Now it's time for everybody's favorite game: Fun with Statistics
Most people are unaware of how the pharmaceutical companies calculate the vaccine "efficacy" numbers about which we have heard so much. To explain it plainly, during a clinical trial, they divide the number of vaccinated participants who get infected with the pathogen that the vaccine targets (we'll call this number nvi - number of vaccinated who were infected), and they divide that by the number of control/placebo participants who get infected (we'll call this number npi - number of placebo participants infected). Then, that percentage (which is known as the attack rate) is subtracted from 100% which results in the stated efficacy percentage. So the formula looks like the following:
100% - nvi/npi
Simple, right?
To use Pfizer as an example, at the time they measured during their clinical trial, 8 vaccinated participants and 162 unvaccinated participants (out of a total of 43,448) became infected at least seven days after receiving the second injection either of vaccine or placebo. Using the formula above, that gives us:
100% - 8/162
8/162 = ~5%
100% - 5% = 95%
Voila! Pfizer claims their vaccine has 95% efficacy. (https://www.nejm.org/doi/full/10.1056/NEJMoa2034577?query=featured_home)
There are a couple of problems with this calculation, however. First, 170 subjects out of 43,448 is an incredibly small sample (less than half a percent). Second, and perhaps more importantly, there is no control over, or even knowledge of, any level of infective exposure to which each participant was subjected. If there is no control over exposure, it is difficult to say why one group is infected more than the other (especially with such a small statistical sampling). Perhaps more people in the control group were exposed.
On to the game. Using the same calculation, let's apply these statistics to a couple of reports recently in the news.
The BBC ran an article on July 17 in which we're told the number of patients being treated for COVID-19 at Bradford Royal Infirmary is rising rapidly. The article laments that almost half of these patients are unvaccinated and have regrets (https://www.bbc.com/news/stories-57866661). Of course, if half of these patients are unvaccinated, that means the other half are vaccinated. So, using our math above, and plugging this 50/50 split (therefore, the actual numbers don't matter), we get:
100% - 50/50
100% - 100% = 0%
Therefore, the vaccines are 0% effective at preventing infection or hospitalization. Right? After all, there's just as much control over the sample here as in Pfizer's clinical trial.
Perhaps we should look instead at a report out of Massachusetts. According to an article published on July 30, 2021 in the CDC's Morbidity and Mortality Report, there was a significant COVID-19 outbreak in Massachusetts. From this report we learn that 469 people were infected (presumably with the delta variant) of which 346 had been fully vaccinated. Again turning to our efficacy formula, we get:
100% - 346/123
100% - 281.3% = -181.3%
Thus we may conclude that those who have received the vaccines are almost twice as likely (181% more likely) to be infected with the delta variant as those who are unvaccinated.
Well, that's all for our game today. Thanks for playing along!