Lies, Dammed Lies and Statistics

 One of the numerical weapons the anti-vaccine cult has been using lately comes from so-called "breakthrough infections", where fully vaccinated individuals contract the virus.

One example comes from Israel, where one report claims that 97% of new cases are in fully vaccinated individuals.

However, the real story from Israel paints a different story.

Another comes from Iceland, where 82% of new cases are similarly from fully vaccinated people.

One fact-checked explanation here....

There is more information about the situation in Iceland here....

Of course, these numbers are being used by the anti-vaccine cult to bolster their claims that the vaccines are not only harmful (or at least harmful by some uncertain time in the future) but are also pretty much useless.

First, vaccines don't generally prevent infection.  If a person is exposed to a virus against which they have been vaccinated, that person's immunity can't really DO anything until the virus is inside that person's body.  In other words, the person has been infected.  Evidence shows, however, that the virus is generally cleared quickly and the person might not even show any symptoms.

What vaccines really do is prevent serious illness and death from specific pathogens.  They continue to do this very well.  It is true, though, that they are not like a Star Wars Force Field and they are unable to keep the pathogen from entering your body.

Second, no vaccine is 100% effective.  The current crop of COVID-19 vaccines seem to have efficacy rates in the range of 90+%.  It is to be expected, therefore, that some immunized people will still get sick and possible that a small number will die.  This will be more noticeable in the current situation where the virus is affecting billions of people all around the world.  The efficacy rates still stand, though.

Third, as vaccination rates increase in various countries, it is to be expected that some cases will be from vaccinated people because those are increasingly the only people left for the virus to infect.  To take an extreme position, if 100% of a population were vaccinated, it would be possible to see 100% of new cases in fully vaccinated people, simply because there are NO unvaccinated individuals left.

This leads to a statistical issue that the current reports seem to be unaware of, something called "base rate bias" or the "base rate fallacy".  An illustration is needed to explain and Wikipedia even has an article describing it:

Imagine a country of 1 million people where seatbelts are mandatory AND where almost everyone (95% - or 950,000) of people in vehicles wear them. You know that in some accidents, some will still die, although the death rate overall in vehicle accidents has fallen dramatically with the use of seatbelts. Suppose that out of 100 deaths, 75 wore seatbelts and 25 didn't. Of course, it could be reported that 75% of those deaths were people who were wearing seatbelts.  The anti-seatbelt group would claim that seatbelts aren't as useful because more people wearing seatbelts were dying than those who weren't wearing them.  This is an example of "base rate bias".  To understand the data correctly, consider the following:

⁠Seventy-five deaths are from the 95% who were wearing seatbelts (75 deaths out of the base number of 950,000 people who wear seatbelts) is a death rate of 0.0079%. 

Twenty-five deaths out of the 5% who weren't (25 deaths out of the 50,000 who don't wear seatbelts) is a death rate of 0.05%. 

In this admittedly contrived example, those NOT wearing seatbelts are dying at a rate of over 6 TIMES the rate of those wearing seatbelts. This is a difference of over 500%.  To state it a different way, unbelted individuals are over 6 times (over 500%) as likely to die as belted individuals.  Look again at the original numbers, 75 deaths belted, 25 deaths unbelted.  The problem lies in the base number used in the calculations.  

Some news reports are simply using the raw numbers to say that more vaccinated people are coming down with the virus than unvaccinated people.  As we can see, it's a misrepresentation of the data by not referring to the base numbers for each of the two groups of people.  And some people will believe it and use this to justify not getting vaccinated.  This is why misinformation is so dangerous.