Why a positive screening test is often not what people assume

There is a piece of arithmetic behind screening tests that is genuinely counter-intuitive, and not knowing it causes a great deal of unnecessary distress.

The short version: how much a positive result should worry you depends not only on how good the test is, but on how common the thing being tested for is in people like you. The rarer it is, the more of the positives are false.

Two different ways a test can be good

Sensitivity describes how good a test is at detecting something when it is present. A highly sensitive test rarely misses.

Specificity describes how good it is at staying quiet when the thing is absent. A highly specific test rarely raises a false alarm.

These are separate properties and they trade off against each other. Moving a cut-off to catch more true cases inevitably catches more false ones too. Screening tests are usually tuned toward sensitivity, on the reasonable grounds that a missed case is worse than a further test.

The arithmetic that surprises people

Imagine a condition present in one person in a thousand, and a test with 99 per cent sensitivity and 99 per cent specificity. Those are good numbers.

Test ten thousand people. Ten of them have the condition, and the test finds about ten of those. Of the 9,990 who do not have it, one per cent test positive anyway — about a hundred people.

So around 110 people get a positive result, and only ten of them have the condition. A positive result from an excellent test, in this population, is wrong about nine times out of ten.

Nothing about the test changed in that calculation. What did the work was how uncommon the condition is.

Why this is not an argument against screening

Screening programmes are designed with this arithmetic in mind. The first test is deliberately sensitive, and a positive result triggers a second, more specific test rather than a diagnosis.

This is why a positive screening result is usually described as requiring further testing rather than as a finding. The two-stage design is the mechanism by which the false positives are removed.

It also explains why screening is offered to defined groups rather than to everyone. Restricting a programme to people in whom the condition is more common improves the proportion of positives that turn out to be real.

What this means for an individual

A positive screening result is a reason to complete the next step, not a reason to conclude anything. The interval before the confirmatory test is genuinely difficult, and knowing the arithmetic does not remove that, but it does put the first result in proportion.

It is reasonable to ask what proportion of positive results at this stage turn out to be confirmed. Many screening programmes publish exactly that figure, and clinicians working in them usually know it.

The same reasoning applies to incidental findings on broad panels. A single unexpected result on a twenty-marker screen ordered without a specific question is much more likely to be variation than a discovery.

The other direction

A negative result from a highly sensitive test is genuinely reassuring for the specific thing that test looks for, which is what such tests are designed to achieve.

It says nothing about anything else. A normal screening result is not a general certificate of health, and symptoms that persist deserve attention regardless of what a screening test showed.