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It has long been assumed by medical experts that the United States is drastically underreporting the actual number of COVID-19 infections across the country due to limited testing and a high number of asymptomatic cases.

Large-scale antibody tests are expected to give researchers an idea of just how widespread the outbreak is, and preliminary results from the first such test in Santa Clara County suggest we are underreporting cases by at least a factor of 50.

In early April, Stanford University researchers conducted an antibody test of 3,300 residents in the county that were recruited through targeted Facebook ads. Researchers hoped to put together a sample that was representative of the county's population by selecting individuals based on their age, race, gender and zip code to extrapolate study results to the larger community.

The results of the study are preliminary and not peer-reviewed, but the general takeaways would seem to strongly contribute to the notion that there have been a large number of COVID-19 cases that went undetected.

Due to questions over the antibody tests' efficacy, researchers adjusted for test performance characteristics by using the test manufacturer's data and a sample of controls tested at Stanford University. Again, the results are preliminary and the study has not been peer-reviewed, but researchers found a raw, unadjusted antibody prevalence of 1.5 percent, which was scaled up to 2.5-4.2 percent when adjusting for population and test performance characteristics.

Researchers estimate that if 2.5 to 4.2 percent of the county has already been infected, the true number of total cases in early April — both active and recovered — ranges between 48,000 and 81,000. The county had reported just under 1,000 cases at the time the study was conducted, which would mean cases are being underreported by a factor of 50 to 85.

“Our findings suggest that there is somewhere between 50- and 80-fold more infections in our county than what’s known by the number of cases than are reported by our department of public health," Dr. Eran Bendavid, the Stanford professor who led the study, told ABC News.

If the study's numbers are accurate, the true mortality and hospitalization rates of COVID-19 are both substantially lower than current estimates, and due to lag between infection and death, researchers project a true mortality rate between .12 and .20. Results also suggest the county is nowhere near "herd immunity," as scientists estimate that 50-60% of the population would need to be infected for the virus to have nowhere to spread.

However, the study's authors caution against extrapolating Santa Clara County results to the rest of the country. The county reported its first case on January 31, and was one of the early national "hot spots" where the virus had gained a foothold. Researchers also acknowledge other limitations of the study, including an overrepresentation of white women between ages 19-64, and "other biases, such as bias favoring individuals in good health capable of attending our testing sites, or bias favoring those with prior COVID-like illnesses seeking antibody confirmation."

In San Mateo County, health officer Scott Morrow made a similar estimation on Monday night.

"I hesitate to give you the following numbers, because first of all they are a guess, and secondly because some will think they are too low to take action," he wrote in a message to the community. "My best guess is that approximately 2-3% of the SMC population are currently infected or have recovered from the infection. That’s around 15-25,000 people and they are all over the county and in every community. I don’t believe this number is off by a factor of 10, but it could be off by a factor of 2 to 3."

At the time of his announcement, the county had 699 confirmed cases of the virus, meaning if Morrow's numbers are correct, the county has identified just 2.7-4.5 percent of its total cases.

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Eric Ting is an SFGATE digital reporter. Email: eric.ting@sfgate.com | Twitter:@_ericting