput are

Dynamic patient grouping and prioritization

used in this study, among other metrics, to evaluate the DGP algorithm compared to the currently used ESI algorithm (in section 4). Triage assessment is a result of complex interactions between health care providers and patients [26]. The qualifications and personal qualities of triage nurses are important for effective triage [12]. The skills or contextual factors needed to make accurate ED triage decisions are not currently known [29]. Much of the decision-making process is based on each individual nurse’s experience, knowledge, and intuition [12, 30–33]. Göransson et al. [29] found that the decision-making of nurses during triage varied; studies have shown differences in decision making between expert and beginner level nurses, while others have found their decision making to be largely the same. Göransson et al. [34] also examined the quality of triage nurses’ decisions using the CTAS algorithm in Swedish EDs, by investigating the relationship between the personal characteristics of registered nurses and the accuracy of their acuity judgments when rating patient scenarios. They concluded that there was no relationship between the personal characteristics of the nurses and the ability to triage, and proposed that decision making could be affected by other factors. Data indicates that, on average, less than 3 % of ED patients are classified as ESI level 1 [35] while the balance exhibits less urgency patients [30, 36]. Different triage systems are typically reliable for assessing urgent triage priority but no consistency exists among them for assessing the least urgent levels [26, 37]. Moreover, patient state might change while waiting at ED, which means that triage decisions should change dynamically [20]. Based upon the increasing crowding in EDs and the shortcomings of existing triage systems, there is a need for a scientific approach that dynamically identifies and assesses the groups and the priority levels of ED patients. The approach should improve the capability of triage systems to make differentiations among the least urgent and waiting patients with the same ESI classification, while lowering the cognitive stress and load on triage nurses, which resulted from the dynamic nature of triage process and the complex environment of EDs, and aiding them to make better and informed decisions. This study uses group technology (GT) as the core of its proposed dynamic patient grouping and prioritization (DGP) triage algorithm. GT is a management philosophy in which the knowledge about groups leads to efficient problem solving [38]. It involves the detection of those attributes by which the members of a population can be clustered into groups. While in a manufacturing context, part families are created based on routing or design information [39,40], in healthcare systems, patient groups can be created based on patient information, such as age, gender, chief complaint, vital signs; and on treatment information, such as expected treatment time, laboratory tests, CT scan.

According to this review of prior work, GT concept has not yet been used for analysis in the healthcare domain. In order to understand how GT impacts the performance, efficiency, and quality and safety of care in an ED environment, this paper proposes an integrative approach to dynamically identify patient groups and their priority based on patient characteristics and treatment requirements, and investigates its impact on system performance metrics.

2 Prior literature on patient grouping El-Darzi et al. [41] argued that in healthcare systems, identifying the groups of patients and their required workload might improve the use of healthcare systems resources. They reasoned that patient differences and uncertainty in healthcare systems make resource utilization unpredictable. Thus, if patients can be grouped according to characteristics (e.g., severity of illness, speed of recovery, resource consumption, length of stay (LOS), discharge destination, and social circumstances), their resource needs could be predicted. Grouping patients into homogenous sets can offer advantages and help improve the planning and management of health facilities [42]. El-Darzi et al. [41] addressed several patient grouping studies. Patient grouping has been used to standardize and manage costs for patients in the same group, who have similar resource consumption and utilization. Other uses of grouping include planning, clinical management, hospital funding, reimbursement purposes, and examining hospital efficiency [41]. Grouping methods such as data mining and clustering algorithms have been used in healthcare settings (e.g., [41, 43]). These tools derive clusters or groups based on a measure of likeness or closeness. Both El-Darzi et al. [41] and Ceglowski et al. [43] reported that in the healthcare domain, algorithmic approaches outperform standard statistical methods in areas such as detecting non-linear relationships and model’s interpretability (e.g., [44]). However, the practical issues of data mining algorithms in healthcare applications have been assessed as still needing more research and study [45]. Existing grouping methods categorize patients according to variety of data types such as clinical, demographic, and resource consumption data. The input to these methods controls the output. Groups can be either clinically similar or homogenous, and based on resource use, or both. The number of groups is varied as well along with their degree of homogeneity. Grouping methods include diagnostic based grouping (e.g., international classification of disease (ICD)), resource consumption based grouping (e.g., diagnostic related groups (DRGs)), patient pathway grouping, multi-stage grouping, and clustering based grouping. Certain drawbacks of these methods are as follows: 1) some involve a huge number and

O.M. Ashour, G.E. Okudan Kremer

fine classifications, which affect their practicality and comprehension; 2) some provide clinically homogenous groups but each group has significant variability with respect to resource consumption, treatment, cost, etc.; 3) some use types of data that are not always available or are expensive; 4) some are derived from collected census data collected, or do not account for seasonal or cyclical behaviors; and 5) some are computationally expensive. Grouping patients based solely on statistical approaches might lead to groups that are meaningless clinically [46]. Approaches that utilize clinical experience coupled with statistical methods are recommended as leading to practical patient groupings [47]. GT combines clinical judgment and experience with a clustering algorithm to identify patient groups in a practical manner. The hypothesized outcome is GT’s ability to determine patient groups that are practically and clinically meaningful. GT has been shown to improve manufacturing systems efficiency [48] and productivity [49]. It should be emphasized that the newly developed DGP algorithm is not intended to be used in planning ED resources; it is intended to aid triage nurses and improve the utilization of these resources while keeping in mind patient safety and health care quality.

3 Group technology (GT) approach Applying GT involves two major steps: 1) developing a coding and classification (CC) scheme, which involves finding the most relevant and important attributes that affect the grouping of patients into clinically, distinct, and meaningful groups; and 2) applying an appropriate algorithm to find these groups and then prioritize the patients within each group. The following sections present these steps. For more information about GT, the reader is referred to [38, 50, 51]. 3.1 Classification and coding (CC) scheme The initial step of identifying the important classification attributes is critical because they are the basis of the classification. Clinical interviews that target health care providers can provide the important patient and treatment attributes to serve as the basis for developing the CC scheme. A study to explore data collection during triage in actual practice has been conducted in the state of New York [52]. One limitation to this study could be that the results might not be generalized to the other geographic areas or demographic populations. Ashour and Okudan Kremer [53] have conducted semi-structured interviews with three health care providers in Hershey Medical Center (HMC) to validate the generality of Castner’s study [52]. The code structure selected is a chain-type structure in which each code digit provides distinct information about

the patient and is arranged to follow the order of information for the patient. For example, when the patient arrives at the ED, the health care provider would recognize if he/she is conscious, disabled or neither. Then his/her vital signs would be taken. Accordingly, the code would begin with a digit representing the status of the patient (conscious or not), followed by a digit to identify disability, followed by digits to represent vital signs, and so on. This procedure would help the health care provider follow the patient information in a systematic way. 3.1.1 Patient code According to the clinical interviews [53] and the available patient data, the suggested CC scheme is shown in Table 1. For a patient arriving in the ED with the following attributes: 19 years old, female, 5 out of 10 pain level, temperature=37 ° C, systolic bp=120 mmHg, diastolic bp=81 mmHg, HR=70 beats/min, respiration rate=20 breaths/min, SaO2= 95 %, and expected treatment time=25 min, the coding number would be 3-2-5-221111-1. Each patient record specifies six vital signs. Table 2 shows an example of the vital signs coding system. Data for this table and the rest of the vital signs was provided by expert nurses and reported by Ashour and Okudan [54]. The decision to code the vital signs was to facilitate the use of the GT algorithm; based on health care providers’ expertise, each range would represent similar severity. If the patient comes with a life-threatening situation, there will be no time to take vitals. Therefore, the maximum value (range) of each digit is given for that patient. A higher value for a digit indicates a worse (severe) situation. Accordingly, the worst case scenario (highest severity situation) would be a patient exhibiting the following code: 4-2-10-555555-3. The worst case scenario is used as a reference to prioritize the patients within the same group as explained in section 3.2.1. 3.2 Patient dynamic grouping and prioritization (DGP) algorithm The first step of the algorithm is to identify patient groups that share similarities in terms of patient and treatment characteristics. The distributed dynamic GT algorithm, developed by Ben-Arieh and Sreenivasan [51] to group parts, has been modified and further developed to prioritize patients within each group. Other heuristic approaches can be utilized, such as Heuristic for Part Family using Opitz Coding System (HPFOCS) [55]. Limitation of HPFOCS is the need for prior knowledge about the number of clusters. Moreover, it is computationally expensive because it is a random heuristic approach, particularly when the number of alternatives and/or attributes expands.

Dynamic patient grouping and prioritization Table 1

CC scheme

A Age

B Gender

C Pain level

D Vital signs

E Expected treatment time

1 - 0–1 year 2 - >1–18 years 3 ->18–65 years 4 –>65 years

1 – male 2 – female

0–10 scale (0 – no pain, 10 – severe pain)

1 – low 2 – relatively low 3 – medium 4 – relatively high 5 - high

1 – 0 min- 60 min 2 – 61 min–120 min 3 –>120 min

To apply GT algorithm, a similarity measure must be used. In this paper, Offodile similarity metric is used. Offodile has been used in many applications of GT (e.g., [38, 55]). It is capable of dealing with categorical data [55], and its output value is between 0 and 1 (already scaled by the range of each attribute). The patient group formation problem can be formulated using the suggested CC scheme that is presented in section 3.1.1 as a matrix P=[pij]. P is called patient-attribute incidence matrix of size NxK, where N is the number of patients and K is the number of attributes for each patient. pij is the coding value of the jth attribute of the ith patient. Thus, each row in the matrix represents a coded patient. Equation 1 shows the incidence matrix. 2 3 p11 ⋯ p1K P¼4 ⋮ ⋱ ⋮ 5 ð1Þ pN 1 ⋯ pN K

changes. The need is for an approach that can handle the dynamic nature of this process. The distributed dynamic GT method has the ability to handle these characteristics [51]. It uses a bidding protocol based on negotiation between agents. Each agent is a patient group representative. The agent accepts the patient as part of the group based on the similarity between the patient and the patient group represented by the agent. The algorithm is solved iteratively, so that an agent negotiates with the rest of agents to trade its most different patients, in terms of similarity between patients in the same group. The process iterates until no agent can trade its patients [51]. 3.2.2 Terminology and definitions Some terminology and definitions should be clarified before presenting the DGP algorithm: Agent (Al): A representation of a patient group. Basically, it calculates and stores the dissimilarities between the center of the cluster and all the patients in that cluster. Agents can negotiate with each other. Where l is the group index, and l=1, 2,…, L. Dissimilarity (dij): The complement of Offodile similarity measure. The Offodile [40] similarity metric can be formulated as follows:

To identify patients’ groups, the solution should maximize the similarities between each pair of patients in the same group. The following section presents the distributed dynamic GT method in detail. 3.2.1 Distributed dynamic group technology (GT) method

Si j ¼

The distributed dynamic GT method provides a way to group patients in an ED in a practical manner. ED patients arrive in random numbers and at random times. Moreover, they come with myriad complaints and characteristics. Patient’s characteristics change with time, and therefore, patient’s status Table 2

Temperature (°C)

1 2 3 4 5

(36.6–37) (35–36.5) (37.1–37.3) OR (33.9–34.9) (37.4–37.8) OR (32.2–33.8) (37.9 or Greater) OR (32.1 or Lower)

wk S i jk

ð2Þ

k¼1

Where, wk the weight of each attribute; health care providers rated the attributes as reported in [56]   p −p  ik jk S i jk ¼ 1− ð3Þ Rk

Codes for temperature

Code

XK

Where, Sijk K

the similarity measure between patient i and patient j on attribute k the total number of attributes considered

O.M. Ashour, G.E. Okudan Kremer

pik pjk Rk

Average dissimilarity: The average dissimilarities between the patients and their group. It is calculated as follows: " # nl X nl X 2 Average Dissimilarity ¼ ð9Þ di j nl ðnl −1Þ i¼1 j¼iþ1

patient coding for patient i on attribute k patient coding for patient j on attribute k the range of attribute k over the population space of patients. Then, dissimilarity can be formulated as:

d i j ¼ 1−S i j

ð4Þ Where;

Center of a cluster (Cl): Center of the cluster can be calculated as follows: 1 Xl p nl m¼1 mkl

nl dij

number of patients in group l is defined in Eq. 4.

n

C kl ¼

ð5Þ

Rank ¼ Patient Group þ ð1− Patient PriorityÞ

Where; Ckl pmkl nl

the center of cluster l along the dimension k patient coding for patient m on attribute k in group l the number of patients in group l.

Then, C l ¼ ½C 1l C 2l …C KL 

ð6Þ

Center of the Global (G): The center of the global is calculated as follows: Gk ¼

N 1X p N m¼1 mk

ð7Þ

Where; Gk pmk N

center of the global on attribute k patient coding for patient m on attribute k total number of patients to be grouped.

G ¼ ½G1 G2 … GK 

Patient rank: The order by which the patients are treated. It is calculated as follows:

ð8Þ

Threshold (Tl): The dissimilarity between the center of cluster l and the center of the global. Dissimilarity between a patient and a cluster: The dissimilarity between the patient and the center of the cluster. Different patient: The patient that has the highest dissimilarity from the center of the cluster. Worst case scenario: The patient who has the highest possible value for each digit in his code.

ð10Þ

Patient group: is the result of phases one and two, Patient priority: is the result of phase three. The original distributed dynamic GT algorithm [51] has two phases: the initial part family formation and the negotiation phase (group optimization phase). In this study, the algorithm is further developed to include a third phase known as the prioritization phase. In the first phase, arriving patients are assigned an agent. Each time a patient arrives, he is assigned to an existing agent or to a new agent. When this happens, the threshold of that agent, the center of the global, and the center of the cluster are recalculated. After a predefined period of time or a predefined number of patients, phase one is terminated to yield the initial patient groups. Phase two is an iterative procedure. Different patients are identified in terms of similarity measures. Agents then try to get rid of these patients by trading them to other agents. The agent with the highest average dissimilarity bids out his different patient and negotiates with the rest of the agents. A remaining agent may accept this patient if his dissimilarity is less than the threshold of that agent. If there is more than one agent such that the dissimilarity of that patient is less than the threshold of each agent, then the patient will be assigned to the most similar agent. The algorithm converges when no agent can trade any patient. In phase three, the Offodile similarity is calculated between each patient and the worst case scenario patient. Next, the average Offodile similarity is calculated for each group. These groups are then sorted in descending order according to their average Offodile similarity. The higher the value of Offodile similarity, the higher priority of that group. Patients within groups are ranked according to their Offodile similarity with the worst case scenario patient. The Offodile similarity value

Dynamic patient grouping and prioritization

for each patient within each group represents the patient priority that is used in Eq. 10. The steps of phases one, two, and three are shown next.

5. Generate the priority graph. 6. Check if there is any new input from phase two. If yes, repeat steps 1 through 5. Otherwise, stop.

Phase one: 3.2.3 Application 1. Set the maximum number of patients or the time to terminate phase one. 2. A new patient arrives. If this is the first patient, then assign him/her to Agent 1. Otherwise, calculate dissimilarity of the new patient from the available agents. 3. If his/her dissimilarity is less than the threshold of any agent(s), then assign the patient to the closest agent. Otherwise, create a new agent, and assign the patient to the new agent. 4. Update the center of the global, centers of clusters, and the thresholds. 5. Check the maximum number of patients or the time to terminate the phase. If the number or the time has been reached, go to phase two. Otherwise, wait for a new patient to arrive and repeat steps 2 to 5. Phase two: 1. Calculate the average dissimilarity for each agent. Sort the agents in descending order with respect to the average dissimilarity. 2. The agent with the highest average dissimilarity bids out the different patient. 3. Calculate the dissimilarity between the different patient and the rest of the agents. 4. If the dissimilarity is less than a threshold for any agent(s), assign the different patient to the closest agent. Otherwise, go to the next agent on the list from step 1. 5. Check if the configuration has been reached twice. If yes, go the next agent on the list from step 1. Otherwise, award the different patient to the closest agent. Save the new configuration. 6. Update the centers of clusters and the thresholds for the altered agents. 7. Repeat steps 1 through 6 until none of the existing agents would trade the different patient or there is no new input from phase one. Phase three:

In order to show the procedure of the DGP algorithm, a group of patients were selected from Susquehanna Health Williamsport (SHW) Hospital in Williamsport, Pennsylvania. The data represents a period of 1 day. It includes 52 patients and 10 criteria: 1) age, 2) gender, 3) pain level, 4) systolic blood pressure, 5) diastolic blood pressure, 6) pulse, 7) respiration rate, 8) temperature, 9) oxygen saturation, and 10) expected treatment time. The expected treatment times have been generated using exponential distributions for each ESI level; these distributions are shown in section 4. The data was coded using the CC scheme developed in section 3.1.1. A Matlab routine was utilized to generate the coded data. The patients are organized based on the time at triage. Random numbers of patients, between 10 to 17 patients, were selected at a time and the algorithm was run. The output is shown in Table 3. It illustrates the group of the patient and the priority of the patient within each group. Figure 1 presents an example of the priority graph for each run on the given day. The x-axis represents patient serial number and y-axis represents patient priority. Priority is the Offodile similarity of any patient to the worst case scenario (most severe patient). Thus, the patient with the highest similarity has the highest priority.

4 Simulation results and analysis This section presents the investigation of the impact of using the DGP triage algorithm, and compares the ED performance measures under the conditions of using the aforementioned algorithm and the widely used ESI triage algorithm. The comparison is based on system performance measures, i.e., time-to-bed (TTB), length of stay (LOS), throughput, time in ED, percentage of tardy patients, and risk associated with tardy patients. 4.1 Conceptual model and process flow

1. Calculate the Offodile similarity between patients and the worst case scenario patient (most severe). 2. Calculate the average Offodile similarity for each agent. Then, sort them in descending order according to their Offodile similarity. 3. Treat agents in descending order. 4. Treat patients within groups (agents) in descending order with respect to their Offodile similarity.

In previous literature, Peck [57] used DES to analyze patient flow in the ED to study the effect of operational changes of the fast track (FT) emergency room (ER) on patient flow. In his study, FT ER accepts patients who are younger than 65 years but not pediatric, and who were assigned ESI level 4 or 5, with the purpose of reducing the LOS of less urgent patients in the ED. Peck’s simulation model was built and validated based on

O.M. Ashour, G.E. Okudan Kremer Table 3

Coded patient data and output

Age

Gender

Pain Level

Systolic BP

Diastolic BP

Pulse

Respiration Rate

Temperature

SaO2

Treatment Time

Group

Priority

3 3 3 . . . 3 3

2 1 1 . . . 1 1

10 10 0 . . . 10 8

2 2 2 . . . 2 5

3 2 3 . . . 1 4

5 5 1 . . . 1 1

1 1 1 . . . 1 1

3 1 2 . . . 1 2

2 1 1 . . . 1 1

2 1 2 . . . 1 1

1 1 4 . . . 4 1

0.615330 0.502117 0.361091 . . . 0.367376 0.512218

*The rest of the table can be found in [56]

his observations at the Newton-Wellesley Hospital (NWH) in Newton, Massachusetts, and thus reflects a realistic scenario. His conceptual model of the observed ED is adopted for this study. The ED has three ERs. The main ER has two sides. Side A has 12 beds and is open 24 h. Side B has 12 beds and is open from 10 am to 2 am. The pediatric ER has 8 beds and is open from 10 am to 2 am. The FT ER has 4 beds and is open from 3 pm to 11 pm. The ED has 3 triage rooms; two are open 24 h and the third is open from 10 am to 2 am. Incoming patient approaches the greeter’s desk to provide basic information and state his/her chief complaint. Greeters pass the information to a triage nurse who works on a FCFS basis unless the severity of the patient injury/illness requires immediate attention. Then the triage nurse conducts a preliminary examination, assigns the ESI level, and sends the patient to the waiting room. Patients under 18 years old are sent to the pediatric ER. In any ER room, patients undergo a nurse examination, nurse treatment, doctor examination, doctor treatment, testing, and consultation. Patients experience one or more of these

processes based on their needs. The patient then is either discharged to home or hospital, to another hospital, or to some other location. 4.2 Input /output The model assumptions and system variables include: interarrival times, treatment times, and delay times (e.g., greeting). The description of the variables can be found in [58]. Table 4 shows the expected treatment times by ESI level. The main ER will accept all ESI levels during the off-shift time of the FT and pediatric ERs. ESI level 1 patients go directly to the main ER or the pediatric ER (if they are under 18 and it is open). Time metrics that describe patient flow are identified as follows: 1) Average length of stay (LOS), defined as the length of time from the moment a patient steps into the ED after being greeted to when he is discharged from the ED system; 2) Average throughput, defined as the number of patients who are discharged from the ED per hour; 3) Average

Fig. 1 Priority for the patients from 1 to 10 in Table 3. (Number beside each dot represents the group of the patient)

1 2 1

1

4

4

3 4

4 3

Dynamic patient grouping and prioritization Treatment times by ESI level

Table 4 ESI level

Greeting time (minutes)

Registration time (minutes)

Triage time (minutes)

Treatment time (minutes)

1 2 3 4

Uniform(1,3) Uniform(2,5) Uniform(2,5) Uniform(2,5)

0 Uniform(5,10) Uniform(5,10) Uniform(5,10)

0 Uniform(15,20) Uniform(15,20) Uniform(15,20)

Exponential(55) Exponential(65) Exponential(60) Exponential(25)

5

Uniform(2,5)

Uniform(5,10)

Uniform(15,20)

Exponential(20)

time in ER, defined as the length of time from the moment a patient steps into the bed up until he is discharged from the ED system; 4) Average time-to-bed (TTB), defined as the length of time from the moment a patient leaves the greeting station up to when his treatment starts in an ER bed; 5) Percentage of tardy patients. In scheduling literature tardiness is defined as [59]:     T j ¼ max C j −d j ; 0 ¼ max L j ; 0 ð11Þ

Where, Tj is the tardiness of job j; Cj is the completion time of job j; and dj is the due date of job j. Lj is called the lateness of job j. The difference between lateness and tardiness is that tardiness can never be negative. There is one more relevant concept that is used in scheduling literature, the unit penalty of job j. Unit penalty can be defined as:  1 if C j > d j Uj ¼ ð12Þ 0 otherwise

In other words, when the tardiness is greater than 0, we assign 1. Otherwise, we assign 0. In our case, we are using the same analogy. Therefore, in our case, the definitions of lateness, tardiness, and the unit penalty function are as follows:     T 0 j ¼ max T T B j −U B j ; 0 ¼ max L0 j ; 0 ð13Þ

0

U j¼



1 0

if T T B j > U B j otherwise

ð14Þ

Where, T′ j is the tardiness of patient j; TTBj is the time-tobed of patient j; and UBj is the upper bound of the waiting time for patient j. The CTAS is used to set the upper bounds of waiting times for each ESI level: 1) Level I patients should have continuous nursing care, 2) Level II every 15 min, 3) Level III every 30 min, 4) Level IVevery 60 min, and 5) Level

V every 120 min [60]. These limits represent the due dates for each ESI level, and the actual TTB values represent the completion times. L' j is the lateness of patient j; and U' j is the unit penalty of patient j. Unit penalty is used to calculate the percentage of tardy patients for each ESI level as follows: X U 0i j j Percentage of Tardy Patientsi ¼ ð15Þ Ni

Where, i represents the ESI level (1, 2, 3, 4, and 5); Ni is the total number of patients who have ESI level i; and U' ij is the unit penalty of patient j with ESI level i. The final metric is 6) Risk associated with tardy patients, defined as the aggregation of the percentage of tardy patients across the ESI levels and weighted by the reciprocal of the ESI level. It is calculated as follows: Risk Associated with Tardy Patients X 51 ¼  % of Tardy Patientsi i i¼1

ð16Þ

Where, i represents the ESI level (1, 2, 3, 4, and 5); and the percentage of tardy patients is calculated using Eq. 15. 4.3 Computer model The computer model was built using Simio® version 4. For the regular ED that uses ESI to route patients, those patients at ESI level 1 do not go to the registration server. They go either to the main ER (age ≥ 18) or to the pediatric ER (age 3) && (PRIORITY > = 0.5) PATIENT_TYPE = 2; ELSEIF (AGE == 1 || AGE == 2) && (GROUP < = 3) && (PRIORITY < 0.5) PATIENT_TYPE = 3; ELSEIF (AGE == 1 || AGE == 2) && (GROUP > 3) && (PRIORITY < 0.5) PATIENT_TYPE = 4; ELSEIF (AGE == 3 || AGE == 4) && (GROUP < = 3) && (PRIORITY > = 0.5) PATIENT_TYPE = 5; ELSEIF (AGE == 3 || AGE == 4) && (GROUP > 3) && (PRIORITY > = 0.5) PATIENT_TYPE = 6; ELSEIF (AGE == 3 || AGE == 4) && (GROUP < = 3) && (PRIORITY < 0.5) PATIENT_TYPE = 7; ELSEIF (AGE == 3 || AGE == 4) && (GROUP > 3) && (PRIORITY < 0.5) PATIENTTYPE = 8; END

Appendix The rules to route patient in the ED system that utilizes ESI algorithm. The age is coded according to Table 1: IF (AGE == 1 || AGE == 2) && (ESI == 1) PATIENT_TYPE = 1; ELSEIF (AGE == 3 || AGE == 4) && (ESI == 1) PATIENT_TYPE = 2; ELSEIF (AGE == 1 || AGE == 2) && (ESI == 2) PATIENT_TYPE = 3; ELSEIF (AGE == 3 || AGE == 4) && (ESI == 2) PATIENT_TYPE = 4; ELSEIF (AGE == 1 || AGE == 2) && (ESI == 3) PATIENT_TYPE = 5; ELSEIF (AGE == 3 || AGE == 4) && (ESI == 3) PATIENT_TYPE = 6; ELSEIF (AGE == 1 || AGE == 2) && (ESI == 4) PATIENT_TYPE = 7; ELSEIF (AGE == 3 || AGE == 4) && (ESI == 4) PATIENT_TYPE = 8; ELSEIF (AGE == 1 || AGE == 2) && (ESI == 5) PATIENT_TYPE = 9; ELSEIF (AGE == 3 || AGE == 4) && (ESI == 5) PATIENT_TYPE = 10; END The rules to route patient in the ED system that utilizes DGP algorithm. The age is coded according to Table 1: IF (AGE == 1 || AGE == 2) && (GROUP < = 3) && (PRIORITY > = 0.5)

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Dynamic patient grouping and prioritization: a new approach to emergency department flow improvement.

The demand on emergency departments (ED) is variable and ever increasing, often leaving them overcrowded. Many hospitals are utilizing triage algorith...
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