Physician Compensation: What is Simpson’s Paradox?

Why is it important?

• Statistics are not ironclad. Often, they are not. For example, if you are a gastroenterologist in a suburban community, there is no minimum compensation or typical scenario.
• Simpson’s paradox is not obscure. It is well-recognized.
• Causal inferences can be hazardous. I do this many colonoscopies, so I should have this base pay. In fact, there are often uncontrolled or unobserved variables that can eliminate what you think should be your base pay or even reverse the association of how many procedures translates to so many dollars.
• Look at this illustration.

Suppose you and your colleague are back in medical school and studying anatomy. Your friend answers a higher proportion of exam questions than you do on two consecutive days. Does that mean your friend answered a higher proportion of them correctly than you when the two days are combined?

Not necessarily!

But how could that happen?

Simpson’s paradox happens when some groups of data show a certain relationship in each group, but when the data is combined, the relationship can reverse.

The point is that there are many variables in determining physician compensation. Statistical data must be carefully analyzed in context.

Here is where coaching comes into play. There is no way to consider all factors when you are practicing medicine and saving lives every day. You just do not have the time nor the proper context. There is the existence of marginal associations of issues related to your practice that you may not have any way of really knowing or appreciating.

When confronted with a reverse paradox such as the illustration above, it is natural to ask whether the partial association is a correct representation of the variables. Assuming the relationships among the variables, perhaps my compensation is average and appropriate, but maybe it is not. Maybe, I deserve better.

Often, we are interested in causal relationships. However, the statistics provide us with no guidance as to whether the marginal association or even partial association is accurate or reversed.

You need substantive information to guide your judgment. What are the parameters in your particular location and environment?
Second, the field of statistics provides us little help in determining when or if Simpson’s paradox will occur. There may be uncontrolled or unobserved variables that we either do not know about or are out of anyone’s control. That is where compensation coaching comes in.

For example, you are only one of three physicians who perform a particular procedure at your institution, but you are paid no differently than others in the same specialty. You have intrinsic value that you need to raise your hand about. It is unsettling to imagine that you are doing your work daily, you believe there is a causal relationship between your work and your pay, but in fact, it may be opposite to what you really are worth, or what the market will bear.

Key Takeaways

• It may be easy to understand how your anatomy partner did not do as well as you thought using the example above. But predicting when Simpson’s paradox will occur is more challenging regarding the real-life issues with physician compensation.
• As long as you have the best information regarding all the additional variables regarding your compensation, Sampson’s paradox should not occur. This assumes that someone can guide you through all the possible covariations. Even if the covariations are related to outcome, in this case, your compensation, Simpson’s paradox should not occur. But don’t you want to know for sure?
• The only way to ensure that happens is to step beyond what you know and believe and leave it to experts to help.

Are you getting paid what you are worth?

Visit us at Contract Diagnostics and learn how to get a 30-minute phone call where we will discuss your specific situation and a better way of presenting compensation data to you. We can show what other physicians in your area are earning by specialty and then help you optimize your compensation to give you the best chance of getting paid what you are worth.

About the Author

Dr. Drew Sutton, MD, has walked the long road of a successful medical career, amassing invaluable insights and expertise. With a wealth of knowledge derived from his time in the trenches, he understands the myriad challenges and opportunities that come with physician contracts and compensation. Dr. Sutton is not just sharing theoretical knowledge; he imparts lessons learned from his own hands-on experience in the medical profession. Dr. Sutton has been where you are, and he’s navigated the path to where you want to be.