StATS: Does prevalence affect sensitivity (January 31, 2008).

Dear Professor Mean, Does lowering the prevalence of a disease have an effect on sensitivity?

Do you know how to lower the prevalence of a disease? If so, thereís a job for you in the Public Health Service. Sorry, I couldnít resist.

What you mean to say is: does the performance of a test change when it is used in a low prevalence population compared to a high prevalence population?

Certainly we know that positive predictive value suffers in a low prevalence population. When you are looking for a needle in a haystack, you get swamped by a bunch of false positives. Thatís why we stop testing for certain diseases like respiratory syncytial virus (RSV) when they are "out of season."

Does sensitivity change in a low prevalence population? Well, any time you change the population that you are testing, there is a chance that sensitivity will change. So the answer it, yes it could change.

Thereís an unspoken assumption that sensitivity is unchanged by prevalence, but there are lots of counter examples of this. What is probably happening is that sensitivity is not affected directly by prevalence, but rather by differences in the populations. For example, a low prevalence population may include more patients with milder disease and the high prevalence population may include more patients with serious disease. Since serious disease is easier to diagnose, the sensitivity is better in a high prevalence population.

Now this is all speculative, of course, because we canít take a child and randomly assign them to either a high prevalence group or a low prevalence group. So we take low birthweight kids (1500 to 2500 grams) and assess the performance of a diagnostic test for a common condition in preemies like Bronchopulmonary Dysplasia (BPD). Then take very low birthweight kids (under 1500 grams) and assess the performance of a diagnostic test for BPD. If the test performs better in the very low birthweight kids, is it because this group has a higher prevalence, because BPD is more overt and easier to diagnose in this group, or because of an unmeasured factor that is present in very low birthweight kids that makes the test perform well?

We canít disentangle these alternate explanations because we canít randomize patients into birthweight categories. That gets at my sarcastic comment earlier. Because we canít experimentally manipulate prevalence, anything that I and others say is driven more by opinion than by fact.

For what itís worth, if sensitivity is affected by prevalence, it is certainly affected to a much lower degree than positive predictive value.

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