The results of the thing i did with just looking at case and death rates rates for the Omicron period are interesting. When I say "Omicron Period" I mean I calculated case and death rates by State using the number of cases and deaths reported for each State December 20, 2021 through May 19, 2022. I picked December 20 because that is the day on which it was announced that Omicron had become the predominant variant (see
https://www.nbcchicago.com/news/local/o ... y/2712039/).
The end of the story is that there is not sufficient evidence to say that vaccination rate is associated with case rates during the Omicron period. When everything is considered, the only thing that "significantly" matters with respect to case rate is population density. Higher vaccination rates are, however, associated with lower death rates. The other thing that matters with death rates is percent of the population
>65.
If you just look at individual associations, higher vaccination rates are actually associated with higher case rates. However, the associations are no longer "significant" when you control for population density.
Here is the correlation matrix:
Yellow highlight means the coefficient is significant at
>95% confidence and <99% confidence. Blue highlight means it is significant at
>99% confidence. Notice that the highest correlation with case rate is population density. But there are also significant correlations between case rates and vaccination rates for associations whereby states with higher vaccination rates tend to have HIGHER case rates.
But that goes away when the effect of each variable is assessed while controlling for the others. I did backwards elimination ordinary least squares regression the same way I typically do it with environmental data with case rate as the dependent variable. I started off with proportion fully vaccinated, proportion boosted, proportion
>65, and population density in the model as the independent variables. Everything dropped out except population density. When you control for population density, there is not sufficient evidence to say there is an effect one way or the other of vaccination rates.
And you can see from the correlation matrix that States with higher population densities tend to have higher vaccination rates. So you can have a thing where people think they are seeing higher vaccination rates "causing" higher case rates when what they may be seeing the effect of population density.
The death rates part of the picture is pretty straightforward and as expected. There are "significant" correlations with vaccination rates such that death rates tend to be lower when vaccination rates are higher. The only weird thing is that the coefficient for fully vaccinated rate vs. death rate is higher than that for boosted rate vs. death rate. I have speculative thoughts about why that may be so.
When I did the backwards elimination ordinary least squares regression thing with death rate as the dependent variable I ended up with the final model including fully vaccinated rate and percent of population
>65. That's pretty much what one would expect. I went ahead and did a model where I skipped the elimination process and just made it boosted rate and percent of population
>65. That worked too.
So, State by State with all other things being equal, higher vaccination rate is associated with lower death rate. At the same time with all other things being equal, more people
>65 tends to mean a higher death rate.