Subramanian et al. reported that increases in COVID-19 are unrelated to levels of vaccination across 68 countries and 2947 counties in the United States; IMO, this was a very wrong interpretation

there IS a clear association & these authors errored in their write-up! 'At the country-level, there appears to be no discernable relationship between percentage of population fully vaccinated'; WRONG

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8481107/

I/we argue that it is not true that there is not an association between the two variables and the link is NOT marginal as they (Subramanian et al.) report and as Switkay shows, there actually is a very strong positive association.

Switkay provides evidence contrary to the findings of Subramanian et al. I am in agreement and we did not really need Switkay. The Subramanian et al. graph itself was showing an association, once interpretated optimally.

SOURCE:

https://pdmj.org/papers/Comment_on_Subramanian_and_Kumar

‘Subramanian and Kumar studied the relationship between new case rates and vaccination rates in 68 countries. Since vaccination rates vary between 0% and 100%, they were treated with the logit function. Since case rates are positive but rarely approach anything near 100%, they were treated with the log function. The transformed variables now have doubly infinite support, so one may explore the strength of a linear association between the transformed variables.

The scatterplot of the transformed variables is shown in figure 1. This corresponds to figure 1 in [1]. However, the points in the lower left corner of figure 1 in [1] are now nicely separated.

Figure 1. Log new case rates vs. logit vaccination rates by country

Figure 2 zooms in on the most densely populated portion of figure 1.

Figure 2. Central portion of figure 1

The positive association is now clear, and the coefficient of determination, R-squared, is a remarkable 0.2409. The p-value is about 0.00002. Even by the standards of [2], that is highly significant.

One may deduce that not only is it not true that there is no relation between the two variables in [1], as their title states, or that the association is “marginal”; indeed, there is a very strong positive association.’