From Davis Balestracci -- Statistical Stratification: Part 2

Published: Mon, 09/22/14

From Davis Balestracci -- Statistical Stratification:  Part 2

Note to plain text readers:  To see the three figures in the body of the newsletter, I suggest you read it by clicking on the "View as Web Page" link immediately below.

[~ 875 words: take 4-6 minutes to read over a break or lunch]

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The Alternative to the "Simple, Obvious, and Wrong" SWAG

Hi, Folks,

My last newsletter demonstrated a common incorrect technique -- based in "traditional" statistics -- for comparing performances based on percentage rates.   This newsletter will use the same data to show what should be done instead.

To quickly review the scenario:  In an effort to reduce unnecessary expensive prescriptions, a pharmacy administrator developed a proposal  to monitor and compare individual physicians' tendency to prescribe the most expensive drug within a class. Data were obtained for each of a peer group of 51 physicians -- the total number of prescriptions written and, of that number, how many were for the target drug.

The Correct Alternative -- a p-chart Analysis of Means

During this time period, these 51 physicians had written 4032 prescriptions, of which 596 were for the target drugs -- an overall rate of 14.8 percent.   The goal of analysis of means (ANOM) is to compare a group of physicians who have what should be similar practice types, a relatively homogenous "system," if you will.  Each is compared to their system's overall average.  Variation is exposed and then there is conversation to discuss the variation, then reduce the inappropriate and unintended  variation.

For each individual physician's performance, one calculates the common-cause limits of what would be expected due to statistical variation from the system's 14.8 target prescription rate.  Based on the appropriate statistical theory for percentage data based on counts (i.e., binomial), a standard deviation must be calculated separately for each physician because each wrote a different number of total prescriptions.  Note that this is similar to what was done for the u-chart ANOM for rates explained in my 25 August newsletter.

The calculation for the p-chart ANOM is as follows:

Once again, note its similarity to the u-chart calculation, as well as the philosophy of its use.  They differ only in this calculation of the common cause band.

As in the u-chart, this result of the square root is then multiplied by three (for "three standard deviations"), then added and subtracted to the overall mean to see whether the actual value for an individual physician is in the range of this expected variation, given an assumed rate of 14.8 percent.

The SWAG graph is shown below and the p-chart ANOM is below that.  

Note that what many of you would consider conservative three standard deviation limits --  calculated correctly -- are in this case comparable to approximately  1.5 standard deviation limit of the incorrect analysis. Another difference: the overall system value obtained from the aggregated summed numerators and denominators of the 51 physicians was 14.8 percent, which differs from merely taking the average of the 51 percentages (15.8).

In ANOM, anyone outside his or her (correctly calculated) unique common-cause band is a probable special cause; these physicians are truly "above average" or "below average." Note that physicians 48 and 49 could still be indicative of a prescribing process at 14.8 percent because of the number of prescriptions written.

Using the previous SWAG analysis, depending on the analyst's mood and the standard deviation criterion subjectively selected, he or she could claim to statistically find one or 11 upper outliers, using two or one standard deviations, respectively.  The ANOM shows eight probable above average outliers, with a lot more certainty than a SWAG.

So, what should we conclude from our correctly plotted graph? Only that these outlier physicians have a different process for prescribing this particular drug than their colleagues, 36 of whom exhibit average behavior -- these physicians between the red lines are indistinguishable, from each other and the system average of 14.8 percent. For some physicians, this outlier variation might be appropriate because of the type of patient they treat ("people" input to their process), and for others it may be inappropriate or unintended due to their "methods" of prescription, but they don't know it. Maybe collegial discussion (including the outliers who are below average) using this graph as a starting point would be more productive than what has become known as "public blaming and shaming."

Stopping the Crazy-Making

And then there are people obsessed with "standards"...

I cringe as I think of these people creating and enforcing standards via the WAG approach:  set a standard above which they "feel" no one should be and give feedback  to those physicians.  In this case, if the standard is 15 percent,  27 physicians would get such feedback (19 inappropriately).  If the enforcers decide to get "tough" and set a 10 percent goal, then 35 or 36 physicians would get feedback.  There is no realization that the current system seems "perfectly designed" to perform at 14.8 percent.

Integrating ANOM with Standards Thinking

If the standard were 15 percent, the first order of business would be to study the eight above average outlier physicians and see whether it is appropriate to bring them into the average red zone with their 36 colleagues.  If the standard were 10 percent, there needs to be fundamental change in all physician behavior, but the discussion could begin by dialoguing with the six physicians who are truly below average.

And look what is lost in all these discussions:  linking all this with observed  patient outcomes for the individual physicians.  Might this put the focus where it should be rather than cost?  I would call this a much better analysis for determining where the process should be -- which I think would beat a WAG in the patients' eyes.

Until next time...

Kind regards,
P.S. I am in the middle of feverishly editing the new edition of Data Sanity

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