Geometric and Arithmetic Values
The risk-adjusted analyses contain both arithmetic and geometric values for the following outcomes:
- Charge
- Cost
- LOS
The 3M™ versions display arithmetic values in the grids by default and the CareScience Analytics versions display geometric values in the grids by default.
It is highly recommended to use the default setting for arithmetic or geometric value because they are coherent to the respective risk-adjustment method.
Calculation Overview
Arithmetic values are calculated with the arithmetic mean and the geometric values are calculated with the geometric mean. Arithmetic and geometric refers to the way the average value is calculated. The main difference between arithmetic and geometric values is the way outliers in the data are handled.
Arithmetic mean calculations are a simple aggregation of the outcomes for all patients in an identified population divided by the total number of patients. As a result, the extreme outliers can have a significant impact on the resulting mean value. In contrast, the geometric mean applies a logarithmic function to the data that constrains the effect of outliers on the mean value.
The geometric mean in QualityAdvisor analyses is typically less than the number returned by the arithmetic mean because of the natural lower bound of zero for cost and LOS data and the reduction in the effect of the extreme outliers on the unbounded upper end of the distribution. Because of the adjustment for extreme values, geometric values are often closer to the center of the mass of data, which can reveal a more representative average outcome of the population.
Why Use the Geometric Mean?
The main advantage to using the geometric mean is that negating extreme values can produce more stable numbers that are more representative of the population because outliers are not impacting the reported values. This can help when identifying variations in care that represent opportunities for improvement.
Comparing Arithmetic and Geometric Values
One of the biggest benefits of the risk-adjusted analyses is that both arithmetic and geometric values are pulled for the same analysis. This can have the effect of revealing the impact of outliers on your data as well as helping you understand the average value more clearly.
In general, the greater the difference between arithmetic and geometric values, the greater the likelihood of outliers in the analysis population. Additionally, if you know that you tend to have dramatic swings in outcomes within a specific population due to outliers, the geometric mean can help in producing a more stable estimate of the outcomes over time that allows the user to identify systematic variations that may be opportunities for improvement.
For example, on a risk-adjusted analysis, if you notice a big difference between the arithmetic and geometric value for the same outcome, you can drilldown into the details to discover extreme values, which enables valuable analysis for specific outcomes.