Clinicians should never order tests on people who are unlikely to have the disease we’re checking for. Intuitively, it might seem like a good strategy “just in case,” but it usually winds up perilous. Here’s why.
Suppose we’re looking for Disease “D”.
Suppose we test 2 groups of people: Population “X” and Population “Y”
- Suppose that among “X”, 10% of people have that disease (called “prevalence”).
- Suppose among “Y”, only 0.1% of people (1 in 1,000) have it.
Suppose that when the diagnostic test for “D” is positive, it’s accurate 99% of the time (this is called “specificity,” and 99% is very high, compared to most of the tests we do). In other words, if the test is positive, it’s false-positive only 1% of the time, and true-positive 99%.
Now we test 1,000 persons in Population X:
- 100 test Positive because they have disease “D” [10% prevalence]
- 10 test False-Positives [99% test specificity = 1% false-positive = 1/100 or 10/1,000]
- So out of 110 Positives, 91% are true-positive, 9% false-positive
Then we test 1,000 persons in Population Y:
- 1 tests Positive because of disease “D” [0.1% prevalence, the “1-in-1,000”]
- 10 test False-Positive [99% test specificity = 1% false-positive = 10/1,000]
- So out of 11 Positives, 91% are False !!!!!
So what’s going to happen to those patients in Population “Y” who test positive? We’re going to do more tests on, or give treatment to, 11 people, when only 1 of them needs it (& we don’t know who). That’s spinning our wheels; but it can be expensive, or even dangerous.
In the 1970’s, some big companies performed screening “exercise treadmill tests” on all their executives, to see who might be at risk of a heart attack. The executives were mostly males, but otherwise didn’t have many heart attack risks (they were relatively young, may have smoked, but had no chest pain or other symptoms). Treadmill tests have relatively low specificity (around 75%). All the “positives” (many false) got a cardiac catheterization to find out for sure (thread a tiny tube up an artery & into the heart). In that era, catheterization may have had a 1-in-100 mortality rate (much less now). Imagine dying, and the initial test was false-positive!
This is why we avoid ordering tests “just to be sure,” when we don’t think the disease is likely, because the vast majority of “positive” results will be false! Maybe the initial screening test is cheap & easy, but the down-the-line treatment or work-up may be another story.