  Background: While increasing the ventilation rate is an important measure to
remove inhalable virus-laden respiratory particles and lower the risk of
infection, direct validation in schools with population-based studies is far
from definitive.
  Methods: We investigated the strength of association between ventilation and
SARS-CoV-2 transmission reported among the students of Italy's Marche region in
more than 10,000 classrooms, of which 316 were equipped with mechanical
ventilation. We used ordinary and logistic regression models to explore the
relative risk associated with the exposure of students in classrooms.
  Findings: For classrooms equipped with mechanical ventilation systems, the
relative risk of infection decreased with the increase in ventilation:
ventilation ranging from 10 to 14 L s-1 student-1 reduced the likelihood of
infection for students by 80% compared with a classroom with only natural
ventilation. From the regression analysis, as confirmed by the predictive
theoretical approach, we obtained a relative risk reduction in the range
12%-15% for each additional unit of ventilation rate per person.
  Interpretation: We need high ventilation rates (> 10 L s$^{-1}$
student$^{-1}$) to protect students in classrooms from airborne transmission;
this is higher than the rate needed to ensure indoor air quality. The excellent
agreement between the results from the retrospective cohort study and the
outcomes of the predictive theoretical approach makes it possible to assess the
risk of airborne transmission for any indoor environment.
