Average length of stay versus median length of stay
March 22, 2023 · 5 min read
Patients are eligible for hospice if they have a terminal diagnosis and a prognosis of six or fewer months to live if their disease runs its natural course. A patient who lives longer than six months can still get hospice care if the medical director or other hospice physician recertifies that the patient is still terminally ill.
What is hospice patient length of stay?
Hospice length of stay is an important metric that is monitored by both CMS and by hospice providers. Hospice length of stay measures the count of days that a patient receives hospice services, from the day that the patient is admitted into hospice until the day the patient is discharged (either alive or deceased). In 2018, 25% of Medicare beneficiaries received hospice care for seven days or less and 54% of Medicare beneficiaries received hospice care for 30 days or less.
Why should a hospice monitor patient length of stay?
Monitoring patient length of stay can aid in detecting cases of possible fraud or abuse – instances where ineligible patients continue to receive the hospice benefit. This metric also helps monitor whether the hospice benefit is being adequately utilized. Although patients are eligible for hospice when they have six months or less to live, most patients receive less than 30 days of hospice care.
Agency patient length of stay is also trended over time and is also compared against the value for patients in the same region, state, or nationwide. The metric may also be analyzed for patients in subpopulations – for example patients with the same disease, race, or ethnicity.
How is patient length of stay calculated?
Patient length of stay is calculated using all patients discharged by the hospice provider during the reporting period. For example, if the hospice would like to compute the length of stay for patients during the 4Q 2022, all patients who were discharged during 1Q 2023 would be included in the calculation. For each patient, the number of days from the date of patient admission until the date of patient discharge is counted; this represents the patient length of stay.
Patient length of stay = [patient discharge date]-[patient admission date]+1
What are common measures of length of stay?
Two common patient hospice length of stay measures are Average Length of Stay (ALOS) and Median Length of Stay (MLOS).
Average length of stay
Average length of stay is the arithmetic mean of the data collected. Specifically, if d is patient length of stay and N is the total number of patients then average length of stay (ALOS) is calculated as follows:
ALOS = ( d1 + d2 + d3 + …. + dn ) /N
Where di = patient length of stay for patient i
Median length of stay
Median length of stay is the middle number in the sequence of numbers. Specifically, compute the length of stay for all N patients. Then, order these N numbers in ascending order. The middle number is the median. If the number of patients is even then there is no middle number. Instead, the median is calculated by taking the average of the two numbers in the middle.
Comparing average and median length of stay
The average is sensitive to outliers in the data. That is, if there are a few patients with a very high length of stay while all other patients have a significantly lower length of stay, the average will be biased by these outliers and will give a misleading assessment of overall patient length of stay. Below, we give an example to provide greater intuition into the impact of outliers on average length of stay and the difference between mean and median length of stay.
Suppose a hospice agency discharged 35 patients during 4Q 2022. The patients’ lengths of stay are as follows:
We compute the average length of stay by summing each of the 35 patient’s length of stay (in the “Length of Stay” column) and dividing that total by 35 (the total count of patients).
Average length of stay (ALOS) = 38.5
We compute the median length of stay by sorting the patient’s length of stay in ascending order and identifying the central number. Since there is an odd number of patients, there will be a single central value. In this case, the central value is 20.
Median length of stay (MLOS) = 20
Average length of stay is almost double the median length of stay. What is leading to these significant differences between ALOS and MLOS? Observe the outliers in the data. There are two patients with length of stay that exceeds 200 days. There are two additional patients with length of stay exceeding 100 days. Since ALOS is sensitive to outliers, ALOS is being pulled to a higher value due to the presence of these outliers.
To provide additional insight, we have plotted a histogram of the length of stay values. A histogram shows the count of observations in the data that fall in each of the specified ranges.
The table on the left shows the count (frequency) of observations of patient length of stay in the data for each of the ranges: 0-10 days, 10-20 days, 20-30 days, 30-40 days, and greater than 40 days. There are 11 patients with length of stay between 0-10 days, 7 patients with length of stay between 10-20 days, 6 patients with length of stay between 20-30 days, 6 patients with length of stay between 30-40 days, and 4 patients with length of stay that exceeds 40 days.
Think about this histogram and now consider the MLOS and ALOS. Median length of stay is 20 days – it falls well in the middle of the data. Average length of stay, however, equals 38.5. It falls, essentially, in the final bar of this histogram and well beyond where the majority of the data lies. The provides a visual demonstration of the impact of outliers on ALOS.
Providers should monitor both ALOS and MLOS. Significant differences between these numbers would indicate the presence of outliers and should be investigated.
Print ‘n take hospice keys
- Understanding the difference between the average (mean) and the median
