Very interesting new preprint by Eran Bendavid and colleagues reports seroprevalence estimates from Santa Clara county. Great to have seroprevalence work start to emerge, but I'd be skeptical of the 2-4% seroprevalence result. 1/8 medrxiv.org/content/10.110…
I'd pay particular attention to the dependence of results on test performance. The authors assume that the antibody test has 99.5% specificity (point estimate) based on manufacturer + Stanford validation samples where 399 out of 401 pre-COVID samples showed as negative. 3/8
Using equation from the appendix we can see how the estimate of prevalence varies with test specificity. A specificity of 99.5% converts an observed 1.5% positive to an estimated prevalence of 1.3%. 4/8 
However, if we assume that the test is just slightly worse and has specificity of 98.5%, then, with observed 1.5% positivity, we'd estimate a prevalence of 0%. 5/8
I've ignored demographic weighting here as it doesn't play into this calculation. 6/8
Given how sensitive these results are to performance of the assay, I don't think it's safe to conclude that infections are "50-85-fold more than the number of confirmed cases". 7/8
Again, important to have this work being done. I'd just urge caution in interpretation. I will note again that I've been using a 10-20X ratio of cases-to-infections, but will be great to have more data here (I'd be happy to be wrong). 8/8
See this thread for a corrected confidence interval to the seroprevalence estimate:
And see here for a full posterior seroprevalence estimate that takes into account uncertainty in sensitivity and specificity of the assay:
