Examining the Robustness of 3 Versus 6 Feet of Physical Distancing in Schools: A Reanalysis of van den Berg et al

To the Editor—A study by van den Berg et al [1] evaluated the effectiveness of school districts’ physical distancing policies in reducing the rate of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection among students in kindergarten through grade 12. Finding no statistically significant differences between 6-ft and 3-ft distancing policies, the authors concluded that the “adoption of greater physical distancing between individuals in school buildings was not associated with significantly reduced rates of SARS-CoV-2 among students and staff” [1]. Almost a year after publication of their article, the authors corrected their original estimates after discovering a data error that affected approximately 5% of district-weeks [2]. This strengthened several observed associations in favor of 6-ft distancing, yet all differences remained statistically insignificant. On attempting to replicate and assess the robustness of these corrected estimates, we found a methodological inconsistency: 2 district-weeks were included in the corrected analyses despite having in-person enrollment <5%. After correctly applying the authors’ stated exclusion criteria, the associations again strengthened in favor of 6-ft distancing after adjustment for community incidence and school district demographics (eg, student incidence rate ratio [IRR], 0.71 [95% confidence interval, .50–1.01]), yet all differences remained statistically insignificant. Nonetheless, we and others [3] affirm that interpreting point estimates alongside measures of precision and statistical significance is best statistical and public health practice [4, 5]. To examine the robustness of the corrected findings [2, row 2 in table 3], we varied the 5% in-person enrollment exclusion criteria. We chose this methodological specification because a rationale for its selection was not provided in the original study and because greater in-person enrollment may modify the association between physical distancing and SARS-CoV-2 risk. Adjusting for district demographics and community incidence, we plotted the IRR comparing 6 versus 3 ft of physical distancing under a range of exclusion thresholds, as shown in Figure 1. If the original study had specified a 10% threshold, a significant association in favor of 6-ft distancing (IRR, 0.69 [95% confidence interval, .49–.97]) would have been observed for student case rates. In fact, all thresholds until <5.00815% showed a statistically significant benefit for 6 versus 3 ft. Adjusted student incidence rate ratios (IRRs) and corresponding 95% confidence intervals (CIs) comparing the effects of 6 versus 3 ft distancing on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) case rates under a range of potential exclusion criteria threshold. We consistently observe lower student IRRs for 6 versus 3 ft after adjusting for district demographics and community incidence. Only when the threshold is set to 5% do we see the CI extend slightly above 1.0 (intersection of dashed and dotted lines; red and blue online). Adjusted student incidence rate ratios (IRRs) and corresponding 95% confidence intervals (CIs) comparing the effects of 6 versus 3 ft distancing on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) case rates under a range of potential exclusion criteria threshold. We consistently observe lower student IRRs for 6 versus 3 ft after adjusting for district demographics and community incidence. Only when the threshold is set to 5% do we see the CI extend slightly above 1.0 (intersection of dashed and dotted lines; red and blue online). We corrected for a methodological inconsistency in the updated analysis by van den Berg et al [2] and showed that the study’s statistical conclusions vary under exceptionally minor methodological changes. We demonstrate that across a range of exclusion criteria, 6-ft distancing is associated with an average 31% reduction in the rate of SARS-CoV-2, relative to 3-ft distancing. Although we focus on only a subset of findings from the original study, we selected models with the most comprehensive statistical adjustment for reanalysis. Furthermore, our focus on students is due to the lack of in-person staff counts in the biweekly enrollment data set. In summary, we observed that the direction and magnitude of the IRR for 6-ft versus 3-ft distancing was robust under a range of methodological specifications. However, the statistical significance of these findings lacked robustness. Therefore, we advocate that future decision making on school reopening be anchored on a summary of several studies. This is particularly necessary in the context of novel variants and established science regarding the airborne transmission of SARS-CoV-2 [6], which require a suite of precautions beyond physical distancing. Acknowledgments. The authors thank Craig A. Weller, Anne Marie Stronach, and Robert C. Curtin from the Massachusetts Reopening K12 taskforce for providing the correct biweekly institutional enrollment data for the 2020–2021 school year; Westyn Branch-Elliman, Rebecca S. Jack, and Emily Oster for sharing the original data used in their study; and Carolina Mattsson, Stefan McCabe, Timothy LaRock, Ryan Gallagher, Sarah Shugars, Jon Green, Beatrice Adler-Bolton, Claudia Sahm, Josh Mound, Matteo Chinazzi, Alessandro Vespignani, David Lazer, and Samuel V. Scarpino for helpful discussions. Potential conflicts of interest. The authors: No reported conflicts. Both authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest.

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