# Post #1044: A little statistical evidence that vaccination is working in Virginia

Posted on March 5, 2021

Let me show you something that has a positive message, for a change.

As of today (3/5/2021), Virginia has fully vaccinated 30% of the oldest old (80+), and has fully or partially vaccinated more than 50% of the oldest old.

By the time you’ve got half of a population vaccinated, you ought to be able to see the impact of that on the infection rate.  And, in fact, you can.

As this post demonstrates.

Now, that all happened in just the last couple of months or so.  And note that there’s a stark contrast in the vaccination rate of the oldest old and (say) adults 20-29.

(In fact, the vaccination rates go in strict age order.  The 20-29s have the lowest rate, the middle-aged adults through younger retirees cluster around a somewhat higher rate.  And, finally, there’s big leap in the vaccination rate when you get to the 70-79 group, and another leap when you get to the 80+ group.)

This is a pretty good example of a “quasi-experiment”.  (And here is the one book that every social scientist should own on that subject).

It’s not a true experiment — they didn’t randomly assign people to get vaccinated and not.  But it’s close enough to be useful.  Based on the rules, one group got very heavily vaccinated, in a short period of time, while others did not.  And because the rule is based on age, people couldn’t choose which group they belonged to.  So this is a pretty clean example of a “pre-post with comparison group” natural experiment, in the jargon of the social sciences.

Let’s do the obvious thing and track the new infection rates in the 80+ population, and contrast that to the least-vaccinated adults — the 20-29 population.

Source:  Calculated from data posted by the Virginia Department of Health, and Census population data.

The obvious assumption here is that the growing gap between those lines is the impact of vaccines.   This is on a log scale, so the distance between the lines shows the ratio of infection rates.  At the start of the year, the oldest and youngest adults had roughly equal new infection rates.  By the last date shown (3/4/2021), the oldest old had just about exactly half the infection rate of the youngest group.

And while that’s plausible, I should point out that this, by itself, is not a very strong analysis.  Those lines might wander around like that all the time, and we just by chance happened to catch this episode.  (And I’ve shown you a “gee-whiz” graph, to boot, to emphasize the gap — the Y axis doesn’t go all the way down to zero.)

We can push this a little further to see if there is a “dose-response” relationship.  If the claim is that reduction in infections is due to vaccination, then we ought to see that the higher the rate of vaccination, the deeper the reduction in infection rates.  (The bigger the dose, the bigger the response.)

And that’s pretty close to a classic dose-response relationship.  If we crudely re-base these so that they all start at the same place, we find that by the end, they line up (almost) perfectly by vaccination rate.  The two heavily vaccinated groups (70-79, 80+) are at the bottom.  The most lightly-vaccinated adults (20-29) are at the top.  And the remaining adult groups bunch in the middle.  Just like the vaccination rates.  (Go re-read the italicized paragraph above.  )

Even so, this might still have occurred merely by chance.  That’s the way it is with natural experiments.  You can never be quite sure.  But your strength of inference increases with every such additional test.  The fact that infections for the oldest old have dropped, relative to young adults, could be purely by chance.  The fact that these line up in (nearly) strict dose-response order, that’s less likely to occur by chance.

If I were then to do this for a different, randomly-chosen state, and find the same thing, that would look even less like it could have occurred by chance.  And so on.

Once you’ve done enough of these, you kind of get a feel for which ones are real, and which are just random will o’ the wisps.  This one has everything going for it.  We have mechanism — we know how the infection rate is supposed to be reduced, because we know the vaccine works.  We have proportionate response — if you vaccinate half the oldest old, well, the infection rate ought to fall roughly by half.  Which it more-or-less does.  And we have dose-response relationship — populations vaccinated less intensively than the oldest old should show a less intense reduction in infections.  And they do.

My conclusion is that vaccination in Virginia is, in fact, making a pretty big dent in the infection rate for the oldest old.  And, by inference, it’ll do the same for all of us, once there’s enough vaccine to go around.

This still does not get to the key issue of herd immunity.  That can’t be tested here, because these groups are not separate populations, but instead, they mingle.  Once we get to herd immunity, infection rate will drop more-than-in-proportion to the vaccination rate, as the immune individuals effectively protect the non-immune from infection (in a probabilistic sense).

That said, if you want some reasonably concrete evidence that things are working out, this is about the best I can give you.  There’s always the possibility that this merely occurred by chance.  But it doesn’t look that way to me, and I’ve looked at a lot of quasi-experiments like this one.  This has all the earmarks of showing the true impact of vaccination on infection rates, here in Virginia.