These days we often get routine medical tests. By routine, I mean those tests that aren't due to symptoms but are screening tests. Sometimes we are informed that the test was positive. And it may be days or a week or more before a test can be retaken.
Frequently I've had clients crying in my office about a positive test result due to the worry that they may have some terrible illness. However, not understanding statistics (which most people don't) makes the results more terrifying. Before you worry, you need more information about test results. In particular, knowing the rate of false positives as well as the underlying base rate (how often it occurs) can make a difference in understanding the results.
Most people believe that if a test has an accuracy rate of 85%, then if they test positive they have an 85% chance of having the disease. But this doesn't account for the base rate fallacy which is misjudging an event due to ignoring the base rate which could mean that the possibility of having the disease is much lower. Even two-thirds of health professionals get this wrong (Bramwell and West, 2006) so you can't always rely on an accurate explanation from your doctor.
To understand this more fully, let's look at the statistics with breast cancer which involves a screening test that many women get yearly.
Usually the more sensitive a test is (good at finding true positives), it will have a higher rate of false positives. So a mammogram has a sensitivity of 84% (Breast Cancer Surveillance Consortium) which may not sound high but is a good rate for a medical test. However, it also has about a 10% chance of indicating cancer when you don't have cancer (false positive).
What this means is that if a woman has yearly mammograms, over a ten year period she has a 50% chance of having a false positive result. So during this time period one out of two women will be told their mammogram was positive for breast cancer when they do not have breast cancer.
Another important piece of information is the base rate of the disease. An approximate base rate for breast cancer is a woman has about 1 out of a 100 chance in a 10-year period of having breast cancer (will vary somewhat by age, ethnicity, and state or country). Interestingly, though, when the base rate is figured into the equation along with the false positive rate, only 8% of the women who were told their mammograms were positive actually have cancer. So instead of having an 84% chance of breast cancer when your mammogram is positive, you really only have an 8% chance or less than one out of 10 chance of having cancer. Sounds pretty different, doesn't it?
I'm not going to go into the details of why this is true. However, for an explanation of the actual formula, a video “Are You REALLY Sick? (false positives)” by Lisa Goldberg, a statistician at UC Berkeley, explains this in more detail. Of course, you can't carry this formula in your head. Most people have trouble understanding it because it is contrary to what our common sense tells us. However, what you may be able to remember is that the higher the false positive rate and the rarer the disease, the lower the likelihood that you have the disease even when you're test results are positive.
This doesn't mean that you shouldn't follow through with medical tests. Just don't be so anxious. And certainly, be wary of proposed treatment without follow-up tests.
Also, keep in mind that whole numbers make more sense to people than percentages. If someone tells you, “You have a positive result on your mammogram. This means you have an 8 out of a 100 chance of having breast cancer. We need to do further tests” you probably wouldn't be as worried as being told “Your mammogram was positive—we need to do further tests.” Yet, we always hear percentages in the media and often from medical professionals. In fact, it's often hard to find the base rates on the internet even for someone who knows what to look for. So, always ask for the numbers when given percentages.
Bramwell, R., West, H. and Salmon, P. (2006). Health professionals’ and service users’ interpretation of screening test results: experimental study. BMJ. DOI: 10.1136/bmj.38884.663102.AE
Breast Cancer Surveillance Consortium (BCSC). Performance measures for 1,838,372 screening mammography examinations from 2004 to 2008 by age -- based on BCSC data through 2009. National Cancer Institute.
National Cancer Institute. Surveillance, Epidemiology, and End Results Program (SEER). http://seer.cancer.gov/statfacts/html/breast.html
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