Previously, CMS implemented Tukey’s outlier removal method when calculating star ratings for Medicare Advantage (MA) and Medicare Part D Prescription Drug Plans (PDP). However, the final rule to be implemented in 2022, Removed use of Tukey outlier removal from quality measures. Based on 2020 historical data, 17% of MA programs had a low star rating In contrast, only 1% would have higher star ratings after Tukey outlier removal. This begs the question, what is a Tukey outlier.
Tukey outlier definition.
Tukey outliers are data points that lie outside the following ranges;
- {Q1 – k(IQR), Q3+k(IQR)}
Here Q1 and Q3 are the first and third quartiles of the data respectively, and IQR is the interquartile range (i.e. the difference between the third and first quartiles).the term k is a multiplier that describes how sensitive you want to be to outliers.john tukey proposed k = 1.5 for “outliers”, and k = 3 means the data is “away from”.
How likely are you to identify outliers using Tukey’s method?
The answer to this question depends on (i) how wide your Tukey range is (ie k) and (ii) the shape of the distribution. Andrey Akinshin created the mock Answer this question for the normal, Gumbel, and exponential distributions. The result is as follows. As you can see below, non-normal distributions (especially exponential distributions) are more likely to observe outliers using Tukey’s method.
Like all outliers, identification is key, but what to do with them depends on the context. If these are data errors or pure anomalies, they may need to be removed. On the other hand, if these are just outliers that occur from time to time, you should leave them in the data and try to get a better idea of whether there are values that are different from the regular data generating process that might generate these outliers. Either way, Tukey’s method is a useful and simple way of identifying outliers, but it won’t tell you what to do with outliers once they’ve been identified.
