Time Series Analysis of Variables Associated With Daily Mean Emergency Department Length of Stay

doi:10.1016/j.annemergmed.2006.11.007

Annals of Emergency Medicine

Volume 49, Issue 3, March 2007, Pages 265-271

Presented at the American College of Emergency Physicians Research Forum, October 2004, San Francisco, CA.

https://doi.org/10.1016/j.annemergmed.2006.11.007 Get rights and content

Study objective

We measure the effect of various input, throughput, and output factors on daily emergency department (ED) mean length of stay per patient (daily mean length of stay).

Methods

The study was a retrospective review of 93,274 ED visits between April 15, 2002, and December 31, 2003. The association between the daily mean length of stay and the independent variables was assessed with autoregressive moving average time series analysis (ARIMA). The following independent variables were measured per 24-hour period: number of elective surgical admissions, ED volume, number of ED admissions, number of ED ICU admissions, number of ED clinical attending hours, hospital medical-surgical occupancy (hospital occupancy), and day of the week.

Results

Three factors were independently associated with daily mean length of stay in time series analysis: number of elective surgical admissions, number of ED admissions, and hospital occupancy. The daily mean length of stay increased by 0.21 minutes for every additional elective surgical admission, 2.2 minutes for every additional admission, and 4.1 minutes for every 5% increase in hospital occupancy. Elective surgical admissions were associated with a maximum of 35 hours of additional ED dwell time. The model accounted for 31.5% of the variability in daily mean length of stay. The final model parameters for the ARIMA analysis were autoregressive term (1) moving average (1).

Conclusion

Hospital occupancy and the number of ED admissions are associated with daily mean length of stay. Every additional elective surgical admission prolonged the daily mean length of stay by 0.21 minutes per ED patient. Autocorrelation exists between the daily mean length of stay of the current day and the previous day.

Introduction

As described by Solberg et al¹ and Asplin et al,² daily emergency department (ED) mean length of stay per patient (daily mean length of stay) and ambulance diversion status are influenced by input, throughput, and output factors. The originators of the model concluded that the most frequent reason for ED crowding is the inability to move admitted patients from the ED to an inpatient bed. A previous study from an urban, university hospital ED supported this conclusion. Chan et al³ found that the number of ED admissions, ED volume, and the number of ambulance arrivals affected length of stay. In a time series analysis from Canada, diversion was found to be associated with the number of admitted patients “boarding” in the ED, in addition to other factors.⁴

The ideal measure of crowding should have utility in tracking individual institutional performance over time, in addition to providing a basis for comparison between different institutions. Length of stay, measured from the patient's arrival to departure from the ED, and ambulance diversion status have been identified and used as surrogate markers of ED crowding in the absence of a universally accepted definition.⁵ They are also frequently used as key process indicators of institutional performance improvement and clinical and operational efficiency.

We chose to focus our analysis on daily mean length of stay as a key benchmark of patient flow.⁶ Ambulance diversion is inherently a more subjective measure of crowding that cannot be applied universally. The criteria for declaring ambulance diversion vary considerably between institutions; by design, many EDs never control input by declaring ambulance diversion.

The goals of our investigation were to measure the association between daily mean length of stay and daily ED input, throughput, and output factors. Knowledge of the relative effects of these factors on daily mean length of stay is important to effectively implement changes that maximize ED efficiency.

Section snippets

Study Design

This was a retrospective review of all ED patients presenting between April 15, 2002, and December 31, 2003. Daily mean length of stay was the outcome variable of the study. The purpose was to measure the association between the daily mean length of stay and independent variables that we believed were related to this outcome variable. The independent variables analyzed per 24-hour period were number of elective surgical admissions, ie, number of patients admitted for elective surgical

Results

The mean and maximum numbers of patient visits per day were 148 and 209, respectively. The daily mean length of stay during the entire study period was 241 minutes, and the range was 120 to 570 minutes. The range for hospital occupancy was 68% to 113%. The median number of elective surgical admissions was 48 per weekday and zero on weekends. Our time-series data proved stationary by the Dickey-Fuller and Phillips-Perron unit root tests and therefore did not necessitate transformation before

Limitations

Our study had certain limitations. This was a retrospective study conducted in a single institution. Our methods were designed to identify an association, but not a direct causative effect, between the dependent and independent variables; however, according to our experience we believe that daily mean length of stay is affected by hospital occupancy, as well as ED and elective admissions. Admittedly, daily mean length of stay is an imperfect measure of ED crowding. It depends on the complexity

Discussion

ED crowding is the result of a mismatch between ED capacity and various input, throughput, and output factors. These factors must be measured to manage the processing of ED admissions, predict ambulance diversion, and improve patient satisfaction. Length of stay is a real-time measure that is calculated with relative ease by electronic tracking systems, whereas mathematic measures of crowding are more complex and have yet to gain uniform acceptance.11, 12 Length of stay over time is therefore

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: Supervising editor: Brent R. Asplin, MD, MPH

: Author contributions: NKR, JC, JO, SDM, SC, BM, LF, and EL conceived the study and designed the trial. NKR, JC, JO, KD, and EL obtained the research funding. DO, SDM, TR, and AC provided statistical advice and analyzed the data. NKR, SC, BM, KD, RS, KL, JMB, LF, LG, and AC supervised the conduct of the trial and data collection. JC, DO, TR, RS, KL, JMB, and LG managed the data for analysis. All authors contributed substantively to the revision of the article. NKR drafted the article. NKR takes responsibility for the paper as a whole.

: Funding and support: This study was funded by the “Urgent Matters” Technical Assistance Grant (#048555) and Demonstration Grant (#048556) from the Robert Wood Johnson Foundation.

: Reprints not available from the authors.

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Health policy and clinical practice/original researchTime Series Analysis of Variables Associated With Daily Mean Emergency Department Length of Stay

Study objective

Methods

Results

Conclusion

Introduction

Section snippets

Study Design

Results

Limitations

Discussion

Ann Emerg Med

Ann Emerg Med

Ann Emerg Med

J Emerg Med

Ann Emerg Med

Ann Emerg Med

Variables that affect patient throughput times in an academic emergency department

Am J Med Qual

Measuring crowding: time for a paradigm shift

Acad Emerg Med

The effect of hospital occupancy on emergency department length of stay and patient disposition

Acad Emerg Med

Health policy and clinical practice/original research
Time Series Analysis of Variables Associated With Daily Mean Emergency Department Length of Stay