Estimating Treatment Space Needs

by Frank Zilm

Estimating bed need first starts with an understanding of arrival patterns, patient mix and the components of the length of stay. Key to the analysis of arrivals is the concept of randomness, meaning the arrival of patients is independent – the appearance of one patient cannot be used to predict the next. Although this concept holds for a given period of time, there are non-random seasonal, day of week, and time of day patterns that predict peak periods of activity. Treatment space utilization should be made based on these peak periods of activity.

In most regions of the United States seasonality in emergency volume is predictable and significant, ranging from five to thirty percent variation. At least five years of historical monthly data should be studied to identify peak demand. Indexing the monthly visits is an important concept to minimize the effect of overall growth in activity. The basic calculation of indexing is to divide each month’s total visits into the average monthly visits for a year (total visits divided by twelve). This results in a scale which averages 1.0. If a given month’s visits are higher than the average, the index will be above 1.0, with a lower monthly visit represented by a value less than 1.0. By averaging each months indexed value, an overall pattern of demand can be calculated and easily graphed, as illustrated in figure 1.

Notice the radial variation in the pattern among the four hospitals. Two of the institutions are located in areas which experience very high tourists in-migration at different times of year – Hospital A is in Arizona and Hospital D is in Alaska. Hospitals B and C are located in Ohio and Florida in areas which do not experience the same tourist impact.


Once the peak month in activity is identified, patterns of visits by day of week and time of day should be studied for peak demand patterns.. Total visits by day of week should be analyzed based on yearly dates to target the busiest day, typically Saturday, Sunday or Monday. The last component of the arrival pattern is the time of day. Arrivals by hour frequently result in a pattern similar to Figure 2. This pattern is surprisingly consistent throughout the country. Note the difference in arrival patterns between adult and pediatric patient populations. Adult arrivals peak at 11 AM and slowly decline through the afternoon. Pediatric patients, on the other hand, peak in late evening.


Future workload forecasts should use these patterns to estimate the inter-arrival rate for patients during the peak period of activity. The inter-arrival rate is the average time between patient arrivals, an important calculation in the analysis of bed need. Figure 3 illustrates the calculation of the inter-arrival rate for a hypothetical ER with 100,000 annual visits.


Figure 3 Sample Calculation of Inter-Arrival Times

The second critical task in bed need calculation is the analysis of current length of stay patterns. An ideal data set should contain major components of the patient visit for each major patient group:

• Arrival to triage
• Triage/registration duration
• Triage to treatment space
• Treatment arrival to first provider contact
• Provider contact time
• Diagnostic times (radiology, lab, etc.)
• Discharge disposition
• Time from admission decision to leaving the department
• Time from decision to discharge

It can be particularly valuable to analyze the utilization of imaging and laboratory services, which will typically be a part of approximately 80 percent of patient encounters. The time for order entry to implementation and the time from results reporting to physician review can account for significant components of the patient stay and areas that can be reduced through digital medical records and patient tracking system.

Delays in admissions have emerged in the last decade as a major factor in long ED length of stays. Nationally, admitted patients currently account for twelve percent of all emergency service visits. Downsizing of hospital beds and a critical shortage in nursing has resulted in extended stay that can create critical log jams in emergency service availability. Forecasts of continued manpower shortage will force many emergency services to develop creative ways to respond to this problem.

One of the resulting effects of the delay in admission is an increase in the average length of stay in emergency services. Frequently the distribution of length of stay follows a bimodal geometry, with admitted patients pushing the average significantly past the modal value as illustrated in figure 4. The percent of patients admitted from the emergency service, inpatient hospital occupancy level, and the development of an emergency service observation/clinical decision unit can extend the clustering of long length of stay patients and raising the overall length of stay.


If it is not possible to collect all of this information in a timely manner, the minimum data set is illustrated in Figure 5.


The final piece of the puzzle is establishing assumptions regarding future patterns. In most situations it is safe to assume that historical arrival patterns and seasonality will continue. Forecasting total visits has proven a daunting task, with most organization underestimating the continued increase in the rate of visits per thousand over the past decade. Careful review of the emergency service’s historical service area, the projected age-specific forecast, emergency service utilization rates and market share should be part of the base analysis. Use of time series regression analysis of historical visits should be used with great caution.

A useful planning technique for establishing forecasts is to develop alternative scenarios which reflect plausible patterns of future development. These scenarios could include assumptions regarding growth or closure of competing hospitals, development of detached urgent care services, or the growth resulting from new hospital clinical initiatives. The goal of scenario analysis is not to pick the most likely future but to understand the implications of the alternative futures on the needs of the emergency services. If all scenarios lead to the same estimate of need then planning should proceed with a high level of confidence. This is seldom the case. As the analysis of bed need develops, each scenario typically reveals variations in estimated bed needs that will require evaluation and judgment decisions regarding the beds that will be used as the base estimate of need and the potential growth target.

Translating Demand into Beds

Three methods are commonly used to estimate bed need for a target demand. The first is to use an estimate of the capacity of each treatment space measured in total annual visits per bed. This ratio has continued to drop as patient length of stay in emergency services increase, dropping from targets of 2000 visits per bed to current recommendations in the range of 1400 visits. Institutional variations in patient length of stay, seasonal peaks in activity and patient mix make the application of suggested ratios arbitrary and high risk. This methodology provides no information on estimated delays in access to treatment areas, or the potential effect of changes in through-put times.

A second approach is to estimate bed need based on target utilization goals. An example of this approach is illustrated in Figure 6. This table estimates the treatment rooms required for a peak workload day; and a maximum achievable utilization level for each type of room. The achieve utilization level will vary based on assumptions regarding the acceptable wait for access to a bed. For high acuity functions, such as trauma and resuscitation, there should be no wait under any circumstances. On the other hand, at peak periods a wait for access to a fast track room will occasionally occur.


Figure 5 Estimating Treatment Rooms Based on Utilization Targets

Although this approach is simple to use, there are serious shortcomings, including the inability to estimate the probability of reaching bed capacity and the resulting total wait time for access to a room.

Simulation Modeling

Simulation modeling has emerged in the past decade as a powerful tool for estimating performance of emergency services. (See “Virtual Ambulatory Care-Computer Simulation Applications’, Zilm, et. al., JACM 26:1-March 2003)

There are three unique characteristics of contemporary simulation modeling:
a. Process/flow – the ability to represent the actual flow of patients through an ambulatory care system over simulated time, monitoring resource utilization, waiting times, and other characteristics.
b. Probabilistic events – Simulation modeling tools can represent the statistical probabilities associated with arrival patterns, service times, and patient characteristics.
c. Animation – the ability to illustrate activities in the model through graphic icons and even floor plans of the service.

Outside of building a new department and observing actual performance, simulation modeling provide the most sophisticated tool for analyzing existing and future emergency service needs. A unique capability of this tool is the ability to test the sensitivity of the performance of an emergency service on interdependent variables – staffing patterns, access time to diagnostic services, travel distances.

This robust characteristic of simulation presents one of the most daunting challenges in using this tool – data. Few institutions regularly maintain detailed data to build a sophisticated simulation. Hopefully these data-gaps will close as electronic medical charting is implanted. Until then, planners must face either extended observation data collection or utilization of surrogate data.

A Simplified Estimating Approach

The data requirements, time, and costs associated with developing a complex computer simulation can make this tool inaccessible. I have developed a model of a simple queuing system in an emergency service and run the model through a range of inter- arrival times and length-of-stay assumptions. The logic of the model assumes unconstrained services – a treatment bed is always available upon demand. It also assumes a log normal distribution on patient length of stays. Given these assumptions, total demand for beds over a 200 hour simulation period was tracked and the resulting demand was graphed, as illustrated in figure 7. Each of the four lines in this graphic documents the simulation result for a length of stay distribution with a given average length of stay, ranging from 90 minutes to 240 minutes. The vertical scale shows the cumulative demand for beds. For example, 80 percent of the time there was a need for 12 or less beds when the average length of stay was 90 minutes.


After running these unconstrained models, additional simulations were developed capping the beds available in the emergency based on the 80% 90% 95% and 99% estimated need. The results of these simulations are summarized in tabular form Figure 8.

Two generalized approaches are suggested using these results. While less precise than a custom simulation developed for a specific circumstance, these techniques nevertheless provide a richer tool than the previously described utilization estimate. The following steps are suggested to use this approach to estimate treatment room needs:

1. Estimating inter-arrival times for the patient population using the peak period analysis previously described.
2. Estimating length of stay for treatment room utilization (not for total ER length of stay)
3. Use the table to look up the average length of stay and inter-arrival rate.
4. Determine the desired protection level for the patient population. For high acuity trauma and emergency patients a 99% protection level should be used. This should result in less than a 1 percent probability that a treatment room will be in use. For non-emergency populations a lower protection level during peak periods is common. Few institutions can afford to build all of the treatment rooms required to assure no waiting in the peak period of the peak month. A protection level in the 80 – 90% during peak period translates into a 95-99 percent protection level over the 24 hour day.


In the arrival calculations illustrated in Figure 3, if we estimate the urgent care arrivals with a 5 minute inter-arrival time, the number of treatment rooms needed would be 22 if the average length of stay is 90 minutes. During the peak period approximately one in four urgent care patients would experience a delay in access to a treatment room. The average wait for all urgent patients would be four minutes and the average wait for the 28% that experienced a delay is estimated at fourteen minutes. By adding two treatment beds (90% protection level), the percent experiencing a delay is estimated at 13% with the average delay less that one minute.

If the length-of-stay distribution is highly skewed then this approach should be used with caution.

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