Mammogram study and doctors trying to do math

Requiring insurers to pay for lots of mammograms is one of the features of Obamacare so presumably this billable procedure is going to become more popular here in the U.S. A new study, however, shows that the billions of dollars per year (NPR estimates) that Americans spend on mammograms is mostly wasted (New York Times).

This reminds me of a conversation that I had with a woman who turned 40 and had her first mammogram. The doctors found something that looked unusual and they told her that there was a significant chance that it was cancerous. I said “Doctors can’t understand basic probability. If you’d had a mammogram last year and the one this year showed something different then they might be correct. But given that this is their first look, the probability of a real problem is vastly lower than the number that they citing. I would wait a couple of years and let them do another one and see if anything has grown. Then let them cut you open.”

The woman accepted the advice of the top physicians at the Massachusetts General Hospital and let them cut her open, removing a portion of her breast tissue for a biopsy. They found nothing but left a scar a substantial bill for Blue Cross.


  1. Matt Henderson

    February 13, 2014 @ 3:52 am


    There’s a good book by John Allen Paulos called “Innumeracy” that presents some eye-opening examples of how doctors can get things very wrong due to a lack of understanding of probability. (It also talks about how mass media compress the distribution of bad news, and making the world seem a much more dangerous place than it really is.)

  2. Thomas Cooper

    February 13, 2014 @ 3:22 pm


    It really is appalling how few doctors understand probability; almost none have even a rudimentary feel for Bayesian probability (which you describe here). Given that much of a doctor’s job is probability (diagnoses), I wonder what they teach in med school.

  3. Sam

    February 13, 2014 @ 6:22 pm


    Actually, in the US, part of a doctor’s job is to avoid a lawsuit. Suppose in your friend’s case that a mammographic mass was found without a prior baseline mammogram, and that the chances were 1% that it could be malignant. How many patients would the doctor see in this situation before a cancer is ‘missed’ because no biopsy was performed? How many before someone whose personal acceptable miss rate is zero gets upset and sues? Since there are no rules to follow that state in black and white what a doctor should do in this situation, in the long run the steady practice of routine biopsy could save many years of unreimbursed time and grief in the court system.

    Of course, there is also lots of money to be made in performing biopsies, so there is that bias in the picture.

    The inclusion of mammography in the ACA is political pandering to ‘women’s health’.

  4. Mark Hurst

    February 13, 2014 @ 7:03 pm


    I’m pretty sure the recent book “The Joy of X” by Strogatz has a “how doctors don’t do probability” example, I believe specifically about breast cancer screening.

    And seconding the vote for Paulos’s “Innumeracy”… fun & good read.

  5. Josh

    February 13, 2014 @ 7:17 pm


    This kind of stuff isn’t exactly new. The reason they want the screenings covered is because pretty much every major medical organization recommends them, and Doctors tend to go by recommendations. People tend not to go to the Doctor to just hear that’s it not probable when things like cancer are involved. Of course the patient always just has the option of saying no.

    “Over the last decade or so, the recommendations that screening should begin at age 40, that it should be done annually, and that it should continue for the rest of a woman’s life became the basis of public health policy with respect to breast cancer, as well as breast cancer awareness campaigns by advocacy groups. Then, in 2009, the USPSTF dropped its bombshell, in which it suggested that this screening campaign was too aggressive, resulted in too much overdiagnosis and overtreatment, and should be scaled back.”

    “The shortcomings of screening, including overdiagnosis, overtreatment, lead time bias, and length bias, are not reasons to give up on screening. They are reasons to learn how to screen smarter.”

  6. Anonymous

    February 14, 2014 @ 10:24 am


    With a few exceptions, medical screening tests are useless. A good medical delivery system may not be as important as many think. Cubans don’t have access to expensive testing and they live just as long as Americans. Hispanics have the longest life expectancy in the US (and don’t get nearly as many mammograms as whites, for example). And… physician strikes may result in a drop in mortality as it was the case in Israel:

    Most centenarians don’t mention “access to excellent preventive medicine” as the reason for their longevity…

  7. CHenry

    February 14, 2014 @ 6:45 pm


    Don’t assume that because the procedure is “billable” that it will automatically become more frequently done. Mammography has always been billable. Making it a mandatory item for health insurance policies was a political act, and had nothing to do with the probability of finding a tumor in a woman of a particular age group. But it helps solidify a voting bloc.

    The issues of “innumeracy” are largely irrelevant. Even if largely true, much of what constitute practice guidelines comes from specialty organizations whose recommendations rely on study data where reasonably powerful data are available. At the same time, there is pressure on the medical community to yield near-perfect rates for early diagnosis which unavoidably requires more testing, including imaging and biopsy which unavoidably results in negative studies and negative biopsies after equivocal and even positive studies, all for the sake of not missing the true positives. Calling the cost of those studies “waste” is plain dishonest. What it is is expensive, as all processes invariably become in their quest for six sigma or whatever other name you wish to give to acceptable error.

    For those not so in the know, mammography is hardly the path to riches, and breast biopsy isn’t either. All the pink ribbons aside, what exists today is a process made to avoid missing treatable breast carcinoma in younger patients, which if missed does carry significant mortality and morbidity. When the public tells us that those misses are acceptable if costs can be reduced, fine.

    I’m not an oncologist or a general surgeon, but I suspect better and more meaningful savings will be had by lowering the cutoff age for screening mammography.

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