In a new analysis, pediatric researchers have estimated that the states’ decisions to close schools last spring likely saved tens of thousands of lives from Covid-19 and prevented many more coronavirus infections.

The findings come amid a worldwide debate on whether, when and how to reopen schools, including for some 56 million American students, kindergarten through high school.

Outside experts cautioned that the effect of school closings is extremely difficult to predict because of unknowns like how infectious children are and because of the difficulty in separating out the effect of school closures from other measures that states took to control the virus. In addition, early in the pandemic, testing was especially limited and spotty, raising questions about how well the number of confirmed cases reflected actual infections.

The paper, published Wednesday in JAMA, is likely to remind school districts and policymakers how consequential their decisions could be for the shape of the pandemic this fall. The study focuses on a six-week period in the spring and concluded that school closure “may have been associated with approximately 1.37 million fewer cases of Covid-19 over a 26-day period and 40,600 fewer deaths over a 16-day period.”

However, they continued, “these figures do not account for uncertainty in the model assumptions and the resulting estimates.” The authors acknowledged that their findings are not broadly applicable today because before closings in the spring, there were no precautions, such as smaller classes and the wearing of masks, that are being recommended for reopening.

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“At the time, there wasn’t any masking in schools, there wasn’t physical distancing, there wasn’t an increase in hygiene and that sort of thing,” said Dr. Katherine Auger, an associate professor of pediatrics at Cincinnati Children’s Hospital and the lead author of the study. “The findings of our studies took place before any of those measures were in.”

Still, Dr. Auger said, she believed that the conclusions of the study supported the idea that decisions on reopening schools should strongly consider the prevalence of Covid-19 cases in the community. “Are there a lot of cases right now, is it a hot spot, is it an outbreak, is it a surge?” Dr. Auger said. She said that the American Academy of Pediatrics guidelines “emphasize making sure that the community numbers are reasonable before trying to open schools, and I think this manuscript sort of bolsters that a bit.”

Experts not involved in the study said that its findings could reflect not only reduced infections at schools but broader disruptions due to students being at home.

“This is a nice study that provides clear interpretations and caveats,” said Lauren Ancel Meyers, a professor of biology and statistics at the University of Texas, Austin. Dr. Meyers said that the school closures in March “not only disrupted daily interactions among students, but also raised awareness of the emerging threat of Covid-19 and forced parents to stay home to care for their children.”

But other experts noted that the impact of preventive measures taken by states — including stay-at-home orders, closures of restaurants and nonessential businesses and limits on large social gatherings — simultaneously or shortly after school closings, made it hard to determine the specific role of schools in such analyses.

“I think we have to be incredibly cautious when interpreting estimates from a study like this,” said Julie Donohue, a professor of public health at the University of Pittsburgh who co-wrote an editorial about the study. “In particular, I think it’s important to emphasize that we really can’t isolate the impact of school closures from other interventions.”

Dr. Donohue added that “even if these numbers were accurate or valid, we don’t know how much of the effect would be derived from reducing contacts among kids at school, versus reducing contacts among parents who have to stay home from work because their children are out of school.”

Given that the study is being published just as districts around the country are struggling with whether and how to reopen schools, some experts expressed concern that its estimates about the impact of closing schools early in the pandemic would be seized upon as an argument that schools should remain closed. Experts on public health and education have recommended that communities and schools should work toward reopening with strong health precautions in place, because in-person schooling has such tremendous value for children’s academic, social and emotional development.

“I do worry that these large estimates of the effect of school closures will lead people to give up because it is going to be challenging to open schools,” Dr. Donohue said. “I do worry that some districts will look at these numbers and say, well, it’s just too hard and it’s not safe to reopen.”

Analyses of cellphone mobility data in March, by The New York Times and others, revealed that people in some states began spending more time at home and less time congregating in public spaces days to weeks before official shelter-in-place orders were enacted.

In the new report, a research team led by Dr. Auger analyzed case counts and deaths in all 50 states beginning on March 7, before the first closings, and ending on May 7, six weeks after the last closing orders. Some states closed their schools a week or more before implementing a more comprehensive lockdown; others did so simultaneously, or close to it. Covid-19 prevalence rates also varied widely, with states like New York and California at the high end and others, like Nebraska and Texas, on the lower end.

The researchers used these differences to help isolate the probable effects of closings from those that were the result of other measures, like closing businesses and stay-at-home policies. The study also accounted for state differences in population vulnerability to the virus, according to an index from the Centers for Disease Control and Prevention that accounts for household income, demographics, underlying levels of chronic diseases and other factors. The earlier a state closed its schools, the fewer cases and deaths accumulated in the weeks that followed, the study found.

A co-author, Dr. Samir Shah, a professor of pediatrics and director of the division of hospital medicine at Cincinnati Children’s Hospital, emphasized the complicated balancing act in deciding whether to reopen schools. “It’s not simply a decision of, what is the risk of Covid,” he said. “It also has to factor in what are the benefits versus harms of not having children in school in person.”