Harmony Healthcare Blog

Length of Stay (LOS) - What is the Best Calculation?

Posted by Kris Mastrangelo on Wed, Dec 10, 2014


Edited by Kris Mastrangelo

C.A.R.E.

Compliance • Audits/Analysis • Reimbursement/Regulatory • Education/Efficiency


Doctor holding clipboard with file in hospital room-1

Every healthcare entity is impacted by the Affordable Care Act and the country's mission to improve quality of care while simultaneously reducing expenditures. Gauging success is no easy feat.  Data collection is the foundation for monitoring progress but in itself is a daunting task.  One of the most considerable areas under scrutiny is Length of Stay (LOS).  In fact, Accountable Care Organizations are using this metric as a deciding factor for SNF program participation.  If the patients are discharged in a shorter period of time than the "imposed benchmark", the SNF is considered to be doing a good job.  If the patients stay longer than the "imposed benchmark”, the SNF is at risk of being ousted from the "ACO". Therefore, the accuracy and consistency of these figures is critical for care, operations, outcomes and analysis.


What calculations are being used?

Once the data has been gathered, the analysis begins......but what formula is the one to use?  The three most often applied calculations include the Average, the Geometric Mean and finally, the Median.

Average:

The most common statistic, which is applicable to many industries, is the average length of stay (ALOS). This average is simply the arithmetic mean of the data. Let d represent the patient days and N represent the total number of patients. Mathematically ALOS becomes,

LOS

The LOS data is positively skewed, meaning it has a long tail to the high side.  The ALOS calculation is biased by the outliers and gives a misleading assessment.

Outlier examples include patients who are admitted for only one day and return to the emergency room. Patients who remain skilled under Medicare for more than 80 day could be another example of an outlier.

Geometric Mean:

The second statistic, and more accurate, is the Geometric Mean.  It is a more precise representation of the central value of an ensemble of points since it is not as sensitive to outliers. Given N patients the geometric mean is the Nth root of the product of the individual patient days. However, the geometric mean calculation is simplified by using natural logarithms as shown below.

Geometric_LOS

Median:

Lastly, the Median statistic is a third alternative.  The median is the middle number in a sequence of numbers. Otherwise defined as the 2nd quartile or 50th percentile and best describes the central value of a distribution.  Harmony Healthcare International compiled the length of stay days for 9552 Skilled Nursing Facility Medicare Patients. The data was taken from homes in New England and New York State between 2012 and 2014. Histograms show that the LOS data follows a Gamma probability distribution. B.M.S.G. Banneheka and G.E.M.U.P.D. Ekanayake well known statisticians in Sri Lanka derived a new point estimator for the median of the Gamma distribution in 2008. The algorithm is based on the ALOS represented by and the standard deviation of the LOS data.  Mathematically,

Median_LOS

What formula is the most accurate?

Patient length of stay (LOS) is a metric used in the Prospective Payment System for Medicare reimbursement in Skilled Nursing Facilities (SNF).  There is a trend to benchmark the LOS with a single number for prediction and comparison purposes.

Conventional wisdom shows that the median is the most meaningful comparison measure for evaluating LOS data.

The cumulative Gamma distribution function for the 9552 HHI patients is presented in Figure 1. This graphic shows the percentile of each length of stay.

  • The ALOS is 24.4 days and has a percentile of 60.9%.
  • In other words, 60.9% of the stays are 24.4 days or less.
  • The median 50% point is at 19.1 days and is the central value.
  • The geometric mean on the other hand is 17.4 days and is at the 45.9%.
The conclusion reached is that the geometric mean is more accurate than the

Patient length of stay (LOS) is a metric used in the Prospective Payment System for Medicare reimbursement in Skilled Nursing Facilities (SNF).  There is a trend to benchmark the LOS with a single number for prediction and comparison purposes.

Conventional wisdom shows that the median is the most meaningful comparison measure for evaluating LOS data. 

The cumulative Gamma distribution function for the 9552 HHI patients is presented in Figure 1. This graphic shows the percentile of each length of stay. 

  • The ALOS is 24.4 days and has a percentile of 60.9%.
  • In other words, 60.9% of the stays are 24.4 days or less.
  • The median 50% point is at 19.1 days and is the central value.
  • The geometric mean on the other hand is 17.4 days and is at the 45.9%.  

The conclusion reached is that the geometric mean is more accurate than the average length of stay.  This chart bears that point out.  However, unquestionably, the median provides the best estimate of the central value of a Gamma distributed set of data.

This chart bears that point out.  However, unquestionably, the median provides the best estimate of the central value of a Gamma distributed set of data

LOS_Graph_fig1

FIGURE 1 

Free RUG Analysis - Compare your facility's utilization with current national CMS data

Conclusion:

To maintain a viable Medicare program in the skilled nursing facility setting, leadership must analyze the admission and discharge process for the Medicare Part A beneficiary, as well as all payor sources who are admitted for post acute care.

In February 2013, the OIG Executive Summary specified recommendations to CMS to include the following:

  • Strengthening regulations related to care and discharge planning.
  • Providing guidance to SNFs to improve care and discharge planning.
  • Increasing surveyor efforts to identify SNFs that do not meet care and discharge planning requirements in order to hold SNFs accountable when they fall short.

This paradigm shift falls in line with how acute care hospitals track, interpret and measure length of stay, a critical factor when considering accountable care and ACO’s.  We also know the IMPACT Act is moving quality measures and benchmarking toward becoming a standard across the continuum.

The key to effectively tracking and interpreting data is ensuring industry wide consistency in the formula. History and research shows that CMS uses varying formulas in different situations.   The above data and analysis depict the need for CMS guidance and standardization on the matter. 

If you need help with LOS calculations or would like to learn more, please click here to contact Harmony Healthcare International or call us at (800) 530-4413.  

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