a b s t r a c t

Background: Although several studies have demonstrated that wait time is a key factor that drives high leave- without-being-seen (LWBS) rates, limited data on ideal wait times and impact on LWBS rates exist.

Study objectives: We studied the LWBS rates by triage class and target wait times required to achieve various LWBS rates.

Methods: We conducted a 3-year retrospective analysis of patients presenting to an urban, tertiary, academic, adult emergency department (ED). We divided the 3-year study period into 504 discrete periods by year, day of the week, and hour of the day. Patients of same triage level arriving in the same bin were exposed to similar ED conditions. For each bin, we calculate the mean actual wait time and the proportion of patients that abandoned. We performed a regression analysis on the abandonment proportion on the mean wait time using weighted least squares regression.

Results: A total of 143 698 patients were included for analysis during the study period. The R² value was highest for Emergency Severity Index 3 (R² = 0.88), suggesting that wait time is the major factor driving LWBS of ESI 3 patients. Assuming that ESI 2 patients wait less than 10 minutes, our sensitivity analysis shows that the target wait times for ESI 3 and ESI 4/5 patients should be less than 45 and 60 minutes, respectively, to achieve an overall LWBS rate of less than 2%.

Conclusion: Achieving target LWBS rates requires analysis to understand the abandonment behavior and redesigning operations to achieve the target wait times.

(C) 2014

Introduction

Patients who leave without being seen (LWBS) are at risk for worsen morbidity due to Delay in diagnosis and treatment of their current conditions [1-5]. In addition, high LWBS rates correlates with high level of emergency department (ED) crowding, which has been shown to negatively impact several domains of quality such as timeliness, safety, and patient centeredness [6-9]. Given this, LWBS rates have been recognized by the Center for Medicare and Medicaid service as an important ED quality metric, which is now requiring hospitals to report on this quality metric annually [10]. In addition to the impact on quality, high LWBS rates are directly associated with lost hospital revenues, with a recent study conducted at an urban academic center estimating an annual loss of $3 million due to

? Author contribution: OAS and RJB conceived the study and designed the trial. OAS supervised the conduct of the trial and data collection. RJB undertook data abstraction; managed the data, including quality control; and analyzed the data. OAS and JL drafted

the manuscript, and all authors contributed substantially to its revision. OAS takes responsibility for the manuscript as a whole.

?? Prior presentations: None.

? Financial support: None.

* Corresponding author. Department of Emergency Medicine, Hospital of University of Pennsylvania, Philadelphia, PA 19104. Tel.: +1 215 615 3477.

E-mail address: olanmd@gmail.com (O.A. Soremekun).

patients who LWBS [11]. The impact on quality and finances has led many ED managers to pay increasing attention to this metric.

The national ED LWBS rate from 1998 to 2006 was 1.7%, and the American College of Emergency Physicians guideline recommends EDs to target an LWBS rate less than 2% [12]. Rates of LWBS vary nationwide, with certain EDs reporting rates as high as 15% [3,13]. Several hospital characteristics such as being located in a metropol- itan area, poor payer mix, and trauma-center designation have been associated with high LWBS rates [12,13]. At the patient level, various studies have shown that wait time was the foremost cause of dis- satisfaction and reason for patients leaving without being seen [1,2]. Interventions focusing on reducing door-to-provider times have, not surprisingly, demonstrated significant reductions in LWBS rates and improved patient satisfaction [14-16].

Although the link between wait times and LWBS has been pub- lished in the literature, limited data on the appropriate wait times for achieving a hospital’s target LWBS rate exist. No studies have presented a methodology or the answer to the question: what should the wait times be for an ED to achieve their goal LWBS rate? Although many ED managers set LWBS goals, many do not set targets for the variable they can actually control–wait times. Although the general consensus among ED managers is that shorter waits will reduce LWBS rates, there is limited research on how these wait times should be adjusted according to triage class to impact LWBS rates.

0735-6757/$ – see front matter (C) 2014 http://dx.doi.org/10.1016/j.ajem.2013.12.047

J. Lucas et al. / American Journal of Emergency Medicine 32 (2014) 342–345 343

Our primary objectives are to describe the probability of LWBS by wait time and triage class and to use our findings to estimate the wait time goals required to achieve an LWBS rate less than the national average of 2% at the study center.

Methods

We conducted a 3-year (2009-2011) retrospective review of data from a tertiary care, adult, urban ED with approximately 60 000 annual visits with a 4-year emergency medicine residency program with a dedicated fast-track area staffed by midlevel providers, sepa- rate psychiatric emergency evaluation center (PEEC), and separate dedicated trauma bay staffed by dedicated trauma team and nurses. At the study center, there was a total of 48 to 56 hours per day of attending physician coverage and 12 to 24 hours of midlevel coverage, plus additional ED and off-service resident coverage for all patients cared for in the main ED.

The study center uses a computerized ED information system (EMTRAC; University of Pennsylvania, Philadelphia, PA) with inte- grated charting and patient tracking that allows, via a Microsoft Access database (Microsoft Corporation, Redmond, WA), to query timestamp data for all patients who present to the ED. We included all patients with Emergency Severity Index triage classes 2 to 5 who presented during the study period. Patients who were triaged directly to PEEC or the labor and delivery unit were excluded from the study. Queuing theory research has shown that for some types of queues, there is a linear relationship between the time customers in a queue are required to wait and the probability that a customer will abandon the queue before being served [17,18]. Therefore, we use linear regression to relate the requirED wait time to the LWBS proportion. To do this, we use pooled data rather than individual patient-level data. Following the methodology validated by Zohar et al [18], we create 504 discrete bins defined by year, day of the week, and hour of the day (3 years x 7 days x 24 hours = 504). For example, one bin represents all patients who arrived between 9:00 AM to 9:59 AM on all Mondays in 2009. For each bin, we calculate the mean required wait time and the proportion of patients who LWBS (we do this calcu- lation separately for each ESI level). To continue the example, 211 ESI 3 patients arrived between 9 AM and 10 AM on Mondays of 2009. As a group, these patients experienced a mean wait time of 0.84 hours, and 1 person Left without being seen (0.47%). This bin represents 1 observation point in the regression analyses below. This bin struc- ture is used to group together periods that are likely operationally similar in terms of busyness, patient mix, and staffing. Other bin structures, such as using shift instead of hour, or including the month,

were tested with similar results.

The mean wait time for each bin is calculated as the average of the required wait times for all patients in a given bin. For patients who stay for treatment, the required wait time is the elapsed time between arrival and placement in an ED. For patients who LWBS, the required wait time is the elapsed time between arrival and when a nurse first attempted to find the patient in the waiting room to place in a treatment room.

We perform Linear regression analysis of the LWBS proportion on the mean wait time using robust weighted least squares regression. The weights used are the number of patients in each bin. The heteroscedastic-robust standard error correction adjusts the standard errors for the fact that the error term is heteroscedastic and not normally distributed by construction.

The resulting slope coefficients indicate the sensitivity of patients to wait time and can be interpreted just like standard ordinary-least- square coefficients: the change in the dependent variable from a 1-unit change in the independent variable. The R² of the regression model measures the explanatory power of the independent variable, wait time. All analyses were performed using Stata 13 MP (Stata Corp,

College Station, TX). The local institutional review board approved this study.

Results

After excluding patients triaged to PEEC and Labor and Delivery (L&D) and directly to the trauma bay, we included 143 698 patients. Table 1 provides descriptive statistics of the study population. Fig. 1 shows the scatter plots of the data as well as the best-fit line and the regression results.

We performed a sensitivity analysis on wait times of ESI 3 and ESI 4 and 5 (patients cared for in our dedicated fast-track area) and the impact on LWBS rate given the estimated LWBS probabilities in Fig. 1 (Table 2). We assumed a wait time of less than 10 minutes for patients with triage class 2 because of the potential impact on patient safety. We assumed that the proportion of each triage class was fixed, as shown in Table 1. Based on these assumptions, our sensitivity analysis shows a range of combinations of wait times for ESI 3 and ESI 4 and 5 patients which achieve LWBS rates less than 2%.

Discussion

Hospitals have designed various ED and hospital level interven- tions such as Physician in triage, bedside registration, dedicated fast- track areas to reduce LWBS rates, improvED patient flow, and reduced ED crowding [16,19,20]. Interventions that aim to reduce LWBS rates focus on reducing door-to-provider times [21]. Although lots of ED managers design interventions to reduce their LWBS, they currently lack the ability to control this rate directly. Patient wait times are a more easily observed and adjusted variable that is strongly associated with abandonment. Our study provides an example of how a hospital can use the association between LWBS and wait times to establish target wait times in order to achieve a desired LWBS rate.

We observe 3 interesting features from our analysis. First, although it is not at all surprising that there is an increasing relationship between wait time and LWBS, it is interesting that the relationship does indeed appear to be approximately linear as predicted by analytical queuing theory models.

Second, we note that the slope is steeper for patients with lower acute condition. This is evidence that sicker patients are less sensitive to wait time than are less sick patients. Stated differently, an addi- tional 30 minutes of wait time leads to a large increase in the per- centage of ESI 5 patients who abandon, whereas it has a small impact on the percentage of ESI 2 patients who abandon. In our data, the marginal effect of wait time on LWBS rates is 4 times larger for ESI 5 patients than for ESI 2 patients. This is likely because the ESI 2 patients are in greater need of care and have more to gain from waiting for treatment. In the language of economic utility theory, for an ESI 2 patient, the benefit of being treated is much greater than the marginal cost of waiting; thus, wait time has little impact on ESI 2 patients.

Table 1

Descriptive statistics by triage class

344 J. Lucas et al. / American Journal of Emergency Medicine 32 (2014) 342–345

Fig. Proportion of LWBS as a function of mean wait time by ESI triage class.

Although ESI 2 patients are higher acuity and need prompt evaluation from a patient safety perspective, an ED manager trying to reduce LWBS rates must focus on the wait times for lower-acuity patients because they are more likely to abandon as wait times increase.

Lastly, we see that the explanatory power of mean wait time varies greatly across the severity levels. Most notably, The R² value is highest for ESI 3 (R² = 0.88), suggesting that wait time is the major factor driving LWBS of ESI 3 patients. This can also be seen in the very tight clustering of the dots around the best-fit line. In contrast, for ESI 2 patients, although the dispersion from the linear fit is small, the R² value is quite small (R² = 0.27), further showing that wait time explains only a small amount of the variation in LWBS among ESI 2 patients. ESI 4 and ESI 5 are somewhat different in that the R² values are of moderate magnitude (0.64 and 0.52, respectively), but the dispersion from the best-fit line is large. This suggests that although wait time is a factor in the LWBS decisions of these patients, either there are other factors that also have large impacts on LWBS or these patients are innately quite heterogeneous in their behavior.

Given different abandonment behaviors by triage level, hospitals

should perform similar analysis to understand the abandonment

Table 2

Estimated LWBS rate by wait time

behavior of their patient population and set target wait times. This will allow hospitals to design interventions that will allow them to achieve these wait times and their goal LWBS rates.

Limitations

The retrospective study design and single intervention may im- pact the generalizability of our findings. The abandonment behavior by triage level may be different at different hospitals with different patient populations and acuity mix. However, although the wait time targets at our study site may be different, our methodology should be applicable to other hospitals. In addition, although our study focuses on wait times and the impact on LWBS rates, there are other factors such as patient safety that must be considered when setting target wait times.

Conclusion

Our study provides a methodology for hospitals to establish the association between LWBS and wait times to establish target wait times in order to achieve a desired LWBS rate. Emergency depart- ment managers can adapt our methodology to their unique hospital environment to set target wait times needed to achieve their goal LWBS rates.

References

1. Baker DW, Stevens CD, Brook RH. Patients who leave a public hospital emergency department without being seen by a physician causes and consequences. JAMA 1991;266:1085-90.
2. Rowe BH, Channan P, Bullard M, Blitz S, Saunders LD, Rosychuk RJ, et al. Charac- teristics of patients who leave emergency departments without being seen. Acad Emerg Med 2006;13:848-52.
3. Bindman AB, Grumbach K, Keane D, Rauch L, Luce JM. Consequences of queuing for care at a public hospital emergency department. JAMA 1991;266:1091-6.
4. Vieth TL, Rhodes KV. The effect of crowding on access and quality in an academic ED. Am J Emerg Med 2006;24:787-94.
5. Clarey AJ, Cooke MW. Patients who leave emergency departments without being seen: literature review and English data analysis. Emerg Med J 2012;29:617-21.
6. Bernstein SL, Aronsky D, Duseja R, Epstein S, Handel D, Hwang U, et al. The effect of emergency department crowding on clinically oriented outcomes. Acad Emerg Med 2009;16:1-10.

   J. Lucas et al. / American Journal of Emergency Medicine 32 (2014) 342–345 345

   Moskop JC, Sklar DP, Geiderman JM, Schears RM, Bookman KJ. Emergency department crowding, part 1–concept, causes, and moral consequences. Ann Emerg Med 2009;53:605-11.

7. Pines JM, Iyer S, Disbot M, Hollander JE, Shofer FS, Datner EM. The effect of emergency department crowding on patient satisfaction for admitted patients. Acad Emerg Med 2008;15:825-31.
8. Hing E, Bhuiya F. Wait time for treatment in hospital emergency departments: 2009. NCHS Data Brief 2012;102:1-8.
9. Centers for Medicare, Medicaid Services (CMS), HHS. Medicare and Medicaid programs: Hospital Outpatient Prospective Payment and Ambulatory Surgical Center Payment Systems and Quality Reporting Programs; Hospital Value-Based Purchasing Program; organ procurement organizations; quality improvement organizations; electronic health records (EHR) Incentive Program; provider reimbursement determinations and appeals. Final rule with comment period and final rules. Fed Regist 2013;78:74825-5200.
10. Pines JM, Batt RJ, Hilton JA, Terwiesch C. The financial consequences of lost demand and reducing boarding in hospital emergency departments. Ann Emerg Med 2011;58:331-40.
11. Pham JC, Ho GK, Hill PM, McCarthy ML, Pronovost PJ. National study of patient, visit, and hospital characteristics associated with leaving an emergency department without being seen: predicting LWBS. Acad Emerg Med 2009;16:949-55.
12. Hsia RY, Asch SM, Weiss RE, Zingmond D, Liang LJ, Han W, et al. Hospital determinants of emergency department left without being seen rates. Ann Emerg Med 2011;58:24-32.e3.
13. Spaite DW, Bartholomeaux F, Guisto J, Lindberg E, Hull B, Eyherabide A, et al. Rapid process redesign in a university-based emergency department: decreasing wait- ing time intervals and improving patient satisfaction. Ann Emerg Med 2002;39: 168-77.
14. Chan TC, Killeen JP, Kelly D, Guss DA. Impact of rapid entry and accelerated care at triage on reducing emergency department patient wait times, lengths of stay, and rate of left without being seen. Ann Emerg Med 2005;46:491-7.
15. Wiler JL, Gentle C, Halfpenny JM, Heins A, Mehrotra A, Mikhail MG, et al. Optimizing emergency department front-end operations. Ann Emerg Med 2010;55:142-160.e1.
16. Brandt A, Brandt M. Asymptotic results and a Markovian approximation for the M(n)/M(n)/s + Gi system. Queuing Systems 2002;41:73.
17. Zohar E, Avishai M, Nahum S. Adaptive behavior of impatient customers in tele- queues: theory and empirical support. Manag Sci 2002;48(4):566.
18. Soremekun OA, Biddinger PD, White BA, Sinclair JR, Chang Y, Carignan SB, et al. Operational and Financial impact of physician screening in the ED. Am J Emerg Med May 2012;30(4):532-9.
19. Nestler DM, Fratzke AR, Church CJ, Scanlan-Hanson L, Sadosty AT, Halasy MP, et al. Effect of a physician assistant as triage liaison provider on patient throughput in an academic emergency department. Acad Emerg Med 2012;19: 1235-41.
20. Sharieff GQ, Burnell L, Cantonis M, Norton V, Tovar J, Roberts K, et al. Improving emergency department time to provider, left-without-treatment rates, and average length of stay. J Emerg Med 2013;45:426-32.