Increasing ventilation reduces SARS-CoV-2 airborne transmission in schools: A retrospective cohort study in Italy's Marche region.

Introduction: 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. Results and discussion: For classrooms equipped with mechanical ventilation systems, the relative risk of infection of students decreased at least by 74% compared with a classroom with only natural ventilation, reaching values of at least 80% for ventilation rates >10 L s-1 student-1. From the regression analysis we obtained a relative risk reduction in the range 12%15% for each additional unit of ventilation rate per person. The results also allowed to validate a recently developed predictive theoretical approach able to estimate the SARS-CoV-2 risk of infection of susceptible individuals via the airborne transmission route. We need mechanical ventilation systems to protect students in classrooms from airborne transmission; the protection is greater if ventilation rates higher than the rate needed to ensure indoor air quality (>10 L s-1 student-1) are adopted. The excellent agreement between the results from the retrospective cohort study and the outcome of the predictive theoretical approach makes it possible to assess the risk of airborne transmission for any indoor environment.

Factorial Invariance and Orthogonal Rotation.

A large number of methods of factor rotation are available in the literature, but the development of formal criteria by which to compare them is an understudied field of research. One possible criterion is the Thurstonian concept of "factorial invariance", which was applied by Kaiser to the varimax rotation method in 1958 and has been subsequently neglected. In the present study, we propose two conditions for establishing whether a method satisfies factorial invariance, and we apply them to 11 orthogonal rotation methods. The results show that 3 methods do not exhibit factorial invariance under either condition, 3 are invariant under one but not the other, and 5 are invariant under both. Varimax rotation is one of the 5 methods that satisfy factorial invariance under both conditions and is the only method that satisfies the invariance condition originally advocated by Kaiser in 1958. From this perspective, it appears that varimax rotation is the method that best ensures factorial invariance.