False Positives and Prevalence

Dark side's calling now
Nothing is real
--John Cafferty & the Beaver Brown Band

The false positive rate (FPR) of CV19 diagnostic tests is currently being quoted at about 0.8%. Pretty low, right? Not if current prevalence (i.e., infection rates) are also low.

An FPR of 0.8% means that, out of every 1000 people tested, eight will be indicated as having the virus who are actually infection free. If 1000 are tested and ten test positive, then only two are likely to actually be infected (10 positive tests - 8 false positives = 2 true positives). The already low unadjusted prevalence of 1% (10 positive cases/1000 tested) is actually 0.2% (2 true positives/1000 tested).

When prevalence is low, false positives comprise the majority of cases and skew indicated prevalence much higher than it really is.

Now, let's suppose that 1000 people are tested and 100 test positive. At a 0.8% FPR, then the number of true positives = 100 - 8 = 92. The unadjusted prevalence of 10% (100 positive cases/1000 tested) drops to 9.2% (92 true positives/1000 tested).

Even at lower FPRs, diagnostic tests can mislead if prevalence is low.