Introducing analysis of means to medical statistics

Mohammed A Mohammed; Roger Holder

doi:10.1136/bmjqs-2011-000477

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Introducing analysis of means to medical statistics

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ANOM Chart: A Chart Worth Getting to Know
Karen Homa
Published on: 13 May 2016

Published on: 13 May 2016
ANOM Chart: A Chart Worth Getting to Know
- Karen Homa, Improvement Specialist
I appreciated seeing an introduction of analysis of means (ANOM) by Mohammed and Holder. As stated in their article, the technique is not well known, but nonetheless I would like to encourage people to learn this useful graphical display to compare groups. I have been using this method in healthcare improvement work (1,2) and would like to share a couple of lessons learned over the years. The proportion ANOM chart should...
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I appreciated seeing an introduction of analysis of means (ANOM) by Mohammed and Holder. As stated in their article, the technique is not well known, but nonetheless I would like to encourage people to learn this useful graphical display to compare groups. I have been using this method in healthcare improvement work (1,2) and would like to share a couple of lessons learned over the years. The proportion ANOM chart should meet most of your needs, since first continuous type data can be converted to a proportion. For example, length of stay (LOS) greater than 2 days can be used in the proportion ANOM chart to compare groups (such as hospitals or providers) versus using LOS in the continuous ANOM chart. Secondly, the proportion ANOM chart is easier to use since it is the p-chart (a statistical process control chart), which people may be familiar with. The only difference between the ANOM for proportions and the p-chart is the control limits on the ANOM are not set at 3 sigma - they are adjusted to account for number of groups being compared. The best reference I have seen on ANOM is in a book by Balestracci & Barlow.(3) Another issue with the ANOM chart is the denominator size - you need the right size for these charts to be most helpful. A good rule of thumb is 5. If you are comparing LOS greater than 2 days across hospitals and 25% is the overall rate then each hospital will need to have 21 or more patients (5/.25 = 20). If there were only 10 patients in each group, then the control limits will be too wide and may not yield useful information. Besides too few patients in the denominator, another issue is too many patients. If your subpopulation of patients is 1,000, then you have 50 times more patients than needed and you may have many groups crossing the limits, which most likely contains Type 1 errors and is also useless information. The primary purpose of the ANOM chart is to find the hospital (or whatever you are comparing) that is performing outside the system result because there will be opportunity to learn from the hospital that is performing beyond the others. One last lesson to keep in mind is the ANOM chart can be somewhat useless if you are analyzing rare events or a proportion that is less than 10%. For example, mortality rate (MR) for a specific procedure is 1.5% and you want to see if there is a difference across 15 hospitals; however, there are on average 100 patients per year that have the procedure. Using the 5 rule, you would need 334 or more patients in the denominator so you will need 3.3 years of data. You may have the data, but most likely you will only find a low performer, which can be motivating information for the low performing hospital but more useful information is finding a hospital that is doing this well. If a hospital had 0% MR, then the ANOM chart will not show the 0% crossing the lower limit with 334 patients in the denominator. The hospital would need to have 2.5 times more patients (835 with 0% MR) and then the result would be significantly different. If ANOM is not in your analytical tool box, I would highly suggest learning more about this method, since the graphical display does so effectively what statistical process charts are suppose to do - point out the difference between common and special cause variation.
1. Homa K. Analysis of means used to compare providers' referral patterns. Quality Management in Health Care 16(3): 256-264, July/September 2007. 2. Homa K, Kirkland KB. Determining next steps in a hand hygiene improvement initiative by examining variation in hand hygiene compliance rates. Quality Management in Health Care 20(2):116-121, April - June 2011 3. Balestracci D, Jr., Barlow JL. Quality Improvement. Practical Applications for Medical Group Practice. 2nd ed. Englewood, CO: Center for Research in Ambulatory Health Care Adminstration; 1998.
Conflict of Interest:
None declared
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Conflict of Interest:
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