Stanford University researchers have moderated their controversial estimate of how many people in Santa Clara County were infected by the COVID-19 virus by early April — but stand by their conclusion that the illness was much more widespread than anyone knew.

In a revised analysis of a startling study published last month, they now estimate that 2.8% of Santa Clara residents were previously infected by the virus but didn’t know it.

That implies that the county had up to 54,000 infections — many more than the 1,000 confirmed cases in the county at the time.

“This suggests that the large majority of the population does not have antibodies and may be susceptible to the virus,” concludes the research paper, published in the online report medRxiv.

If true, it means that the large majority of people who contracted COVID-19 in the early days of the pandemic have recovered without ever knowing they were infected. With so many undetected infections, it also means that the death rate is lower than presumed.

The team’s initial study was slightly higher, placing the estimate of infected residents between 2.5% to 4.15%, which suggested up to 81,000 infections.

That study, the first of its type in the nation, incited a fierce debate over the paper’s methodology, with statisticians taking to Twitter to debate sampling methods and test reliability.

The Stanford researchers tested 3,330 people on April 3 and April 4 at three locations spaced across Santa Clara County — two county parks in Los Gatos and San Jose and a church in Mountain View — to gain a snapshot of how many people in the county already had been infected but weren’t seriously sick and didn’t realize it they had ever had the virus. They looked for antibodies to the pathogen, a marker of past infection that suggests it may be safe for them to go back to work and school.

The research revision — there’s now a version 1 and version 2 — reflects the reality of scientific publishing in this fast-moving world of COVID-19 research, when “preprint’ manuscripts are made public almost immediately, before they have been peer reviewed.

While it unshackles scientists from sluggish journals, it also creates the risk that weak work can be publicized and get overblown in the media.

Critics said the new revision corrects some of the statistical imperfections with new data and analyses.

“The new report is an improvement on the first version,” wrote Andrew Gelman, a professor of statistics and political science and director of the Applied Statistics Center at Columbia University.

But there’s continued concern about the methodology. Volunteers for the test were recruited from Facebook — so its sampling was neither random nor representative of the community as a whole. The new paper aims to appease that by offering a more thorough look at all their data.

The major problem with the study related to test specificity. It used a kit purchased from Premier Biotech, based in Minneapolis with known performance data discrepancies. Although it was the best test at the time of the study, it had a high “false positive” rate that can skew results, critics say — especially with such a small sample size.

To improve results, they included about 3,000 “validation samples” for the test kit, reducing the false positive rate for the kit to less than 0.5%.

That explains why the estimate changed — and narrowed down the number of likely infections, said Dr. Jayanta Bhattacharya, professor of medicine at Stanford University.

In their revision, the team softened some of the certainty in their conclusions. But their approach proves the feasibility of such surveys to inform our understanding of the pandemic’s progression, estimate of community vulnerability, and monitor infection fatality rates in different populations over time.

The Stanford team said it welcomed the input — “massive crowdsourcing of helpful comments and constructive feedback” — that led to the new estimates.

“More studies are needed to improve precision,” they wrote. “Repeated serologic testing indifferent geographies, spaced a few weeks apart, is needed to evaluate the extent of infection spread over time.”