I& #39;m a bit confused about the conclusions of the new preprint on serological testing in Santa Clara county. https://www.medrxiv.org/content/10.1101/2020.04.14.20062463v1">https://www.medrxiv.org/content/1...

In the supplement they say 2 out of 371 + 35 known negative samples tested positive. This means that the 95% confidence interval for the false positive rate is [0.06%, 1.77%]. In their samples from Santa Clara County they had 50 / 3,349 = 1.5% test positive.

This means that not only is their data consistent with the reported number of positive cases, but it& #39;s also consistent with all of their positives being false positives and there being 0 positive cases in their sample! (I don& #39;t think either of these are actually plausible).

It seems likely that we& #39;re missing cases, but I& #39;m just pointing out (as others have) that having even a moderate amount of uncertainty in the false positive rate of these tests makes it difficult to get precise estimates of prevalence when the true prevalence is low.

On a technical note, I& #39;m not sure why the confidence intervals in Table 2 are so small -- maybe it has to do with using the delta method (relies on asymptotics) when for the specificity there are only 2 positive tests, but I& #39;m not sure.