Fuzzy AHP and utility theory based patient sorting in emergency departments

332 Int. J. Collaborative Enterprise, Vol. 1, Nos. 3/4, 2010 Fuzzy AP and utility theory based patient sorting in emergency departments Omar. Ashour* The arold and Inge arcus Department of Industrial and anufacturing Engineering, The Pennsylvania State University, 201 Engineering Unit B, University Park, PA 16802, USA Fax: 814-883-7229 E-mail: oma110@psu.edu *Corresponding author Gül E. Okudan The arold and Inge arcus Department of Industrial and anufacturing Engineering, and School of Engineering Design, The Pennsylvania State University, 213T ammond Building, University Park, PA 16802, USA E-mail: gek3@engr.psu.edu Abstract: Triage, a classification system used to separate patients based on the acuity of their condition, is considered in this study. Triage process relies on the nurse s interaction with the patient (e.g., a conversation on symptoms, visual observation, and vital sign measurements), and the subsequent severity classification. owever, potential miscommunication, and thus uncertainty could be present in this process. In order to account for this uncertainty, a triage algorithm that uses fuzzy analytic hierarchy process (FAP) along with the multi-attribute utility theory (AUT) to sort the patients is presented. FAP is used to get an acuity score on the chief complaint, and AUT integrates this score with age, gender, and pain level to provide a final prioritisation. In the paper, a clinical case study is provided for which we used an expert nurse s judgments to build the FAP and the utility functions. Keywords: decision making; fuzzy analytic hierarchy process; FAP; multi-attribute utility theory; AUT; triage; emergency department; ED; healthcare. Reference to this paper should be made as follows: Ashour, O.. and Okudan, G.E. (2010) Fuzzy AP and utility theory based patient sorting in emergency departments, Int. J. Collaborative Enterprise, Vol. 1, Nos. 3/4, pp.332 358. Biographical notes: Omar. Ashour is a PhD candidate in the Department of Industrial and anufacturing Engineering at Pennsylvania State University. e received his Sc and BSc in Industrial Engineering from Jordan University of Science and Technology in 2007 and 2005, respectively. is research interests include decision making, healthcare engineering, and human factors. Copyright 2010 Inderscience Enterprises Ltd.

Fuzzy AP and utility theory based patient 333 Gül E. Okudan received her PhD in Engineering anagement and Systems Engineering from University of issouri-rolla. er research interests focus on applied decision-making to improve products and systems (e.g., healthcare delivery systems). er published work appears in journals such as Journal of echanical Design, Journal of Engineering Design, Journal of Intelligent anufacturing, Journal of Engineering Education, European Journal of Engineering Education and Technovation. She is a member of IIE and ASE. She is also a National Research Council-US AFRL Summer Faculty Fellow of the uman Effectiveness Directorate for 2002, 2003 and 2004. The results of her research efforts have been presented in publications (two books, one book translation, 28 journal articles, 101 refereed conference papers, and nine other articles). These research efforts have received funding and other support from several sources (e.g., National Science Foundation (NSF), Air Force Research Laboratory, GE Transportation, Autodesk, Inc., and Veeder Root, Inc.). 1 Introduction Emergency departments (EDs) are considered as vital components of the nation s healthcare safety net (Richardson and wang, 2001a; 2001b; Weinick and Burstin, 2001), which are responsible for 45% 65% of hospital admissions (ahapatra et al., 2003). There were 119.2 million visits to hospital EDs in 2006 (Pitts et al., 2008). Thus, the ED performance is a very critical issue. ost EDs in major areas are often overcrowded, and hence, hospitals utilise a triage system to sort patients according to the severity of the illness/injuries (Andersson et al., 2006). any hospitals in the USA utilise the five-level emergency severity index (ESI) to sort patients into five groups with clinically meaningful differences in projected resource need and therefore, associated operational needs. The ESI designates the most acutely ill patients as level 1 (highest level) or 2, and uses the number of resources a patient needs to determine levels 3 to 5 (lowest level) (Tanabe et al., 2004). Level-1 and 2 patients can be taken directly to the treatment area for rapid evaluation and treatment, while level-3 to 5 are sent to the waiting area (Gilboy et al., 2005). Even though the number of resources is the primary decision rule to determine levels 3 to 5, physiological and descriptive variables can be used to determine a priority order for patients (Claudio and Okudan, 2010). The physiological variables include heart rate, systolic and diastolic pressure, respiration rate, body temperature, and oxygen level. Indeed, Claudio and Okudan (2010) presented a utility theory based patient prioritisation, which takes into account the patient vital signs. The descriptive variables include age, gender, primary patient complaint, and pain level as described by the patient. Ashour and Okudan (2010) presented a utility theory based approach accounting for the ESI, gender, age, and the pain level. In the ED setting, the triage nurse assigns the ESI level, and then decides which patient will be treated first. The skills or the contextual factors that are needed to make accurate ED triage decisions are not known to this date as the triage decision making is a complex process (Göransson et al., 2008). uch of the decision making is mainly based on nurse s experience (Patel et al., 2008), knowledge, and intuition (Andersson et al., 2006; Benner and Tanner, 1987; Cone and urray, 2002; Gurney, 2004). owever, Göransson et al. (2008) presented findings revealing that the triage nurse decision making

334 O.. Ashour and G.E. Okudan during ED triage varied, some studies showed that there is a difference between the expert and the beginner level nurses, while others found that less experienced and more experienced triage nurses decision making was largely the same. oreover, Göransson et al. (2006) investigated the quality of the triage nurse decisions. In their study, they used the Canadian Triage and Acuity Scale (CTAS) in Swedish EDs, and they studied the relationship between the personal characteristics, e.g., triage experience, of the registered nurses (RNs) and the accuracy in their acuity rating of patient scenarios. They concluded that there is no relationship between personal characteristics of the RNs and their ability to triage, and they expected that the decision making might be affected by intrapersonal characteristics, e.g., RNs decision-making strategies. They recommended more research on the RNs decision making during the triage process to identify the essential characteristics of the triage nurse during the triage process (Göransson et al., 2006; 2008). In general, patient prioritisation is a decision making problem. Decisions in EDs involve a lot of uncertainty with respect to what a patient s illness and/or injuries are (Claudio and Okudan, 2010). Similar symptoms for different illness types and uncertainty due to subjective variables, individual differences, e.g., ESI and pain level variables complicate triage decision making. The uncertainty in the decision making process could also come from inadequate understanding, incomplete information, and undifferentiated alternatives (Krishnamurthy, 2005). In addition, a study done by Fields et al. (2009) investigated the discrepancies in decisions made across nurses in three clinical settings: Susquehanna ealth Williamsport ospital (SW), ount Nittany edical Center (NC), and ershey edical Center (C). In this study, Spearman s rank correlation comparison method was used. The results show that there are differences in patient rankings among nurses at different hospitals, and even within the same hospital. As per the summary presented above, the ESI algorithm, currently in use at hospitals, is lacking in many ways. First, it does not consider prioritisation of patients who are sent to wait (i.e., ESI levels 3 5); it assumes a first come first served routine. It neither takes into account the descriptive variables (i.e., age and gender), nor the pain level. Beyond these issues, while based on our interviews we ascertained that the relative importance of the vital signs change based on the primary patient complaint, the current ESI algorithm does not take this shift in relative importance into account. These problems are addressed in this paper through a structured process that takes into account uncertainty consideration, and uses fuzzy analytic hierarchy process (FAP) and multi-attribute utility theory (AUT) in a complementary fashion. The approach presented builds upon our preliminary work. Accordingly, we first review our preliminary work below, and then present the algorithm in detail. 2 Preliminary work Emergency records are records of the patients from the moment of arrival to the ED until they are discharged to another area or to home. Figure A1 (in Appendix A) shows an actual record for a patient with chest pain complaints. ost EDs keep these records. In the example shown, patient name and personal information were omitted due to privacy concerns. In our preliminary work (Ashour and Okudan, 2010), we used the utility theory to prioritise patients at an ED. A clinical data set, which has collected from SW, was used to build the overall utility function. Patients age range varied between 3 92.

Fuzzy AP and utility theory based patient 335 Patients were ranked based on ESI and three descriptive variables: age, gender and pain level. The utility theory takes into account the uncertainty that comes from the subjectivity in the decision making process, for example, the pain level (i.e., two patients might have the same symptoms and have the same illness/injury but one of them gives five and the other eight out of ten for the pain level). The overall utility function is shown below: 1 n U( x1, x2, L, xn) = ( KkU ( ) 1) 1 i 1 i i x i + (1) K = 4 1 i i i 0.9569 i= 1 U( x1, x2, x3, x4) = ( 0.9569 ku ( x ) + 1) 1 U( x1, x2, x3, x4) = ({[ 0.9569 0.5435 ( 0.250x1+ 1.236) + 1] 0.9569 x2 [ 0.9569 0.6016 ( 0.02524 + 0.01 exp ( )) + 1] 19.437 [ 0.9569 0.1031 (x 1) + 1] [ 0.9569 0.8000 x4 ( 0.09569 + 0.09569 exp( )) + 1]} 1) 8.204 3 (2) In this preliminary work, though we contributed to the triage decision making problem, our solution had shortcomings. While physiological variables influence patient symptoms, and hence the nurse decisions during triage, they were not considered explicitly; they were implicitly covered within the ESI level. Patel et al. (2008) studied the decision making process of nurses in the general ED and concluded that nurses decisions are based on generated hypotheses based on both the information given by the patient and on single symptoms perceived as being characteristic of diagnosis. Further, based on our interviews at clinical settings, while we have ascertained that the relative importance of vital signs changes across different complaints, neither the complaints nor the relative importance shifts were considered. In this study, we are aiming to extend the utility function presented in our previous study (Ashour and Okudan, 2010) to incorporate the relation between the patient complaints and the vital signs as well as the descriptive variables. The relation between the vital signs and the complaints are operationalised as the changing relative importance of vital signs. What we mean by the relation is that the nurse might differently interpret the vital signs of two patients if one of them has a chest pain and the other has a headache (i.e., relative importance of vital signs might change dependent on the complaint the patient has). Consequently, the vital signs might contribute to the overall utility value in different weights. The overall utility function aggregates the utilities of descriptive variables (age, gender, and pain level) and the pretreated values of the physiological variables (pulse, blood pressure, temperature, respiration rate, and oxygen saturation level). The values of the vital signs are treated using the FAP, and the FAP output is used in the overall utility function. The main goal for having the utility function is to quantify and minimise the associated potential hazard that might cause harm to the patient, or the clinical risk, and hence to arrive at an appropriate patient priority ranking.

336 O.. Ashour and G.E. Okudan 3 Fuzzy analytic hierarchy process In ED settings, it is generally difficult to ascertain the patient information because of the dynamic nature of the patient status. For example, the vital signs change over time, and assessment of certain variables, such as pain level, is subjective (Fields et al., 2009). The use of fuzzy set theory allows the decision makers to incorporate unquantifiable information, incomplete information, non-obtainable information and partially ignorant facts into decision model (Kulak et al., 2005), and hence is appropriate for such settings. The data relevant to the criteria (incomplete data) can be expressed as fuzzy data. The fuzzy data can be linguistic terms, fuzzy sets, or fuzzy numbers. If the fuzzy data are in linguistic terms, they are transformed into fuzzy numbers. Then, these numbers (or fuzzy sets) are assigned crisp scores. The analytic hierarchy process (AP) is a systematic procedure to structure a complex problem in the form of a hierarchy and to evaluate a large number of quantitative and qualitative factors under multiple potentially conflicting criteria. Developed by Saaty (1980, 1994), AP has a number of shortcomings. Lee et al. (2001) summarised these as: 1 AP is mainly used in crisp decision applications 2 although the use of discrete scale of 1 9 has the advantage of simplicity, AP does not take into account the uncertainty associated with mapping one s judgment to a number 3 subjective judgments, selection and preference of decision makers exert a strong influence in the method. Fuzzy logic is introduced to AP to overcome these shortcomings. Therefore, when the input information or the relations between criteria are imprecise or uncertain, the adoption of fuzzy logic is recommended. FAP algorithm is described below (Lee et al., 2001): 1 construct a hierarchical structure for the problem to be solved 2 establish the fuzzy judgment matrix (A) and weight vector (W) 3 calculate weight values, from fuzzy scores of alternatives 4 rank the fuzzy scores to determine the optimum alternative. 4 Proposed algorithm Our proposed decision algorithm is illustrated in Figure 1. The process starts by identifying the patient status as one would in the current ESI algorithm (Gilboy et al., 2005). Then, if the patient requires any immediate intervention, he is considered to be in critical state. After this stage, the procedure progresses as described below: 1 Is the patient in need of immediate intervention? If the response is affirmative, he is a critical state patient. If no, he goes to Step 2. 2 The triage nurse asks the patient about his complaint, pain level, age, and gender, and takes his/her vital signs.

Fuzzy AP and utility theory based patient 337 3 The complaint and the vital signs data are treated using the FAP as explained above to yield what we referred to as pretreated data. 4 The data from Steps 2 and 3 is processed by the overall utility function to give the utility value for each patient. 5 Patients with high utility values go to the treatment area first, and the others with the lower value can wait in the waiting room. Then they are treated in descending order of priority based on the overall utility values. This algorithm is applied to a clinical data set as explained below. Figure 1 Proposed algorithm Incoming patient Require immediate life-saving intervention Yes Critical state Immediate treatment No igh risk situation OR Confused/lethargic/disoriented? OR Severe pain/distress Yes Record: chief complaint, vital signs, age, gender, pain level No Apply FAP and utility theory Sort patients based on the utility value Very high value? Yes No Send him/her to the waiting room eta-stable state or Stable state

338 O.. Ashour and G.E. Okudan Table 1 Patients data

4.1 Data set Fuzzy AP and utility theory based patient 339 The actual clinical values in the data set were collected from the ED of SW. Susquehanna ealth is a three-hospital health system including Divine Providence ospital, uncy Valley ospital and the Williamsport ospital & edical Center located in north central Pennsylvania. The ED at The Williamsport ospital is divided into two separate treatment areas: Emergency department and UrgiCenter. The Emergency area is staffed and equipped to provide care in life threatening situations or in times of emergency. In addition, ambulance patients are also treated in this area. Patients with less critical medical conditions receive care and treatment in the UrgiCenter. These two areas allow for a flow of patients in a timely and efficient manner based on their injury or illness (Susquehannahealth Official Site, 2009). The triage area is a separate room where the patient can talk privately to the nurse about his/her needs. The nurse will assess the patient vital signs such as blood pressure and temperature and ask questions about his/her illness or injury to determine whether the emergency room or the UrgiCenter is most appropriate for his/her specific needs. During triage, the nurse may also determine the need for X-rays prior to see a care provider. The provider can then see the patient and his X-rays, eliminating delays. If his/her illness or injury is life threatening, the patient will be taken to an examination room and treated immediately. Otherwise, the patient will be seated in the waiting area until registered. Table 1 shows the collected data set for 19 patients, where each patient record has the following information: the assigned ESI level, age, gender, pain level, systolic and diastolic blood pressure, pulse, respiration rate, body temperature, and oxygenation level (SaO 2 ). 4.2 Patient complaint Every patient who comes to the ED has a chief complaint. These complaints are classified into 17 categories as follows (Claudio et al., 2009): 1 neurological complaints 2 chest pain complaints 3 abdomen/male 4 abdomen/female 5 seizure 5 headache 7 psychiatric complaints/suicide attempt 8 head/face trauma 9 general medicine complaints 10 respiratory complaints 11 alleged assault 12 multiple trauma

340 O.. Ashour and G.E. Okudan 13 motor vehicle crash 14 extremity complaint/trauma 15 back pain/injury 16 skin rash/abscess 17 eye, ear, nose, throat & dental complaints As shown in Step 2 (of Figure 1), the nurse records the patient complaint, and the physiological and descriptive variables. After that the nurse assigns the ESI level for the patient. Beyond what is commonly applied during triage as prescribed by Gilboy et al. (2005), there is no systematic way to assign the ESI levels. Due to the presence of the uncertainty in taking such decisions we adopt the FAP approach (Lee et al., 2001). Our selection of this approach stems from the interviews we conducted with expert triage nurses. As per these interviews, we have identified that the relative importance of vital signs changes given the complaint the patient has. In other words, the triage nurse assigns weights to the vital signs unequally based on the patient complaint, and then identifies the ESI level based on that weighting. In order to ascertain how the relative importance weights of vital signs changes, we have conducted further interviews with expert triage nurses, where nurses rated each vital sign for their importance with respect to the patient complaint using the fuzzy number scale presented in Table 2. The hierarchy of this problem is illustrated in Figure 2. In the FAP, vital signs get different weights. In addition, each patient s vital signs are rated based on Tables (B1 B6); these tables were extracted with the aid of expert triage nurses. Then, the final score for each patient is calculated using the FAP as illustrated by Lee et al. (2001). These scores are then converted via a utility function into utility values in order to calculate the overall utility value (or priority ranking) for each patient. Tables (B7 B23) present the ratings of the vital signs with respect to each chief complaint. Table 2 Fuzzy numbers for linguistic variables Fuzzy Number Attribute (temperature, pulse,, etc) 1 % Low (L) 3 % Relatively low (RL) 5 % edium () 7 % Relatively high (R) 9 % igh () Figure 2 Problem hierarchy (* 17 complaints) (see online version for colours)

Fuzzy AP and utility theory based patient 341 5 Fuzzy analytic hierarchy process implementation In this problem, we have 19 alternatives (patients) and six criteria (vital signs). The first step in the procedure is to build the problem hierarchy. Figure 2 shows the problem hierarchy. The fuzzy judgment matrix for all patients is provided in Table 3. A atlab code was used to do the calculations for the FAP. After carrying out the fuzzy multiplication and addition, the fuzzy scores, the mean, and the standard deviation for all patients, which are listed in Table 4, are obtained. The utility function is built for the mean value in the next section. This way, the patient complaint, which is better represented due to the more appropriate consideration of vital signs, is considered in the overall utility value. Table 3 Fuzzy ratings of patients with respect to each criterion and the weight vectors # Systolic blood pressure Diastolic blood pressure Pulse Respiration rate Temperature SaO 2 Weight vectors P1 3 3 1 1 1 1 1 9 9 9 9 9 P2 3 1 3 1 1 1 5 5 5 5 5 5 P3 1 1 3 1 7 1 1 5 5 5 5 5 P4 5 3 9 1 1 3 5 5 5 5 5 5 P5 1 1 1 1 3 1 5 5 5 5 5 5 P6 3 5 3 1 3 1 5 5 5 5 5 5 P7 5 5 1 1 3 1 1 5 5 5 3 3 P8 5 5 1 9 5 1 5 5 5 5 5 3 P9 7 5 9 1 1 1 1 9 9 9 9 9 P10 7 5 3 1 1 1 1 5 5 5 3 3 P11 3 1 1 1 3 1 5 5 5 5 5 3 P12 3 1 1 1 3 1 1 5 5 5 5 5 P13 1 1 1 5 3 1 5 5 5 5 5 5 P14 3 3 1 1 1 1 1 9 9 9 9 9 P15 3 1 1 1 3 1 5 5 5 5 5 3 P16 3 1 1 1 1 1 1 9 9 9 9 9 P17 1 1 5 1 1 1 5 5 5 5 5 3 P18 3 3 1 1 3 1 5 5 5 5 5 5 P19 5 1 1 3 1 1 5 5 5 5 5 5

342 O.. Ashour and G.E. Okudan Table 4 ean and standard deviation of the fuzzy scores # Fuzzy scores ean Standard deviation P1 36 52 168 85.33 0.8649 P2 18 50 154 74.00 0.8427 P3 28 66 170 88.00 0.9006 P4 42 100 224 122.00 1.4407 P5 18 40 140 66.00 0.7047 P6 24 80 196 100.00 1.2827 P7 24 60 168 84.00 0.9360 P8 52 118 246 138.67 1.6216 P9 96 112 252 153.33 1.2276 P10 22 58 162 80.67 0.8809 P11 16 48 148 70.67 0.7902 P12 16 38 134 62.67 0.6562 P13 24 60 168 84.00 0.9360 P14 36 52 168 85.33 0.8649 P15 16 48 148 70.67 0.7902 P16 36 38 150 74.67 0.7096 P17 22 48 148 72.67 0.7376 P18 18 60 168 82.00 0.9980 P19 24 60 168 84.00 0.9360 6 ulti-attribute utility theory implementation The exponential distribution is used to model the utility functions for the variables: age, pain level, gender, and the pretreated value of the vital signs. The equations (3 6) that are necessary to formulate the single attribute utility functions are provided below. In the formulas, A and B are scaling factors that scale the utility values (U i (x i )) between 0 and 1 (Thevenot et al., 2007): U ( x ) = A B. exp ( x / RT ) (3) i i i in( xi) in( xi) ax( xi) A = exp / exp exp RT RT RT in( xi) ax( xi) B = 1/ exp exp RT RT (( ) ) RT = CE ln 0.5 U ( ax( x )) 0.5 U ( in( x )) + A / B (6) i i i i i i where RT: risk tolerance in (x i ): minimum value for attribute i across all alternatives (4) (5)

Fuzzy AP and utility theory based patient 343 ax (x i ): maximum value for attribute i across all alternatives CE: certainty equivalent The attributes are not mutually preferentially independent, i.e., vital signs pretreated value is not independent from the others, and hence a multiplicative aggregation form is adopted. The sign of risk tolerance (RT) depends on the risk behaviour of the decision maker (D) regarding a specific attribute. RT is negative for risk prone, and positive for risk averse behaviour. The value of CE is calculated using a lottery with 50% probability to get the best or the worst alternatives. In general, the decision maker is asked a series of lottery questions in order to discern the utility functions, and so was done for this study. The overall utility function combines all the physiological and descriptive variables. In the preliminary work, the overall utility function was calculated based only on the descriptive variables: age, gender, and pain level and the assigned ESI level (Ashour and Okudan, 2010). In this study, the utility function from the preliminary work is corrected by excluding the single utility function of the ESI level, and including all the single attribute utility functions of the pretreated value of the vital signs. The following subsections illustrate the procedure of constructing the utility functions for the pretreated value of the vital signs. 6.1 Single attribute utility function of the pretreated value of vital signs The D was asked several questions regarding his opinion on the criticality of the patient at several levels of pretreated value of the vital signs (i.e., the mean). The D has a risk prone attitude towards the mean. e would give higher utility values, if the mean increases from the certainty equivalence level (CE) to its maximum value in comparison to the increases from the smaller consequence values to the CE. Therefore, the RT has a negative value. Accordingly, CE should be greater than the expected value of the utility function but less than the maximum consequence value. The expected utility value is calculated by setting all the rates with respect to each vital sign and the weight vector to 5, % which is the medium value. We infer that the CE for the mean is equal to 270. Solving equations (4 6) iteratively, we get the RT = 147.89756. The utility function for the mean is given in equation (7). 1 1 (x 1 /147.99756) U (x ) = 0.114978817 + 0.099086806exp ) (7) 6.2 Single utility functions of age, gender, and pain level Single attribute utility functions for patient age, gender, and pain level were used as developed in the preliminary work (Ashour and Okudan, 2010). See equation (1) for x 2 : patient age, x 3 : patient gender, and x 4 : patient pain level. 7 Attribute tradeoffs In order to calculate attribute-scaling parameters, we follow the procedure provided by Keeny and Raiffa (1993). The first step is to rank the attributes in order of importance. The nurse ranked these attributes in order of importance. The resultant order is: pain level

344 O.. Ashour and G.E. Okudan (the scaling parameter k 4 ) > the mean (k 1 ) > the age (k 2 ) > the gender (k 3 ). In order to determine k i values, we start with the most important attribute (k 4 ), the pain level. By using lottery questions, the indifference point of comparing two choices is found as shown in Figure 3. Figure 3 ean scaling factor lottery p U(358, 90, 2, 20) = 1 CE 1-p U(22, 18, 1, 0) = 0 or U(22, 18, 1, 20) EV(CE) = p*(1) + (1-p)*0 In the figure, on the left, a lottery is presented where the best consequence is achieved with a probability of p; and on the right, the certain case for getting the best value for k 4, and the worst for rest of the attributes is presented. The D should find the value of probability, p, such that the D is indifferent between the two choices. The attributes in Figure 4 are arranged in the same order as (mean, age, gender, pain level). The D indicated that the value of p = 0.8 makes him indifferent between the two choices. Therefore, the value of k 4 = 0.8: p*(1) + (1-p)*(0) = k 1 *(0) + k 2 *(0) + k 3 *(0) + k 4 *(1) => k 4 = p = 0.8 (8) Additional decision problems are constructed to find the values of the remaining scaling factors. The first decision problem compares pain level and mean. The following equality was constructed to make the two choices indifferent: U (pain level, 22) ~ U (0, mean) (9) The first choice contains an unknown value of pain level and the lowest value of mean. The choice is compared to the lowest value of pain level and unknown value of mean. The D indicated that the indifference point is achieved when pain level is 18 and the mean is 330. The utilities are then calculated using the pain level s single attribute utility function and the mean single utility function to obtain a relationship between k 4 and k 1 as shown below: U (18, 22) ~ U (0, 330) (10) k 4 *U 4 (18) + k 1 *U 1 (22) = k 4 *U 4 (0) + k 1 *U 1 (330) (11) k 4 * 0.762792+ k 1 *(0) = k 4 *(0) + k 1 *0.80769 (12) k 1 = 0.754 (13)

Fuzzy AP and utility theory based patient 345 A similar decision problem is constructed between pain level and age: U (pain level, 18) ~ U (0, age) (14) The D determined that the indifference point is achieved when the pain level is 14 and the age is 80 years. The utilities are then evaluated using single utility functions for the pain level and the age. The value of k 2 is calculated as follows: U (16, 18) ~ U (0, 80) (15) k 4 *U 4 (16) + k 2 *U 2 (18) = k 4 *U 4 (0) + k 2 *U 2 (80) (16) k 4 *0.43152+ k 2 *(0) = k 4 *(0) + k 2 * (0.58781) (17) k 2 = 0.587 (18) Finally, another decision problem was built between pain level and gender: U (pain level, 1) ~ U (0, gender) (19) The nurse says that the indifference point is achieved when the pain level is 10 and the gender is 2. The utilities are then evaluated using the single functions of the pain level and the gender. In addition, the value of k 3 is calculated as follows: U (10, 0) ~ U (0, 2) (20) k 4 *U 4 (10) + k 3 *U 3 (0) = k 4 *U 4 (0) + k 3 *U 3 (2) (21) k 4 * 0.228079+ k 3 *(0) = k 4 *(0) + k 3 *(1) (22) k 3 = 0.182 (23) The values of k i s are shown in Table 5 below. Table 5 Values of k i s k i Value k1 0.754 k2 0.587 k3 0.182 k4 0.800 8 Aggregated utility The multiplicative form (Keeney and Raiffa, 1993) can be used to form the overall utility function: n U( x) = (1/ K) ( K ku ( ) 1) 1 i 1 i i x = i + (24)

346 O.. Ashour and G.E. Okudan where U(x): the multi-attribute utility of x x i : the performance level of attribute i U i (x i ): the single attribute utility for attribute i i = 1, 2,, n attributes k i : attribute-scaling parameter for attribute i K: normalising constant The normalising constant, K, is derived by the following relationship using the scaling parameters. n 1 + K = (1 + Kki ) (25) i= 1 Solving for K, yields K = 0.9804. Now we can calculate equation (24) to get the overall utility function value for each patient. Table 6 provides the summary of the values for each attribute and for each patient, the utility value for each attribute, the calculated overall utility, and the ranking of the patients. 9 Results Table 6 shows the ranking of the patients based on the results of this study and our preliminary work study (Ashour and Okudan, 2010). For both studies, the first and the last patient in the rank are the same, patient #8 and patient #12. In order to test the correlation between these ranking, Spearman s rank correlation method is applied. The ranking association is tested between the overall utility rankings for the previous and current study. initab was employed to get the ranking of the patients, Table 7 provides the patients ranking for the overall rankings; the ranks are in ascending order. In general, a smaller value of correlation represents a smaller ranking association. We have also tested whether the value of the correlation (ρ) is significantly different from zero, the value of ρ is always between 1 and 1. Student s t-distribution with degrees of freedom n-2 is used for testing; the value of t is calculated using equation (26): 2 t = ρ / (1 ρ )/( n 2) (26) The calculated values for the ρ and the t are 0.849 and 6.625, respectively. For the level of significance α = 0.01, there is a high association between the overall utility rankings. On the other hand, the rankings of the two methods are different, thus, patient s chief complaint has an impact on the decision making process at EDs. Patel et al. (2008) concluded that the decision making process of nurses in the ED is based on generated hypotheses on both the information given by the patient and on single symptoms (chief complaint) perceived as being characteristic of diagnosis.

Fuzzy AP and utility theory based patient 347 Table 6 Patient ranking based on utility theory function

348 O.. Ashour and G.E. Okudan Table 7 Overall ranking in ascending order # U (patient*) Ranking U (patient) Ranking P1 0.552 15 0.279 8 P2 0.444 7 0.333 11 P3 0.340 2 0.144 3 P4 0.550 14 0.479 18 P5 0.342 3 0.132 2 P6 0.536 12 0.396 16 P7 0.478 9 0.378 12 P8 0.919 19 0.870 19 P9 0.466 8 0.217 5 P10 0.590 16 0.394 15 P11 0.493 10 0.388 13 P12 0.267 1 0.031 1 P13 0.411 6 0.299 9 P14 0.495 11 0.263 7 P15 0.591 17 0.390 14 P16 0.536 13 0.314 10 P17 0.356 5 0.228 6 P18 0.352 4 0.153 4 P19 0.598 18 0.405 17 Note:* Results based on the previous study. Source: Ashour and Okudan (2010) In the preliminary work we showed that a patient with ESI2-level should be served after a patient with an ESI3-level, and we explained that due to the nurse s decision making (Ashour and Okudan, 2010). We also pointed out studies that showed the possibility of undertriage or overtriage (Cooper, 2004; Tanabe et al. 2004; Wuerz et al., 2000; Wuerz, 2001). Under estimation (over estimation) of emergency level occurs when the triage nurse allocates a triage level of higher (lower) urgency than the required. Overtriage decision might not affect the overtriaged patient himself, but it might affect other patients by increasing their waiting time. On the contrary, the undertriaged patient might be affected because his waiting time until medical intervention will be increased. According to Beveridge et al. (1999) and Considine et al. (2004), overtriage and undertriage situations might occur in the Australian Triage Scale and in the Canadian Triage and Acuity Scale, respectively. ence, the reason behind prioritising some patients with ESI2- level after some patients with ESI3-level could be that the triage nurse might overtriage these patients and give them higher priority than needed. 10 Conclusions Sorting patients in EDs is a decision making problem. This problem involves a lot of uncertainty as it depends on the nurse s knowledge, experience, and intuition and on the

Fuzzy AP and utility theory based patient 349 subjectivity of patient s attributes, such as, pain level. FAP and the AUT were selected to incorporate uncertainty appropriately to the decision making process. FAP and AUT help D to improve his consistency, reliability, and repeatability which means the same decision can be suggested for the same scenario. Our model incorporates the physiological and the descriptive variables in one model. It can be used to sort patients based on vital signs, age, gender, and pain level; thus, it reduces the stress and the strain on triage nurses and improve service quality for patients. oreover, the proposed methodology is a step in validating the triage nurse decisions. It should be acknowledged that using more data will improve the accuracy of the presented model. Overall, the algorithm presented is an aid to help the nurse make complex triage decisions, and hence reduce the cognitive stress, improve productivity and the quality of the healthcare delivery in the EDs. The Spearman s rank correlation showed that there is a high association between the overall utility rankings of the previous and the current study confirming that the preliminary study validates the current outcomes. We assert, however, a larger data set should be used to build a more accurate model. A real-time adjustment for the patient sequence can be implemented using our approach and wireless wearable devices that transmit patients vital signs on a real-time basis. References Andersson, A.K., Omberg,. and Svedlund,. (2006) Triage in the emergency department-a qualitative study of the factors which nurses consider when making decisions, Nursing in Critical Care, Vol. 11, No. 3, pp.136 145. Ashour, O.. and Okudan, G.E. (2010) Utility function-based patient prioritization using emergency severity index and descriptive variables, International Journal of Industrial Ergonomics, under review. Benner, P. and Tanner, C. (1987) Clinical judgment: how expert nurses use intuition, The American Journal of Nursing, Vol. 87, pp.23 31. Beveridge, R., Ducharme, J., Janes, L., Beaulieu, S. and Walter, S. (1999) Reliability of the Canadian emergency department triage and acuity scale: interrater agreement, Ann Emerg ed, Vol. 34, pp.155 159. Claudio, D. and Okudan, G.E. (2010) Utility function based patient prioritization in the emergency department, European J. Industrial Engineering, Vol. 4, No. 1, pp.59 77. Claudio, D., Ricondo, L., Freivalds, A. and Okudan, G.E. (2009) Physiological and descriptive variables as predictors for emergency severity index, Proceedings of the IIE Annual Conference and Expo 2009, (IERC 2009), ay 30 Jun 3, 2009, iami, FL. Cone, K.J. and urray, R. (2002) Characteristics, insight, decision making, and preparation of ED triage nurses, Journal of Emergency Nursing, Vol. 28, No. 5, pp.401 406. Considine, J., LeVasseur, S.A. and Villanueva, E. (2004) The Australasian triage scale: examining emergency department nurses performance using computer and paper scenarios, Ann Emerg ed, Vol. 44, pp.516 23. Cooper, R.J. (2004) Emergency department triage: why we need a research agenda, Ann Emerg ed, Vol. 44, pp.524 526. Fields, E., Claudio, D., Okudan, G., Smith, C. and Freivalds, A. (2009) Triage decision making: discrepancies in assigning the emergency severity index, Proceedings of the IIE Annual Conference and Expo 2009 (IERC 2009), iami, FL, ay 30 June 3, 2009. Gilboy, N., Tanabe, P., Travers, D.A., Rosenau, A.. and Eitel, D.R. (2005) Emergency Severity Index, Version 4: Implementation andbook, ARQ Publication No. 05-0046-2, Agency for ealthcare Research and Quality, Rockville, D.

350 O.. Ashour and G.E. Okudan Göransson, K.E., Ehnfors,., Fonteyn,.E. and Ehrenberg, A. (2008) Thinking strategies used by registered nurses during emergency department triage, Journal of Advanced Nursing, Vol. 61, No. 2, pp.163 172. Göransson, K.E., Ehrenberg, A., arklund, B. and Ehnfors,. (2006) Emergency department triage: is there a link between nurses personal characteristics and accuracy in triage decisions?, Accident and Emergency Nursing, Vol. 14, pp.83 88. Gurney, D. (2004) Exercises in critical thinking at triage: prioritizing patients with similar acuities, Journal of Emergency Nursing, Vol. 87, No. 1, pp.514 516. Keeney, R.L. and Raiffa,. (1993) Decisions with ultiple Objectives: Preferences and Value Tradeoffs, Cambridge University Press, Cambridge, UK. Krishnamurthy, S. (2005) Normative decision making in engineering design, in Lewis, K.E., Chen, W. and Schmidt, L.C. (Eds.): Decision aking in Engineering Design, pp.21 34, ASE, New York. Kulak O., Durmusoglu,.B. and Tufekci, S. (2005) A complete cellular manufacturing system design methodology based on axiomatic design principles, Computers & Industrial Engineering, Vol. 48, No. 4, pp.765 778. Lee, W.B., Lau,., Liu, Z. and Tam, S. (2001) A fuzzy analytic hierarchy process approach in modular product design, Expert Systems, Vol. 18, No. 1, pp.32 42. ahapatra, S., Koelling, C.P., Patvivatsiri, L., Fraticelli, B., Eitel, D. and Grove, L. (2003) Pairing emergency severity index5-level triage data with computer aided system design to improve emergency department access and throughput, in Proceedings of the 2003 Winter Simulation Conference, ONIPRESS, adison, WI, pp.1917 1925. Patel, V.L., Gutnik, L.A., Karlin, D.R. and Pusic,. (2008) Calibrating urgency: triage decision making in a pediatric emergency department, Advances in ealth Sciences Education, Vol. 13, pp.503 520. Pitts, S.R., Niska, R.W., Xu, J. and Burt, C.W. (2008) National ospital Ambulatory edical Care Survey: 2006 Emergency Department Summary, National ealth Statistics Reports, No. 7, available at http://www.cdc.gov/nchs/data/nhsr/nhsr007.pdf (accessed on 06/01/2009). Richardson, L.D. and wang, U. (2001a) Access to care: a review of the emergency medicine literature, Academic Emergency edicine, Vol. 8, pp.1030 1036. Richardson, L.D. and wang, U. (2001b) America s health care safety net: intact or unraveling?, Academic Emergency edicine, Vol. 8, pp.1056 1063. Saaty, T.L. (1980) The Analytic ierarchy Process, cgraw ill, New York, NY. Saaty, T.L. (1994) ow to make a decision: the analytic hierarchy process, Interfaces, Vol. 24, No. 6, pp.19 43. Susquehannahealth Official Site (2009) Available at http://susquehannahealth.org (accessed on 06/01/ 2009). Tanabe, P., Gimbel, R., Yarnold, P.R., Kyriacou, D.N. and Adams, J.G. (2004) Reliability and validity of scores on the emergency severity index version 3, Academic Emergency edicine, Vol. 11, pp.59 65. Thevenot,.J., Steva, E.D., Okudan G.E. and Simpson T.W. (2007) A multi-attribute utility theory-based method for product line selection, Transaction of the ASE, J ech Design, Vol. 129, No. 11, pp.1179 1184. Weinick, R.. and Burstin,. (2001) onitoring the safety net: data challenges for emergency departments, Academic Emergency edicine, Vol. 8, pp.1019 1021. Wuerz, R. (2001) Emergency severity index triage category is associated with six-month survival, Acad Emerg ed, Vol. 8, pp.61 64. Wuerz, R.C., ilne, L.W., Eitel, D.R., Travers, D. and Gilboy, N. (2000) Reliability and validity of a new five-level triage instrument, Acad Emerg ed, Vol. 7, pp.236 242.

Appendix A Fuzzy AP and utility theory based patient 351 Figure A1 Emergency nursing record, chest pain complaints

352 O.. Ashour and G.E. Okudan Figure A1 Emergency nursing record, chest pain complaints (continued) Appendix B Table B1 Fuzzy ratio scales for temperature Fuzzy Number Temperature ( o C) Low (L) (36.6 37) Relatively low (RL) (35 36.5) edium () (37.1 37.3) OR (33.9 34.9) Relatively high (R) (37.4 37.8) OR (32.2 33.8) igh () (37.9 or greater) OR (32.1 or lower)

Fuzzy AP and utility theory based patient 353 Table B2 Fuzzy ratio scales for systolic blood pressure Fuzzy number Systolic blood pressure (mmg) Low (L) (89 119) Relatively low (RL) (120 139) OR (81 90) edium () (140 159) OR (71 80) Relatively high (R) (160 174) OR (61 70) igh () (175 or greater) OR (60 or lower) Table B3 Fuzzy ratio scales for diastolic blood pressure Fuzzy number Diastolic blood pressure (mmg) Low (L) (60 80) Relatively low (RL) (81 89) OR (56 59) edium () (90 99) or (51 55) Relatively high (R) (100 109) OR (41 50) igh () (110 or greater) OR (40 or lower) Table B4 Fuzzy ratio scales for pulse Fuzzy number Low (L) (60 90) Relatively low (RL) (51 59) OR (90 100) edium () (46 50) Relatively high (R) (41 45) igh () (40 or lower) OR (100 or greater) Table B5 Fuzzy ratio scales for respiration rate Fuzzy number Low (L) (15 20) Relatively low (RL) 14 OR 21 edium () 13 OR (22 and 23) Relatively high (R) 12 OR (24 and 25) igh () (Less than 12) OR (greater than 25) Table B6 Fuzzy ratio scales for oxygen saturation level Fuzzy number Low (L) (95 or Greater) Relatively low (RL) (93 94) edium () (91 92) Relatively high (R) (89 90) igh () (90 or lower)

354 O.. Ashour and G.E. Okudan Table B7 Neurological complaints Neurological complaints Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L Table B8 Chest pain complaints Chest pain complaints Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L Table B9 Abdomen/male Abdomen/male Systolic blood pressure (mmg) Diastolic blood pressure (mmg) Table B10 Abdomen/female Abdomen/female Systolic blood pressure (mmg) Diastolic blood pressure (mmg)

Fuzzy AP and utility theory based patient 355 Table B11 Seizure Seizure Systolic blood pressure (mmg) Diastolic blood pressure (mmg) R R R R R Table B12 eadache eadache Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L RL RL Table B13 Psychiatric complaints/suicide attempt Psychiatric complaints/suicide attempt Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L Table B14 ead/face trauma ead/face trauma Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L

356 O.. Ashour and G.E. Okudan Table B15 General medicine complaints General medicine complaints Systolic blood pressure (mmg) Diastolic blood pressure (mmg) Table B16 Respiratory complaints Respiratory complaints Systolic blood pressure (mmg) Diastolic blood pressure (mmg) R R R R Table B17 Alleged assault Alleged assault Systolic blood pressure (mmg) Diastolic blood pressure (mmg) RL R R R R R Table B18 ultiple Trauma ultiple trauma Systolic blood pressure (mmg) Diastolic blood pressure (mmg) R

Fuzzy AP and utility theory based patient 357 Table B19 otor vehicle crash otor vehicle crash Systolic blood pressure (mmg) Diastolic blood pressure (mmg) R Table B20 Extremity complaint/trauma Extremity complaint/trauma Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L Table B21 Back pain/injury Back pain/injury Systolic blood pressure (mmg) Diastolic blood pressure (mmg) L R R Table B22 Skin rash/abscess Skin rash/abscess Systolic blood pressure (mmg) Diastolic blood pressure (mmg) RL R R

358 O.. Ashour and G.E. Okudan Table B23 Eye, ear, nose, throat and dental complaints Eye, ear, nose, throat and dental complaints Systolic blood pressure (mmg) Diastolic blood pressure (mmg) RL RL RL R R