Whenever you write a report in Trendstar that asks for ALOS (average length of stay), you are prompted for whether the ALOS computation should be arithmetic or geometric. We believe the answer in general ALOS reporting should always be the first choice, arithmetic. Here is some more background to help you understand why.

The geometric computation of your own ALOS is offered as an option in TRENDSTAR because the Medicare geometric ALOS is still offered as one of the comparable LOS standards to display. The geometric ALOS was originally offered because it was the basis for the now defunct LOS outlier calculation. Some TRENDSTAR clients felt that if the geometric standard ALOS were used in a report, that it was only proper to apply the same formula to the hospital’s own data, a point that remains debatable today.

The geometric ALOS formula essentially weights the average by the frequency of each LOS occurrence. Rarely occurring extreme values will have less impact than the most frequently found LOS values. This effectively damps down the effects of extreme LOS cases and generally produces a value closer to the modal (most frequently found) value, but it is harder to explain and defend than arithmetic mean or median values. If fact, TRENDSTAR supported the geometric ALOS computation years before it offered the ability to compute median and standard deviation values. Availability of these newer and more commonly used measures of dispersion reduces the need to use the geometric ALOS calculation.

Computing your own ALOS using the geometric ALOS may make sense if you are if you are trying to develop a more aggressive ALOS standard using your own history. The results can be stored in a benchmark table for later use. Use of the geometric ALOS will require an explanation to your users. You may find it easier to defend development of the benchmark ALOS by eliminating cases more than 2 or 3 standard deviations outside the DRG mean ALOS.

Here is a variation on the explanation on Page 201 of the CCA manual:

Geometric Means

To compute the geometric mean, each LOS value is raised to the power of the number of cases associated with that value. The resultant figures are multiplied together and the Tth root of the product is calculated, where T is equal to the total number of cases for all values. That is:
Tth root of (LOSm to the Y * ...*LOSn to the Z)
…where the different LOS values are included in range from M to N, Y is the number of cases with LOS value M, Z is the number of cases with LOS value N, and T is the total number of cases of all LOS values. You can see that each LOS value is thus weighted by the number of cases that occurred with that LOS.

The geometric mean is important primarily because it was the mean used by HCFA to determine LOS outlier status, and to calculate transfer payments. The geometric mean was chosen by HCFA because it minimizes the effects of high values and thus minimizes the effects of extreme outliers.

Finally, it may be useful to use your own history or statewide data to compute median, mean, geometric, standard deviation and average LOS by DRG, severity adjusted DRG, patient age group, payor or other factors. TRENDSTAR’s ability to freeze this type of data in tables for later precise comparison to actual, essentially adjusting for volume and mix changes automatically. Benchmark tables created in this fashion are superior to comparable LOS options because of the great flexibility and power available to the user.
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