[blueash]

It would be very misleading not to do the same analysis for the negative tests. Here the utilized kit is only sensitive at about 80%. A good test is at least 90%, but it is what they were using. This means that of the 3280 negative results between 13% = 425 and 28 % = 918 were wrongly reported and should have been positive. Think about that, they reported 50 positives, but based on the poor quality of the test and of the sample, instead did calculations saying that there were really 139 positives [4.16% times 3330]. Do you see the possibility of a wide range of error?

Hold on, those are not the numbers used because the authors elected to try to use their sample and re-balance so it would better represent the population of Santa Clara county. This is standard. Their sample was badly unbalanced, again possibly reflection selection bias. 63% were female where the county is 50%, 76 % were between 19-64 where the county is 62%, 5% were over 64 where the county is 13%.

The authors balanced 63% female: the real county = female 50, balanced data 50
They balanced the ethnicity tested white 64%; real white = 33%, balanced data 35%
They strangely "balanced" tested over 64 5% : real over 64 = 13% to over 64 = 4.5 % I see no explanation why they failed to correct their data for age which is a major risk factor for disease. And the elderly represent much of the county reported positives.

The study does not break down how many in each tested group were positive. They obviously did not test people in nursing homes or hospitals. The authors did not correct for age but felt they needed to correct for zip code.

Using the correction to balance for the atypical sample population, they then estimate the "real" rate of persons who have had COVID in the county is 50 to 85 times higher than the positive PCR results reported. As you can see there are some significant problems, IMO, with the test used and the way they ignored age as a factor in their analysis. As of today, 26% of positive tests PCR tests in Santa Clara are in people over 64. If you undercount the elderly in your sample, of course you will miss positive cases. PM me if you want to run through some of the math.

And there is more: