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It seems like every few months a new study points out the inefficacy of yet another wide-scale cancer screening. In 2009 the U.S. Preventive Services Task Force suggested that many women undergo mammograms later and less frequently than had been recommended before because there seems to be little, if any, extra benefit from annual tests. This same group recently issued an even more pointed statement about the prostate-specific antigen test for prostate cancer: it blights many lives but overall doesn’t save them.
More recently, researchers at the Dartmouth Institute for Health Policy and Clinical Practice announced that just because a mammogram (almost 40 million are taken every year in the U.S.) detects a cancer does not mean it saves a life. They found that of the estimated 138,000 breast cancers detected annually, the test did not help the vast majority of the 120,000 to 134,000 women afflicted. The cancers either were so slow-growing they did not pose a problem, or would have been treated successfully if later discovered clinically, or else were so aggressive that little could be done about them. Chest x-rays for lung cancer and Pap tests for cervical cancer have come under similar criticism.
Individual cases dictate what tests and treatment are best, of course, but one factor underlying all these tests is a bit of numerical wisdom that, though well known to mathematicians, bears repeating: when one is looking for something relatively rare (not just cancer but even for, say, terrorists), a positive result is very often false. Either the “detected” life-threatening cancer is not there, or it is of a sort that will not kill you.
Rather than looking at the numbers for the prevalence of the above cancers and at the sensitivity and specificity of each of the tests mentioned, consider for illustration cancer X, which, let us assume, afflicts 0.4 percent of the people in a given population (two out of 500)
at a certain time. Let us further assume that if you have this cancer, there is a 99.5 percent chance you will test positive. On the other hand, if you do not, we will assume a 1 percent chance you will test positive. We can plug these numbers into Bayes’ theorem, an important result from probability theory, and get some insight, but working directly through the arithmetic is both more illustrative and fun.
Consider that tests for this cancer are administered to one million people. Because the prevalence is two out of 500, approximately 4,000 (1,000,000 x 2/500) people will have it. By assumption, 99.5 percent of these 4,000 people will test positive. That is 3,980 (4,000 x 0.995) positive tests. But 996,000 (1,000,000 – 4,000) of the people tested will be healthy. Yet by assumption, 1 percent of these 996,000 people will also test positive. That is, there will be about 9,960 (996,000 x 0.01) false positive tests. Thus, of the 13,940 positive tests (3,980 + 9,960), only 3,980/13,940, or 28.6 percent, will be true positives.
If the 9,960 healthy people are subjected to harmful treatments ranging from surgery to chemotherapy to radiation, the net benefit of the tests might very well be negative.
The numbers will vary with different cancers and tests, but this kind of trade-off will always arise in that nebulous region between psychology and mathematics. A life saved because of a test, though not that common, is a much more psychologically available outcome than the many substantial, yet relatively invisible, ill effects to which the test often leads.
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11 Comments
Add CommentIt's more about knowing your ok.
Reply | Report Abuse | Link to thisI don't understand the logic behind careless thinking.
There is no logic behind careless thinking. It's laziness, or just bad habits.
Reply | Report Abuse | Link to thisThe author of this very appropiate article is right when pointing the risk of overdiagnosis that some cancer screening tests do generate, and that the whole subject of breast imaging for early breast cancer detection is under discussion, but previous studies, and also the official statements of organizations such as ACS, ASCO, or ESMO do support the idea that breast cancer screening saves lives, as Colon cancer screening does, and also, the populations at high cancer risk, in which starting sooner the screening tests is adequate, are being more precisely defined. The Pap test continues saving women's lives, and will continue to do so, just some increased level of anxiety among women lead to an increase in PAP frequency not supported by evidence, and that represented and overload for the health personnel involved in women's care. It's not acceptable putting in the same basket Cervical, Breast and Colorectal cancer with the subject of chest X-Ray for lung cancer, it was shown that Chest X-ray is purposeless for Lung cancer screening, but recently, some point that a low radiation level, spiral CT screening in a selected group of people at high risk for lung cancer can be of help. Readers should not make a mix in their mind about three very different cancers: Cervical cancer, Breast cancer, and Lung cancer, and above all, discussing the subject with your doctor is the best approach. Don't forget, undiagnosed hypertension or diabetes mellitus probably harms more people's health than not having cancer screening does, and it's much cheaper and easier measuring cholesterol, arterial pressure, sugar levels, and HbA1c levels. Salut +
Reply | Report Abuse | Link to thisCochrane Database says mammography worse than useless, no lives saved. BMJ and Annals of Internal Medicine have research stating same for PSA test. Try looking at thennt.com---they do the reading of research for many medical procedures and find most of them severely or totally lacking for any efficacy/effectiveness. Try it, you won't like it but you will be way better informed
Reply | Report Abuse | Link to thisKeep in mind the difference between a diagnostic test and a screening test that often comes first. The odds of a positive findings on a screening test are related to the proportion of the problem in the population, plus or minus the standard error of measurement. The odds of a positive finding on a diagnostic or second screening test is---GET THIS--50%. The result is either POS or NEG--either a hit or a miss--50%!
Reply | Report Abuse | Link to thisIt is possible to use or develop another method for confirmation of results like sonography beside the mamography or blood analysis for lung cancer.If we take two metrhods then, we have 28+28+56%
Reply | Report Abuse | Link to thiswith third method we have 28x3= 84%
I am using this article as an illustrative example in my lectures on Bayes' rule so please do not remove it from the internet!
Reply | Report Abuse | Link to this"Weighing the (False) Positives" hit me with a stunning relevance. First my father --a retired math teacher, interestingly--was railroaded by his doctors into a full-blown medicalized response to his prostate cancer based on small changes in his PSA levels (which should never have been drawn for screening a man his age). His life has been "blighted" (to use the author's own terminology) by the side effects of a surgery that was very likely unnecessary.
Reply | Report Abuse | Link to thisSecond, as a politically aroused citizen, I found the extension of mathematical reasoning to the subject terrorism to be all too appropriate. America's full-blown militarized response to the false positive screening for terrorism in Iraq continues to blight us all.
John Allen Paulos opinion in “Weighting the positives” is part of a campaign to discredit screening tests that is misleading and dangerous. Screening tests’ goal is to narrow the population that needs to undergo further testing, like expensive imaging studies that can not be performed in the whole population. All screening tests warn that diagnosis should not be made on the sole basis of that particular test. Therefore it is false that people will be subjected to surgery or chemotherapy after the screening test, if that has happened it is just result of bad medical practice. Using Paulos example, after the screening test, the probability of diagnosing cancer rose from 0.4% to 28.6%, and reduced the population that qualifies for imaging studies from 1 million to ~14,000 a feasible number for more expensive diagnostic procedures (1.5 cases/hour in one year, assuming a MRI machine works 24-7). In fact, according breastcancer.org and cancer.ca in both US and Canada breast cancer rates have decreased steadily since mid 1980s.
Reply | Report Abuse | Link to thisLet’s weight peoples’ lives and not just the math.
Screening Test is now very important part for every type of Industry. And it is available with good technology options, professional support networks and onsite drug testing. Well, it's good post.
Reply | Report Abuse | Link to thisYou can visit at http://cmm.com.au for more details.
Thank You !!!
Nice post. Thank you for sharing valuable information. This is very essential for every industry. Now it is available with good technology options, professional support networks and onsite drug testing.
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