Dahabreh’s Paradox

In the Feb 23, 2011 issue of JAMA, there is an article that discusses a little-recognized but important paradox.  I think it’s as important as Simpson’s Paradox, which I plan to write about in a future blog.  However, unlike Simpson’s Paradox, which is widely appreciated, Dahabreh’s Paradox is not well-recognized.

In many diseases, for example with patent foramen ovales (PFO) or a hole in between the right and left side of the heart, there is a well documented paradox:

  • Patients who present with stroke of a certain type have a very high incidence of PFO. The hole allows small material such as clots to bypass the natural filtration of the lungs and go straight to the brain and cause the stroke.  So hole in the heart is a risk factor for stroke.
  • However, multiple studies have shown that patients who have had a stroke and have the hole does NOT increase the risk of a second stroke compared to patients who have had a stroke and do not have a hole in the heart.

This paradox is found in many other diseases.  For example, taking aspirin protects against first heart attacks but seemingly increases recurrence rate.  Smoking increases the risk of heart attacks but seems to improve prognosis.  Patients with thrombophilia have higher rate of first clot in the leg but not for recurrence.

The paradox arises from what is essentially a selection bias.  There are several other risk factors for stroke, including age, diabetes, hypertension, smoking, and so forth.  Patients with PFO will often have a stroke despite not having any of the other risk factors.  This means that when you add up all the risk factors (PFO plus all other risk factors) the patient is not going to be at any higher risk than the general population.  If you want the do the analysis properly, you have to adjust for the fact that the other risk factors are lower.

Let me give a concrete example.  Let’s say you’re working in the ER and a 38-year old woman, a smoker, comes in with chest pain.  You do the work-up and she turns out to have a heart attack.  Well, virtually the only 38-year olds who have heart attacks are smokers, except in very unusual circumstances.  You treat her, and she’s discharged.  That woman is not going to have a higher risk of having a heart attack than a 65 year old man with a heart attack you treated last week who had hypertension, diabetes, and hypercholeterolemia but who is not a smoker.

On the other hand, if you adjust for her lack of other risk factors, then smoking will emerge as a risk factor–for example, if you compare her against other 38-year old women with no cardiac risk factors.

Another name for this bias is index event bias, although I think a catchier name would be Dahabreh’s Paradox. The JAMA article isn’t available without a subscription but here is a link to an explanation of collider bias, which is more general form of the bias.

You can account for this bias, at least partially, if you recognize the paradox, but as I mentioned, this paradox is not a well appreciated problem.  The paradox will be particularly pernicious for certain types of epidemiological studies, but conduct and interpretation of randomized clinical trials are also affected this bias under certain circumstances.

We need to be careful about not mistaking a case of Kelley’s Paradox with Dahabreh’s Paradox. Kelley’s Paradox is an instance of regression to the mean. Kelley’s Paradox is encountered when you look at exceptionally high or low scoring (on standardized tests) students from a socioeconomic group, and follow their academic performance. They tend to regress to the mean in terms of their performance, because often their scores merely reflect the normal variation inherent in such tests.