The Impact of Input and Output Factors on Emergency Department Throughput

The Impact of Input and Output Factors on Emergency Department Throughput Phillip V. Asaro, MD, Lawrence M. Lewis, MD, Stuart B. Boxerman, DSc Abstract Objectives: To quantify the impact of input and output factors on emergency department (ED) process outcomes while controlling for patient-level variables. Methods: Using patient- and system-level data from multiple sources, multivariate linear regression models were constructed with length of stay (LOS), wait time, treatment time, and boarding time as dependent variables. The products of the 20th to 80th percentile ranges of the input and output factor variables and their regression coefficients demonstrate the actual impact (in minutes) of each of these factors on throughput outcomes. Results: An increase from the 20th to the 80th percentile in ED arrivals resulted in increases of 42 minutes in wait time, 49 minutes in LOS (admitted patients), and 24 minutes in ED boarding time (admitted patients). For admit percentage (20th to 80th percentile), the increases were 12 minutes in wait time, 15 minutes in LOS, and 1 minute in boarding time. For inpatient bed utilization as of 7 AM (20th to 80th percentile), the increases were 4 minutes in wait time, 19 minutes in LOS, and 16 minutes in boarding time. For admitted patients boarded in the ED as of 7 AM (20th to 80th percentile), the increases were 35 minutes in wait time, 94 minutes in LOS, and 75 minutes in boarding time. Conclusions: Achieving significant improvement in ED throughput is unlikely without determining the most important factors on process outcomes and taking measures to address variations in ED input and bottlenecks in the ED output stream. ACADEMIC EMERGENCY MEDICINE 2007; 14:235 242 ª 2007 by the Society for Academic Emergency Medicine Keywords: crowding, hospital emergency services, bed occupancy, patient care, regression analysis Emergency department (ED) overcrowding, especially in urban academic EDs, is a nationally recognized problem that continues to threaten the health care safety net. 1 3 Reasons for overcrowding are complex and many, 4,5 but increasing volume and lack of inpatient beds are clearly important factors. 6 8 It is also clear that the causes of overcrowding interact and must be addressed within an overall conceptual framework if progress is to be made, giving rise to conceptual models such as the input-throughput-output model, 9 the Fields chaos model, 10 and the ED Cardiac Analogy Model. 11 Patient care process outcomes (e.g., wait time to be seen, ED length of stay [LOS]) are affected by individual patient and disease characteristics as well as system-level factors. In a study of surgical critical care patients, ED From the Emergency Medicine Division (PVA, LML), Health Administration Program (SBB), Washington University School of Medicine, St. Louis, MO. Received March 2, 2006; revisions received August 14, 2006, and September 26, 2006; accepted October 30, 2006. Contact for correspondence and reprints: Phillip V. Asaro, MD; e-mail: asarop@msnotes.wustl.edu. LOS was most significantly affected by diagnostic evaluation such as computed tomographic scans and special procedures performed in the ED. 12 System-level factors relate to the general environment of care, including patient care processes within the ED and the hospital as a whole (e.g., ED staffing, ED arrivals, and hospital census). The throughput and output components of the input-throughput-output model relate to these ED and hospital environmental and process issues. Efforts at consensus on a usable definition of overcrowding have been under way for several years. 13 Much of this work has revolved around establishing meaningful and usable measures of busyness and crowding. Progress has been made, with several published proposals for measures and indices. 14 16 Recently, the National ED Overcrowding Study demonstrated a simple measure of ED overcrowding across multiple institutions. 2,17 A better understanding of the relative contribution of various system-level factors to measurable patient care process outcomes may provide further direction to this avenue of research. Our study objective was to quantify the impact of ED input factors and output factors on ED process outcomes while controlling for patient-level variables. ª 2007 by the Society for Academic Emergency Medicine ISSN 1069-6563 doi: 10.1197/j.aem.2006.10.104 PII ISSN 1069-6563583 235

236 Asaro et al. IMPACT OF INPUT AND OUTPUT ON THROUGHPUT METHODS Study Design This was a descriptive retrospective study using existing data from multiple sources. The study was approved by the Human Studies Committee of Washington University with waiver of informed consent. Study Setting and Population The study was performed on data from a large urban, academic medical center ED with more than 78,000 visits per year. Patients seen in either the main area of the ED (excluding the trauma and critical care unit) or in the urgent care (fast track) area of the ED from January 2004 to March 2006 are the study population for this analysis. We collected data from three separate sources: our ED information system (Healthmatics ED; Allscripts, Chicago, IL), hospital inpatient census logs, and ED staffing logs. Visit records with missing data or apparent time stamp and interval calculation errors were excluded. Exclusions for missing data included patients with missing age, gender, acuity assignment, and chief complaint. Time stamp related exclusions were for missing or negative patient care process intervals, wait time greater than eight hours, treatment time less than 10 minutes, LOS less than 15 minutes, and LOS greater than 20 hours (36 hours for admitted patients boarded in the ED and observation patients). We also excluded patients seen during relatively rare ED information system downtimes, because patient care process times are unreliable in this situation. Study Protocol, Measures, and Data Analysis The time stamps used for calculation of process times came from the ED information system tracking board. Arrival time is generated in the system upon first contact in the triage process. Disposition time is obtained from discharge or admission orders placed by physicians in the tracking system. The end of the ED stay is the time at which the patient was released from the tracking board. The time of transition from waiting to a treatment bed is obtained from bed assignment in the tracking system. We constructed a set of queries that constitute a filtering algorithm to ignore bed assignments that are changed after a brief time, as sometimes happens when a room assignment for a waiting patient is superseded by the urgent need for a room for a patient arriving by ambulance. Despite the filtering algorithm, there are some time stamp and interval calculation errors that our exclusion criteria attempted to filter out. Multivariate linear regression models were constructed with dependent variables of LOS (arrival to end of ED stay), wait time (arrival to treatment bed placement), treatment time (treatment bed placement to admission or discharge order), and boarding time (admission order until transfer to an inpatient bed). SPSS version 14.0 (SPSS Inc., Chicago, IL) was used to construct the linear regression models. We constructed system-level variables to represent ED input factors and inpatient hospital census factors. Aggregation of patient-level data from the ED information system yielded ED arrivals (patient arrivals for the day: midnight to midnight) and admit percentage for the same 24-hour period. From hospital census logs (data as of 7 AM), we constructed the variables of inpatient bed utilization (the sum of occupied inpatient beds and reserved inpatient beds) and ED holding patients (patients in the ED awaiting inpatient bed placement). Emergency department staffing logs were used to construct registered nurse (RN) and patient care technician (PCT) staffing variables. These variables, RN percent and PCT percent, represent staffing levels for the 24- hour day (6 AM to 6 AM) as a percentage of the median staffing level for the study period. Patient-level independent variables in the regression models include age, gender, triage acuity, chief complaint, and time of day of arrival. Acuity was determined at triage by a trained RN as 1 (highest acuity) to 5 (lowest acuity). During most of the study period, acuity was assessed using the Emergency Severity Index, previously shown to be reliable and valid. 18,19 During the first eight months of our study period, acuity was assessed using the Canadian Triage and Acuity Scale, which has also been shown to be reliable. 20 Chief complaints were assessed at triage by an RN and grouped into 53 categories for analysis. Time of day of patient arrival was categorized into six four-hour blocks: the first block from midnight to 4 AM, the next from 4 AM to 8 AM, and so on. For urgent care patients, we added variables indicating whether laboratory tests, radiology tests, and specialty consultations were performed during the visit. The conceptual approach to construction of our regression model views independent variables as either patient level or system level. Patient-level variables are generally considered unmanageable and unpredictable. Some system-level variables can be potentially managed as they relate to ED or hospital resources (e.g., RN staffing and scheduled inpatient admissions), others are not manageable but are somewhat predictable (e.g., daily ED volume), and some are neither manageable nor predictable (e.g., admit percentage). Construction of the models was guided by the intent to determine relative contribution to outcomes (dependent variables) by manageable and predictable factors (independent variables) while controlling for unmanageable, unpredictable factors (also independent variables). Linear regression coefficients, as reported throughout this study, represent the change in the dependent variable (in minutes) per unit change in the independent variable. To understand the relative impact of various factors, we have calculated the product of the regression coefficient of each independent variable and its common range, defined as the difference between the 20th and 80th percentile values for each variable. This product reflects the variability in the outcome (dependent variable) due to that factor (independent variable). Comparing these products across factors provides an intuitive measure of the impact that changes in each factor have on the outcome measure. Our analysis focuses on the patients seen in our 32-bed main ED or our 12-bed urgent care (fast track) area using separate regression models. These areas have separate waiting queues and separate staffing. The models include variables reflecting staffing of the specific area for that day. Many of the patients seen in the separate six-bed trauma-critical area are very ill, arrive by ambulance, never enter a waiting

ACAD EMERG MED March 2007, Vol. 14, No. 3 www.aemj.org 237 queue, are prioritized in the allocation of resources such as radiology testing, and are often admitted promptly to an intensive care unit or the operating room. The process times for these patients are therefore less subject to many of the factors of primary interest in this study. However, the distribution of ED and hospital resources to these patients is a part of the system we are studying, and this competitive demand for resources is represented in the models through the system variables of ED arrivals and admit percentage, which include all ED patients. A small number of patients were seen primarily in the ED observation unit and were excluded from analysis; this typically occurs on busy days when many of the ED patient rooms are occupied by boarded patients. The Durbin Watson statistic was computed to determine the presence of first-order autocorrelation in each of the linear regression models. RESULTS There were a total of 176,110 patient records from the 27-month period (January 2004 to March 2006), 166,854 (95%) of which had fully usable data by our inclusion criteria. Although excluded patient records were for visits with all of the disposition categories, a disproportionate share were for patients who left without being seen or were transferred to other facilities, situations in which incomplete data capture or unusual patient process is more likely. The mean age of the patients in the population was 43.8 years (SD 18.9 years), with 56.2% being female. Figure 1. Study flow.

238 Asaro et al. IMPACT OF INPUT AND OUTPUT ON THROUGHPUT Table 1 Comparison of Triage Acuity, Disposition, and Process Times for Main ED Visits Versus Urgent Care (Fast Track) Visits Entire ED Main ED Urgent Care Mean age (yr) 44 47 36 Acuity (%) 1 0.9 2 28.6 37.9 1.2 3 46.4 53.4 37.7 4 21.5 7.6 55.5 5 2.6 1.1 5.6 Disposition (%) Discharge 66.9 66.3 93.8 Admit 23.5 30.4 3.7 Leave without being seen 7.5 1.1 1.3 Other 2.1 2.2 1.2 Mean process time (min) Wait time 81 79 86 Length of stay 385 445 265 Treatment time 227 268 146 Boarding time 249 260 The patient population was 65.1% African American, 31.9% white, 0.6% Hispanic, 0.6% Asian, and 1.8% other or unknown. Of the patient records usable for our analysis (see Figure 1), a total of 136,235 (81.7%) were for patients seen either in the main ED or the urgent care area. Patient characteristics for these two areas are shown in Table 1, along with those of the entire ED for comparison. About 7.5% of patients either left without being seen or were seen and disposition was determined before placement in treatment rooms. All of these patients are reflected in our models through the ED arrival and admit percentage variables. Mean values of each of the system-level factors are provided in Table 2, overall and by day of week. Regression Model s (Raw Results) The regression coefficients for system factors and time of day of arrival are shown in Tables 3 and 4. Patient-level variable coefficients are available as a Data Supplement (http://www.aemj.org/cgi/content/full/j.aem.2006.10.104/ DC1). Along with the coefficients, we show the significance expressed as p-value and 95% confidence intervals. The regression coefficients represent additional time in minutes attributable to that variable per unit change in that variable. For example, in the main ED models (Table 3), LOS for admitted patients increased by 1.4 (95% confidence interval = 1.3 to 1.6) minutes per additional ED arrival. The staffing variables PCT percent and RN percent represent the number of additional minutes in the outcome variable attributable to an increase of 1% in staffing time for the day. For example, given the RN percent coefficient of 2.0 for LOS admits, a change from seven to eight RNs on each of two shifts per day (an increase of 14%) would be expected to lower LOS for admitted patients by 28 minutes ( 2.0 14 = 28). Time of day of arrival is represented as a group of dummy variables, using arrival between 4 AM and 8 AM as the reference. For example, for a discharged patient seen in the main ED, an additional 93 minutes in LOS is attributable to arriving between 8 PM and midnight as compared with arriving between 4 AM and 8 AM. The computed Durbin Watson statistic for all but three of the regression models did not show first-order autocorrelation to be a problem. The statistic did indicate autocorrelation in the models for main ED wait time, urgent care wait time, and urgent care LOS, with Durbin Watson statistics of 1.41, 0.86, and 1.39, respectively. Summing the Variable Contributions To assist in the interpretation of the results, and to give the reader an idea of how the factors collectively impact the outcomes, we have used the regression model coefficients along with common ranges of the independent variables to illustrate potential resultant overall effects on the outcomes (Table 5). We determined the 20th and 80th percentile values of each independent variable from our data. These values represent the range over the central 60% of day values for each variable, with 20% of days falling above and 20% falling below. This common range is then multiplied by the variable coefficients from the relevant model to calculate a potential effect for each variable. These products are then summed to represent the difference between hypothetical overall good-flow and overall bad-flow days. Adjusted R-square for Regression Models Table 6 shows the adjusted R-square of each regression model along with the adjusted R-square of two modifications of that model. One modification includes only system variables and time-of-day variables; the other modification includes system variables. Adjusted R- square is a measure of the proportion of variability in the outcome (dependent) variable that is explained by Table 2 Mean Values for System-level Factors by Day of Week Sunday Monday Tuesday Wednesday Thursday Friday Saturday All Days Inpatient bed utilization 756 833 902 930 928 912 815 868 Boarded ED admits 2.7 3.5 11.2 11.4 11.0 10.8 5.9 8.1 ED arrivals 209 232 225 216 214 213 205 216 Admit percent 24.1 24.4 23.9 23.4 24.1 25.6 24.2 24.3 RN percent main ED* 101 97 101 101 101 95 103 100 PCT percent main ED* 95 93 112 115 106 103 100 104 RN percent urgent care* 102 98 100 100 100 97 102 100 PCT percent urgent care* 91 135 131 157 149 144 109 131 PCT = patient care technician; RN = registered nurse. * Staffing level for each day as a percentage of the median value for the study period.

ACAD EMERG MED March 2007, Vol. 14, No. 3 www.aemj.org 239 Table 3 Impact of System-level Factors* and Arrival Timey on Process Times for Admitted and Discharged Patients Seen in the Main ED LOS Admits (n = 26,672) (95% CI) p-value Arrival 12 AM to 4 AM 9.7 ( 4.9, 24.4) LOS Discharges (n = 56,948) (95% Cl) Wait Time Admits/Discharges (n = 69,988) (95% CI) p-value Treatment Time Admits (n = 26,672) Treatment Time Discharges (n = 56,948) (95% CI) p-value Boarding Time Admits (n = 27,653) (95% CI) p-value 0.193 48.9 (43.5, 54.3) 4.3 ( 12.8, 4.2) 0.325 6.3 ( 10.9, 1.7) 0.008 11.2 ( 22.7, 0.3) 0.057 4 AM to 8 AM Reference Reference Reference Reference Reference 8 AM to 12 PM 3.7 0.559 13.7 2.1 0.574 0.2 0.942 17.1 0.001 ( 16.1, 8.7) (8.4, 19.0) ( 9.2, 5.1) ( 4.7, 4.4) ( 26.9, 7.4) 12 PM to 4 PM 7.6 0.219 67.3 13.5 <0.001 3.0 0.209 28.8 <0.001 ( 4.5, 19.8) (61.9, 72.7) ( 20.5, 6.4) ( 7.7, 1.7) ( 38.3, 19.2) 4 PM to 8 PM 4.7 0.455 91.7 18.0 <0.001 2.3 0.337 32.7 <0.001 ( 7.7, 17.2) (86.2, 97.2) ( 25.3, 10.8) ( 2.4, 7.0) ( 42.5, 22.9) 8 PM to 12 AM 9.5 0.157 93.2 12.8 0.001 0.7 0.767 24.1 <0.001 ( 3.7, 22.6) (88.0, 98.4) ( 20.5, 5.2) ( 3.8, 5.2) ( 34.4, 13.8) ED arrivals 1.44 <0.001 1.11 0.06 0.214 0.04 0.255 0.69 <0.001 (1.28, 1.60) (1.03, 1.18) ( 0.03, 0.15) ( 0.03, 0.10) (0.57, 0.82) Admit percent 2.68 <0.001 2.02 0.60 0.035 0.19 0.369 0.15 0.706 (1.72, 3.65) (1.55, 2.49) (0.04, 1.17) ( 0.22, 0.59) ( 0.61, 0.90) Inpatient bed 0.14 <0.001 0.01 0.01 0.716 0.04 <0.001 0.11 <0.001 utilization (0.09, 0.19) ( 0.03, 0.02) ( 0.03, 0.02) ( 0.06, 0.02) (0.07, 0.15) Boarded ED 8.52 <0.001 3.40 0.18 0.338 0.50 <0.001 6.84 <0.001 admits (7.90, 9.15) (3.09, 3.71) ( 0.19, 0.54) (0.23, 0.77) (6.34, 7.33) PCT percent 0.08 0.258 0.03 0.02 0.648 0.07 0.025 0.09 0.089 ( 0.06, 0.22) ( 0.04, 0.09) ( 0.10, 0.06) (0.01, 0.12) ( 0.01, 0.20) RN percent 1.98 <0.001 1.09 0.41 <0.001 0.28 <0.001 1.04 <0.001 ( 2.25, 1.70) ( 1.22, 0.95) ( 0.57, 0.25) ( 0.39, 0.16) ( 1.26, 0.83) LOS = length of stay; PCT = patient care technician; RN = registered nurse. * Expressed as multivariate linear regression coefficients representing minutes of additional time in the outcome measure per unit change in the systemlevel factor. y Expressed as multivariate linear regression coefficients representing additional time as compared with the reference period of 4 AM to 8 AM. Table 4 Impact of System-level Factors*, Arrival Timey, and Required Servicesz on Process Times for Patients in the Urgent Care Area LOS (n = 41,605) Wait Time (n = 42,403) Treatment Time (n = 41,605) (95% CI) p-value (95% CI) p-value (95% CI) p-value Arrival 12 AM to 4 AM 130.4 (113.9, 146.8) <0.001 135.6 (125.3, 145.9) <0.001 6.8 ( 19.4, 5.8) 0.291 4 AM to 8 AM Reference Reference Reference 8 AM to 12 PM 62.7 ( 69.5, 55.9) <0.001 70.9 ( 75.1, 66.6) <0.001 8.4 (3.1, 13.6) <0.002 12 PM to 4 PM 7.1 ( 14.0, 0.2) 0.042 21.7 ( 26.0, 17.4) <0.001 14.5 (9.2, 19.7) <0.001 4 PM to 8 PM 4.1 ( 11.1, 2.8) 0.242 19.0 ( 23.3, 14.7) <0.001 16.6 (11.3, 22.0) <0.001 8 PM to 12 AM 56.8 ( 64.2, 49.4) <0.001 55.9 ( 60.5, 51.3) <0.001 3.0 ( 2.7, 8.7) 0.301 ED arrivals 1.1 (1.1, 1.2) <0.001 1.0 (0.9, 1.0) <0.001 0.1 (0.1, 0.2) <0.001 Admit percent 1.7 (1.4, 2.0) <0.001 1.6 (1.4, 1.8) <0.001 0.1 ( 0.2, 0.3) 0.702 Inpatient bed utilization 0.0 (0.0, 0.1) <0.001 0.0 (0.0, 0.0) <0.001 0.0 (0.0, 0.0) 0.601 Boarded ED admits 2.0 (1.8, 2.2) <0.001 1.7 (1.5, 1.8) <0.001 0.2 (0.0, 0.3) 0.057 PCT percent 0.1 ( 0.1, 0.1) <0.001 0.1 ( 0.1, 0.0) <0.001 0.0 (0.0, 0.0) 0.184 RN percent 0.1 (0.0, 0.2) 0.003 0.1 ( 0.1, 0.1) <0.001 0.2 (0.1, 0.2) <0.001 No lab or x-ray Reference Reference Reference Lab only 45.7 (42.6, 48.9) <0.001 4.4 (2.5, 6.4) <0.001 39.6 (37.2, 42.0) <0.001 X-ray only 68.1 (64.7, 71.4) <0.001 0.3 ( 2.3, 1.8) 0.815 67.9 (65.3, 70.5) <0.001 Lab and x-ray 154.7 (150.8, 158.5) <0.001 5.6 (3.2, 7.9) <0.001 145.5 (142.6, 148.4) <0.001 No consult Reference Reference Reference Consult 100.6 (95.8, 105.5) <0.001 0.1 ( 3.0, 2.8) 0.928 97.7 (94.0, 101.4) <0.001 LOS = length of stay; PCT = patient care technician; RN = registered nurse. * Expressed as multivariate linear regression coefficients representing minutes of additional time in the outcome measure per unit change in the systemlevel factor. y Expressed as multivariate linear regression coefficients representing additional time as compared with the reference period of 4 AM to 8 AM. z Expressed as multivariate linear regression coefficients representing additional time as compared with the references of no lab or x-ray and no consultation.

240 Asaro et al. IMPACT OF INPUT AND OUTPUT ON THROUGHPUT Table 5 Individual and Summed Effects on Wait Times, Length of Stay, and Treatment Times of Input and Output Variables over a Range Representing the Difference between a Fairly Good-flow Day and Fairly Bad-flow Day (20th to 80th percentile) Main ED Urgent Care 20th to 80th Both Admitted Discharged Percentile Range Wait LOS Treatment Boarding LOS Treatment LOS Wait Treatment ED arrivals 34 (200 234) 42 49 2* 24 38 1* 38 33 5 Admit percent 5.5 (21.5 27.0) 12 15 3 1* 11 1* 9 9 0* Inpatient bed utilization 138 (798 936) 4 19 1* 16 1* 6 5 4 0* Boarded ED admits 11 (2 13) 35 94 2* 75 37 6 22 18 2* Sum of effectsy 92 177 3 114 86 0 74 64 5 Sum of effectsz 92 177 6 115 85 2 74 64 7 All values are expressed in minutes. LOS = length of stay. * Indicates that the corresponding linear regression coefficient was not statistically significant in that model. y Sum of effects using only the statistically significant variables. z Sum of effects using all of the variables. the regression model adjusted for the number of factors included in the model as well as the number of observations. For example, system variables explained 7.6% of the variability in main ED wait time; however, incorporation of time of day into the model explained an additional 9% of the variability. The full model, including patient variables, explained 25.6% of the variability. DISCUSSION Many of us who work in the ED recognize that there are scores of little things that, taken together, add up to significant delays in patient care and overall patient throughput. What we have done in this study is to quantify the impact that input and output factors have on throughput. This study did not attempt to drill down to the level of individual throughput steps, as might be done with typical process improvement initiatives. Our approach allows estimation of the impact of changes in major system-level factors on throughput. While the bottlenecks and the exact causes and effects of them may vary between facilities, our results should prove illustrative. Analyses such as these may be used to increase awareness of the effect of factors, both internal and external to the ED, on ED patient throughput. Influence of ED Input Factors Emergency department arrivals vary significantly by day of week, with Monday being the busiest day of the week on average, followed by Tuesday. Admission percentage can be viewed as a modulator of the overall resource demand of patients presenting to the entire ED for the 24-hour day. This percentage is a significant factor in the variability of LOS and wait time. Admit percentage influences LOS through two mechanisms. First, admitted patients typically require more diagnostic and treatment resources (including time in a treatment bed). However, in a system with a queue for inpatient beds, higher admit percentage translates into more boarded patients and decreased ED resources available to care for arriving patients. Unlike ED arrivals, little of the variability in admit percentage is predictable by day of week. Adjustment of ED resources to deal with unexpected demand related to such unpredictable, unmanageable variability has to be handled dynamically. This would call for a monitoring system capable of early detection of a trend, plus mechanisms for rapid adjustment in resources. Influence of Inpatient Census Together, the two measures, inpatient bed utilization and boarded ED admits, provide a reflection of the inpatient Table 6 Proportion of Variability in Process Times Explained by Variable Groups Regression Model Models with All Variables* Adjusted R-square Without Patient Variablesy System Variables Onlyz Main ED LOS, admits 0.098 0.067 0.066 26,672 Main ED LOS, discharges 0.169 0.076 0.033 56,948 Main ED wait time 0.256 0.166 0.076 69,988 Main ED treatment time, admits 0.065 0.003 0.001 26,672 Main ED treatment time, discharges 0.142 0.015 0.005 56,948 Main ED boarding time 0.086 0.067 0.065 27,653 Urgent care LOS 0.197 0.100 0.045 41,605 Urgent care wait time 0.232 0.210 0.086 42,403 Urgent care treatment time 0.099 0.010 0.004 41,605 LOS = length of stay. * Including system variables, time of day of arrival of the patient, and patient variables. y Including system variables and time of day of arrival of the patient. z Including only system variables. n

ACAD EMERG MED March 2007, Vol. 14, No. 3 www.aemj.org 241 bed status from the perspective of the ED. Boarded ED admits was a statistically significant predictor in all of the wait and LOS models. Inpatient bed utilization as of 7 AM provides additional predictive power in some of these models. Inpatient census factors in our institution are highly predictable by the day of the week. It is not difficult to see why efforts at smoothing inpatient bed demand through management of scheduled admissions can be highly effective. 21 Contributions of System and Patient Factors to Outcomes The observed ranges of our system factors have substantial effects on wait time and boarding time (Table 5) but a negligible effect on treatment time. Relative contributions from system versus patient factors can also be seen in the regression model adjusted R-square values in Table 6. Contributions to wait time in the main ED are roughly equally split among patient characteristics, time of day of arrival, and system factors. In contrast, wait time for urgent care is not influenced significantly by patient characteristics, because patients in this queue are generally served on a first-come first-served basis. Treatment times are affected much more by patient factors than by system factors. However, most of the effect on boarding time is from system factors. The finding of a primary effect of ED crowding on wait time is intuitive and supported by the findings of others. 22 That treatment times would be minimally affected is not so intuitive. This finding suggests that variation in the input and output factors does not significantly vary the demand on our internal ED resources and is probably an artifact of the structure of our ED, where a fixed number of treatment beds are often filled to capacity. Quantification of the influence of various factors on ED patient flow could direct research efforts on real-time ED monitoring tools. Such tools might monitor the input stream (patient arrivals), throughput measures (ED processes such as unfilled orders and turnaround times), and status of the output stream (inpatient bed availability), triggering mechanisms to adjust ED resources and inpatient bed management strategies when indicated to lessen the impact of unexpected fluctuations. Recently developed measures of ED overcrowding, including the National ED Overcrowding Study score, include a real-time measure of ED patients awaiting inpatient beds rather than the once-daily measure we had available for this retrospective study. As ED electronic tracking systems and more integrated hospital information systems become commonplace, it should become increasingly feasible to obtain automated measures of ED saturation and hospital resource utilization, enabling the development of automated predictive tools for anticipating ED overcrowding. While linear regression models can produce important and interesting results as we have shown, they have important limitations. First, by definition, linear regression models provide estimates of the mean value of the dependent variables for given levels of the independent variable. They do not allow us to determine probability distributions. Questions such as what percent of the patients will have waiting times no longer than a prescribed value cannot be answered. Second, linear regression models assume that the dependent variable is linearly related to the independent variables over their entire range of values, an assumption that is likely invalid in situations near or beyond the extremes of those represented in the data used to construct the models. In contrast, discrete event simulation models can accurately model nonlinear relationships and produce probability distributions as a function of observed distributions in input values. Once constructed, such models could prove very useful for estimating the effects of surges and proposed interventions for surges in ED volume that may occur either as an extreme of usual daily variation or as a result of catastrophic events. LIMITATIONS This study was limited to data from one institution. Specific results of similar analyses at other institutions may be different. A limitation of linear regression modeling is the assumption of linearity of the effect of each variable over the range of study. Especially toward the extremes, the linearity assumption is unlikely to be true. Although there is a high degree of consistency in the effects of input and output factors across all of the models in this collection, the finding of first-order autocorrelation renders the significance of the factors in three of our models less conclusive. Despite this limitation, the presence of autocorrelation in the models for wait time and LOS is consistent with our intuition that process times are affected by prior patient arrivals. Our future work will focus on discrete event simulation modeling, an approach that naturally accounts for the interaction of sequential events and circumvents the problems encountered with autocorrelation. Despite inclusion of all of the variables to which we had access, our models resulted in adjusted R-square values of about 0.25 at best. As any clinician can appreciate, the patient-level variables available in our data capture only a portion of actual patient-to-patient variability. Other sources of unmeasured variability include differences in physician practice pattern, variability in laboratory and radiology turnaround times, and variable response times of consultants. CONCLUSIONS Significant improvement in ED throughput is unlikely to be achieved without determining the most important factors on process outcomes and taking measures to address variations in ED input and bottlenecks in the ED output stream. References 1. Trzeciak S, Rivers EP. Emergency department overcrowding in the United States: an emerging threat to patient safety and public health. Emerg Med J. 2003; 20:402 5. 2. Weiss SJ, Derlet R, Arndahl J, et al. Estimating the degree of emergency department overcrowding in academic medical centers: results of the National ED Overcrowding Study (NEDOCS). Acad Emerg Med. 2004; 11:38 50.

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