Number Needed to Vaccinate: n+1

Inspired by Toby Rogers excellent article on the number of individuals that need to be vaccinated in order to prevent a single death, or the Number Needed to Vaccinate (NNV), I have decided to throw Alberta’s hat into the ring.

NNV is calculated by using 1/(absolute risk) where absolute risk = deaths / population. As absolute risk is a percentage, this number can theoretically be infinite (if the absolute risk is extremely low). If there is no absolute risk, then NNV is, of course, undefined.

This is an interesting, but imperfect, exercise. There are three main problems with NNV as far as I can tell.

1. It is still influenced by bias in data collection. As I have stated previously, we have reasons to believe there is a strong upward bias on the number of COVID deaths. At best, we have to say that NNV in this context only implies that the number of needed vaccinations will (might) prevent the death of someone that tested positive shortly before dying; and,

2. This metric is an average of the population being measured and does not say anything about individuals with distinct characteristics; and,

3. Because we are not able to do a large-scale study, we are assuming that everyone received the same standard of care on average. That is to say, we can assume that this is the number needed to vaccinate in lieu of doing nothing, standard hospital care, or so on.

Yet, I believe it is an exercise worth performing especially considering I am in an age group that is not at risk.

Here we go.

In 2020, there were 1531 deaths in Alberta due to the virus. As always, excluded are unknown age groups and deaths labelled “probable”. In totality, the data includes 1527 deaths once exclusions are considered. Not a bad sample.

While Toby essentially considered a 4 month period at 80% effectiveness, discounting the first months and last month due to poor and waning “immunity”, I have instead decided to consider the cases of 100% effectiveness and 51.8% effectiveness (as calculated here). This is both the absolute best case scenario and real world effectiveness from Alberta. Instead of 4 months, I have used 6 months in order to provide a stronger case for the vaccinations.

Here are the results for all age groups:

As you can see, the risk for those under 20 is undefined because no one less than 20 died in Alberta of the virus in 2020. Even assuming the vaccine had 100% efficacy, the NNV is extremely high in most age groups. Even if we assume a death only occurs in 50,000 vaccinations (a number governments regularly cite as the risk of a blood clot death), then the vaccines will not prevent a single death until 50+. When adjusted to real world effectiveness (labelled efficacy in the graph but I am too lazy to change it), it looks much worse.

When we get to the higher age groups, things begin to look ok, especially for those 80+. The thing is… this still does not strengthen the argument to get vaccinated for grandma. Age cohorts tend to interact with each other, and other interactions can be tightly regulated by regular tests for care home workers, for example.

The above graph shows a weighted average that does not include those less than 20 (you cannot weight something that is undefined). It is pretty clear that if a society pushes to get the young vaccinated to protect the old then the society is making a trade. They are trading young lives, and many life years lost, for the old, who in the case of COVID deaths almost unanimously have a high level of comorbidites (ie. cancer), which would mean we are dealing with days or months gained. If that sounds cold to you, I am sorry. But no grandparent would willingly trade their grandchild’s life for their own.

So… how did Alberta do in 2021?

Here are their vaccination numbers:

88.4 percent of 12+ population has received at least one dose (75.2% total population)

83.2 percent of 12+ population fully vaccinated (70.7% total population)

Pretty good, right!? The pandemic should be over. Below is a graph showing vaccination rates by age groups and annual deaths in 2021. I have also included expected lives saved (at 70.7% of the population vaccinated, 4th column, and half that amount, 5th column). Further, I have listed the expected deaths given the NNV and the extra deaths that occurred.

Well, one can argue that the vaccination only protects the vaccinated (though, NNV can be done for cases, too, so cases should have gone down as well…). But as we saw in my previous posts, a large amount of these deaths are in the vaccinated. Basically, this means the NNV’s calculated earlier are much too low, which means the real world effectiveness is much too high. In fact, this may even support the vaccinated causing the spread of the virus…