Problems with breast cancer screening illustrated

This article which was found at http://understandinguncertainty.org/node/182 is an excellent explanation and illustration of the problem with mammography screening.  Please go to the original post which contains a very clever graphic display of the statistical analysis.
Screening for breast cancer
Posted June 17th, 2008 by mlc40

Since 1988, women over 50 in the UK have routinely been offered screening for breast cancer, even if they have no other symptoms, and in 2004/05 1.7 million women were screened. Those with a positive mammogram are recalled for further investigations, at considerable cost in anxiety, resources and pain and discomfort. But how many of these women really have breast cancer?

First of all, we need some information about how the test performs. It has been estimated that in women between 50 and 70 years old, mammography will detect approximately 85% of breast cancers. In other words, out of 100 women with breast cancer, we expect around 85 to have a positive result, and 15 to have a negative result.

We also need to know how accurate the test is with women who don’t have cancer. It has been estimated that around 10% of women with no cancer will still receive a positive result. In other words, out of 100 women without breast cancer, we expect around 10 to have a positive result, even though they don’t have cancer. The remaining 90 will receive a correct (negative) result.

Finally, we need to know something about the underlying incidence of breast cancer in this population. This varies quite a lot by ethnicity and nationality, but in the UK it has been estimated that around 10 out of 1000 women aged 50 to 70 have breast cancer.

These numbers might seem a bit confusing, but we can use the animation below to see what we would expect to happen to 1000 typical women age 50-70 from the UK who attend screening.

Of these, we expect around 10 to have breast cancer. Of those 10, we expect roughly 9 (rounded to nearest whole woman!) to have a positive mammogram, and we expect around 1 to have a negative mammogram.

This leaves 990 who don’t have cancer. Of these, we expect around 99 (10%) to have a positive result, and 891 (90%) to have a negative result.

So, what proportion of those with a positive test result will have the cancer? In total, out of 1000 women, we expect around 9 + 99 = 108 will test positive. Of these, we expect around 9 will actually have cancer. That is, around 9/108, or 8%, of those with a positive result will actually have cancer. This seems a bit surprising — even if you have a positive mammogram, you still probably don’t have cancer. This is despite the fact that 85% people with cancer receive a positive result!

What about those who have a negative result? In total, around 892 (the vast majority!) will have a negative result. Of these, only 1 actually has cancer — that’s around 0.1% — so if you screen negative it is quite reasonable to be reassured.

More information on breast cancer screening in the UK can be found on the Cancer Research UK website, who also provide the estimates of the mammogram accuracywhich we have used.

When deciding whether to roll out a new mass screening programme (for example, for diseases such as prostate cancer), the benefits must be weighed against the costs of the test, the risks of taking the test, and cost to people who receive a positive result, and must undergo further invasive, stressful and possible risky testing, even if they do not actually have the cancer. This kind of analysis illustrates that even fairly accurates tests can lead to substantial investigations of people who turn out not to have the disease.

Author(s):
mlc40

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