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What are my chances, Doc? Why Biostatistics should matter to every physician

Numbers and statistics may seem to be the furthest thing from creativity. They are objective and unwavering. Yet numbers can tell stories, and the pictures they paint can dramatically alter the interactions that physicians have with their patients.

 Consider the following example:

Your patient undergoes a screening test which is known to have a sensitivity and specificity both of 99% (it detects 99% of the cases and rules out 99% of those without the disease). Based on risk within the general population, your patient is estimated to have a 1/1,000 chance of having the disease before they are tested. Their test comes back POSITIVE. Knowing that the test is only “wrong 1% of the time,” what are the chances that your patient has the disease?

a) >95%      b) 70-90%      c) 30-50%      d) <10%

With that answer in mind, how would you counsel this patient?

a) “It’s an accurate test, and you had a positive result, so…”

b) “These kinds of tests can definitely be wrong, so we should probably repeat it”

c) “It’s hard to say for sure what one test means, so we can confirm it with a different screening test”

d) “A positive test result still means cancer is pretty unlikely, so we’re going to try to confirm it with a more specific test.”

The question itself feels like a basic arithmetic question, but the answer clearly has implications for the patient’s well-being. The numbers need not be purely hypothetical either—based on data from the National Cancer Institute, the average 60 year old’s chance of developing a new colorectal cancer in a given year is roughly 1 in 1,000.1 Screening for such colorectal cancers can involve colonoscopy every 10 years, but one non-invasive option includes yearly tests which look for hidden blood in the stool, as this may be indicative of cancer. New fecal immunochemical tests have been estimated to have sensitivity ranging from 61-91% and specificity of 97-98% for such colorectal cancers.2  Imagine, then, that a patient in this age group (with an annual risk of new colorectal cancer of 1/1,000) had a positive finding on a test similar to a fecal immunochemical test and came to you seeking advice. Take a second and consider how you would respond to the prompts above. What is the chance that this patient has colorectal cancer? Even if you don’t know how to calculate it, what does your gut (or heart) say?

I’d like to communicate an understanding of biostatistics concepts without relying on rote memorization of formulas, so you can use the pictures to guide you to the answer:

If you start with 1000 people:


1/1000 people will have the disease (denoted by the red)


If a test is 99% sensitive and 99% specific, it will miss 1% of people with the disease (essentially no one) and will falsely capture 1% of people who do not have the disease (10/1000, blue dots).


So if we look just at the people who had positive tests (red dots being true positives and blue dots being false positives)…


Even if the test were 1/10th as inaccurate, and had 99.9% specificity and sensitivity…


So, returning to our question, if pre-test probability is 1/1,000 and sensitivity and specificity are both 99%, the chance that our patient has this disease is <10% and you might counsel the patient that disease is still relatively unlikely and you will try to confirm with a more specific test such as colonoscopy. Even if the test had 99.9% sensitivity and specificity, the patient has a 50% chance of having the disease. Do those numbers seem low to you?

This approach is difficult clinically – we may not know the exact sensitivity or specificity of a test, or the rate of disease in the patient’s specific demographic, but these calculations can be a useful exercise. They highlight the implications of pre-test risk, and caution us to only screen in populations which we might expect to have a certain rate of disease. They remind us of the difference between a screening test (designed to seek out disease in the absence of symptoms) and a diagnostic test (intended to confirm the presence of disease based on certain signs and symptoms, which raises the pre-test probability of having the disease). And, thinking again of creativity and narratives, this should make us wonder, how would we treat our patients differently if we thought of these statistics as stories, rather than just numbers and formulas that we haven’t actually dusted off since a first year epidemiology course? How many patients have false-positive results, with experiences that are colored by the words that follow their positive test as much as the results themselves? How can we better equip ourselves to counsel a patient when they come to us with a “positive screening test,” scared and seeking advice?

Show 2 footnotes

  2. Whitlock EP, Lin JS, Liles E, Beil TL, Fu R. Screening for Colorectal Cancer: A Targeted, Updated Systematic Review for the U.S. Preventive Services Task Force. Ann Intern Med. 2008;149:638-658. doi: 10.7326/0003-4819-149-9-200811040-00245
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