First, our assessment of percentage of counties experiencing an increase over the two time windows in the original research letter did not consider the “size of the increase”. We examined the percent change in cases over the two time periods and the percentage of people who are fully vaccinated across US counties (Fig. 2). As is evident, the overall inference drawn in the research letter remains unaltered.
Second, we wish to reiterate that in the original letter we already present a sensitivity analysis, in the associated Supplementary File, where we considered a one-month lag on the independent variable “percentage of population fully vaccinated” and confirmed the robustness of our findings for both countries and US counties .
Third, in our research letter, we also included an interactive data dashboard (https://tiny.cc/USDashboard) that allows users to visualize the patterning of cases per 100,000 people in the last 7 days and percentage of population fully vaccinated (in categories) along with other data metrics since April 12, 2021, with automatic updates as new data is released.
Fourth, we elected to use boxplots across various categories of percentage of population fully vaccinated because it was the most appropriate way to describe the underlying data, which is the primary goal of any statistical analysis. Specifically, in the case of the two variables we focused on, the variation between counties within a category of fully vaccinated is readily apparent—especially in the US—regardless of the average for any category.
We thank Mulot et al. for analyzing the two variables from the same data source we considered in the analysis using more formal statistical models (Supplementary Analysis of their comment)  that analyze the relationship using a continuous scale of fully vaccinated. Mulot et al. selectively interpret the higher end of the distribution of fully vaccinated to suggest a negative correlation with “cases per 100,000 in the last 7 days” . However, the variation between counties at higher levels of vaccination is evident in their figure, reinforcing our interpretation that a county could be high or low in cases at different levels of vaccination, and the appropriateness of boxplots to characterize the data.
It is precisely because of this finding we concluded that there should be a consideration of other known non-pharmacological interventions in addition to vaccines. For instance, in a recently published simulation study of a university campus, it was shown that surveillance testing, and isolation of positive cases are important mitigation strategies, even if 100 percent of the students are vaccinated .
Finally, we concur with the concern around observed and unobserved confounding variables in any observational data analysis. This is especially true for the country-level analysis. While we acknowledge this particular limitation in our original research letter, space constraints inhibited us from elaborating in greater depth. It is precisely because of our recognition of a whole variety of country-level differences that we deliberately restrained from overinterpreting the statistically positive counterintuitive association observed across countries. Instead, we leaned towards interpreting an association that is descriptively self-evident.