By Cristina Roure @crouren
The BMJ recently published the results of a randomized Canadian study which shows that annual mammography in asymptomatic women under 60 does not bring any advantage in reducing mortality from breast cancer compared with physical examination without mammography and, instead, it leads to more than 20% over diagnosis. The article is accompanied by an editorial entitled "Too much mamography" which suggests the need to rethink the breast screening policies as it has done with PSA screening in the case of prostate cancer.
It can be somewhat counterintuitive to think that a test that can detect cancer early and therefore provide the opportunity to treat it early, does not reduce mortality, but often not only the citizens but also the professionals have difficulty interpreting the benefits and risks of screenings and to communicate them clearly to patients when making the decision to participate or not in the program. Gerd Gigerenzer, Director of the Max Planck Institute for Human Development in Berlin explains it very well in his book Calculated Risks. How to know when numbers deceive you1.
We can do the test
The probability that a 40 year old woman has breast cancer is about 1% (prevalence). If she has it, the likelihood of testing positive in the screening is 90% (sensitivity). If she doesn’t have it, the probability that the test comes out positive is 9% (false positive rate).
Question: Given a positive screening test result, what is the probability of actually having breast cancer?
Most of the professionals who were asked this question answered values close to 90% when in fact it’s only about 10%. Weird, right? Well, let's see if I can explain. Imagine 100 women undergoing screening. Of these 100, one (1%) has breast cancer (probabilistic question) and almost certainly will come out positive in the screening. Of the remaining other 99 women, despite not having breast cancer, 9 will test positive in the screening (remember the false positive rate).
The probability of actually having cancer if the result comes out positive is the number of true positives (1) divided by the total number of positive results (true or false: 1 + 9). Therefore, from 100 women that undergo screening, 10 will have a positive result, but only one of them has cancer (10%).
Although in 2006 and then in 2011, the Cochrane revisions were published and they concluded that it was not clear whether the benefit/risk balance was favourable, mammography screening programs for breast cancer are perceived as very positive2,3. Gigerenzer explains that in a 2008 survey of 20 gynaecologists, 17 of them strongly recommended mammography. None of them assessed the risk of over
diagnosis and overtreatment.
The BMJ recently published the results of a randomized Canadian study which shows that annual mammography in asymptomatic women under 60 does not bring any advantage in reducing mortality from breast cancer compared with physical examination without mammography and, instead, it leads to more than 20% over diagnosis. The article is accompanied by an editorial entitled "Too much mamography" which suggests the need to rethink the breast screening policies as it has done with PSA screening in the case of prostate cancer.
We can do the test
The probability that a 40 year old woman has breast cancer is about 1% (prevalence). If she has it, the likelihood of testing positive in the screening is 90% (sensitivity). If she doesn’t have it, the probability that the test comes out positive is 9% (false positive rate).
Question: Given a positive screening test result, what is the probability of actually having breast cancer?
Most of the professionals who were asked this question answered values close to 90% when in fact it’s only about 10%. Weird, right? Well, let's see if I can explain. Imagine 100 women undergoing screening. Of these 100, one (1%) has breast cancer (probabilistic question) and almost certainly will come out positive in the screening. Of the remaining other 99 women, despite not having breast cancer, 9 will test positive in the screening (remember the false positive rate).
The probability of actually having cancer if the result comes out positive is the number of true positives (1) divided by the total number of positive results (true or false: 1 + 9). Therefore, from 100 women that undergo screening, 10 will have a positive result, but only one of them has cancer (10%).
Although in 2006 and then in 2011, the Cochrane revisions were published and they concluded that it was not clear whether the benefit/risk balance was favourable, mammography screening programs for breast cancer are perceived as very positive2,3. Gigerenzer explains that in a 2008 survey of 20 gynaecologists, 17 of them strongly recommended mammography. None of them assessed the risk of over
This difficulty in understanding statistics is common not only among health professionals but also among other professionals and citizens. The origin is multifactored and has nothing to do with people’s intelligence but a lot to do with poor mathematical background. For health professionals, we can add the use that medical journals and pharmaceutical advertising make of opaque and unintuitive statistical measures, leading them to overestimate the benefits of interventions by expressing them in relative risk reductions and to minimize the risks by expressing them in natural frequencies.
Bibliography
- Gerd Gigerenzer. Calculated Risks. How to know when numbers deceive you. Simon & Schuster New York. 2002. ISBN 0-7432-5423-6.
- Gøtzsche PC, Nielsen M. Cribatge for breast cancer with mammography. Cochrane Database of Systematic Reviews 2011, Issue 1: CD001877.
- Gøtzsche PC, Nielsen M. Cribatge for breast cancer with mammography. Cochrane Database of Systematic Reviews 2006 Oct 18;(4):CD001877.
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