Disease Screening Fallacy

With modern medicine, there remain very few diseases that are a virtual death sentence. However, the fear of terminal illness still lurks in the shadows. How prominent is breast cancer among women ages 18-25? How likelyis it that Huntington’s will be passed from parent to child? Can Diabetes really be prevented? These are all questions that float around the medical world. But do we ever question the diagnostic tests? We certainly ask for a second opinion, but when those test results come in that say “positive”, do we question it? Maybe we should.

Every screening test has it’s own strength ratings (i.e. how good it is at detecting a disease). These are known as sensitivity and specificity. Sensitivity is the probability that a person who has the disease will test positive (or 1- P(false negative)). Specificity measures the rate at which a person without the disease will test negative (or 1-P(false positive)). For many screening tests, these parameters are extremely high. Does that mean we can trust any outcome we get? Not quite. We tend to disregard the original base-rate of these diseases when evaluating the likelihood of testing positive with the screening test. This is better illustrated through an example.

In clinical studies conducted by the manufacturer, the OraQuick oral fluid rapid HIV test was found to have a sensitivity of 99.3% and a specificity of 99.8%. We also know that approximately 0.5% of people in the United States are infected withHIV. Let’s look at a scenario that demonstrates these probabilities (for ease ofnumbers, we have estimated the sensitivity and specificity as both 99%):

100,000 people were given the oral fluid rapid test. Here are their results:

		Test HIV
		Positive	Negative
True HIV	Positive	495	5	500
	Negative	995	98,505	99,500
		1490	98,510	100,000

We use Bayes theorem:

In this case, we apply events A and B to the likelihood of having HIV (A) to the likelihood of testing positive for HIV (B). Here we have P(B|A) = sensitivity, P(A) = probability of having HIV, P(B) = probability of testing positive for HIV.

Using Bayes Theorem, we see that the probability of having HIV given that a person has tested positive, is still only 33%. Crazy, right? We think so. Conversely, however, the likelihood of not having HIV given a person has tested negative is approximately 99.99%. We see that high specificity and sensitivity guarantee a strong ability to detect when an individual does not have a disease, but given a low base rate for the disease (meaning it is not very prominent), screening tests suffer at determining true positive results.

The take home message (we think) is that next time you walk into a clinic to have a screening test, keep Bayes Theorem in mind.