Fun With Numbers
Now that we have provided the news as was presented in the media, I would like to take a slightly deeper dive into what the implications are based on the numbers provided.
How Concerning is the Johnson & Johnson Announcement?
Obviously any time a new intervention leads to an adverse reaction, the ultimate being a fatal reaction, it is concerning. Nobody – not the scientists, medical care providers, nor the recipient and family of the individual affected by adverse reaction – wants to see a poor outcome from an intervention undertaken. There is a time and a place to take on risk though. The definition of when that is the case is when the risk outweighs the benefit.
Starting with risk as reported by Johnson & Johnson, there have been six cases of a vascular incident shortly after vaccination in females aged 18 to 49 years. While it was reported that more than 6.8 million doses have been administered, the number of those that were administered to that same subset of the population was not released. As far as the general population goes therefore, the risk of a cerebral venous sinus thrombosis post-vaccination is on the order of 1 case for every 1.13 million doses of vaccines administered.
Is 1 case for every 1.13 million significant, or even due to the vaccine? That is unclear at this time. Part of the difficulty in assessing such is knowing what the natural incidence of such a concern is. A 2016 paper by Devasagayam, et al in Stroke found that the incidence was likely higher than the 2 to 5 cases per million per year that had been previously established. This was based on a review of nearly 1 million patient records in an Australian hospital center, finding an incidence of 15.7 cases per million per year. Women were slightly more likely to suffer from the condition (52%) and the median age effected was 49 years. Of the women who suffered a cerebral venous thrombosis, 31% were taking oral contraceptives. Overall, 48% of affected individuals were found to have some form of coagulation issue that could have contributed.
Based on the numbers above, there may or may not be any increased risk from the vaccine with respect to cerebral venous sinus thrombosis. We will return to some risk-reward regarding this version of the COVID vaccine in a bit.
Hey Doc! Did you notice that almost 6000 vaccinated people got COVID even though they were vaccinated? Why bother?
First and foremost, and this has been stated repetitively in prior posts, there are no vaccines that are 100% effective. So every time you see in the media that [insert favorite name] got COVID three weeks after their second vaccine, take a deep breath, you are being baited. As a prime example, the headline of an article in last weeks NY Post was titled “Brooklyn women gets COVID 3 weeks after Johnson & Johnson vaccine.” It’s the title of the article, and it implies its newsworthy. You have to get to the last couple of paragraphs for there even to be mention that all the vaccines possess something less than 100% efficacy. It’s not news, it’s not shocking. But it does make a lot of people think the vaccine is a waste of effort and is bothersome to see for that reason.
So how is the vaccine working in real life? To truly answer this question one would need to delve into the world of calculus, as the number of vaccinated individuals increases with time, and those that were more recently vaccinated have a smaller timeframe for being exposed. While I like math, I have no interest whatsoever in trying to tackle this problem to that level of detail. I will go with the KISS method instead (Keep It Simple, Stupid).
Start with the fact that there are 5,800 reported cases among about 77 million fully vaccinated individuals. Without a doubt, you see these numbers used to arrive at conclusions such as “only 1 in 13,275” vaccinated acquired COVID. As aforementioned, many of those fully vaccinated individuals became such over the last month and haven’t had tremendous opportunity to acquire COVID, so one expects that number to change for the worse. Let’s get crazy and say, that in the end, it is found to be protective in only 10% of the current reported values leading to 1 in 1,328 individuals getting COVID despite vaccination. That is not a weekly or a monthly number. That is cumulative after being fully vaccinated.
How much would it need to change for us to even want to not consider obtaining its protective benefit? Nationally, we have continued to average more than 450,000 new cases of COVID every week. Based on the population of the entire country, 1 in 740 people get infected with COVID every week. Put simply, there is virtually no chance that being vaccinated does not provide significant protection.
Yo! There Were 74 Deaths Among the Vaccinated?
For months now, I have always attempted to emphasize that case numbers are a consideration, but the most important data to track are hospitalizations and deaths. It would be acceptable to have tons of cases if they were all rendered mild in nature. The game is not necessarily about elimination, rather mitigation. It is possible, albeit unlikely, that the vaccine could prevent a majority of infections, but not alter the number of serious ones or deaths.
Again, in analyzing the death data in fully vaccinated individuals, it is not as simply as saying there were only 74 deaths out the 77 million fully vaccinated. But let us take a quick look at the national data in conjunction to look for some guidance as to effectiveness of the vaccine in a real life setting. As vaccination started around the beginning of the year, the first number to work with is the number of COVID deaths in 2021. For the United States, that number is 165,503 people. That 165,503 includes the 74 fully vaccinated deaths.
For the purposes of demonstration of how effective the vaccine has been to date, let us assume that only 1.5 million of the 77 million fully vaccinated were vaccinated by the middle of January (number arrived at from Our World in Data). Using that 1.5 million as the baseline population for all 74 deaths (that’s right, assuming none of the other 75.5 million vaccinated are among the deaths), the odds of dying from COVID if vaccinated would be 1 in 20,270 fully vaccinated individuals. Using the US population of 330 million, and the total number of deaths in 2021 as above of 165,503, you arrive at an odds of dying of 1 in 2,012 individuals.
Bottom line is even using ridiculously extreme extrapolations of the data, you would be ten times less likely to die if vaccinated. Does it need to work that much better to change your mind? Reality is that you are quite likely hundreds of times less likely to die if vaccinated.
The Johnson & Johnson Issue
In discussing the Johnson & Johnson vaccine for young women, it is imperative to make the assumption that there is insufficient supply for them to have free choice over which vaccine to get. Ultimately, I expect the FDA to either provide some additional warning for younger women or to simply exclude that subset of the population from their indicated use, pending full analysis of the data.
In viewing the data from national numbers, I am not stratifying by sex, though there are subtle differences in case rates and deaths based on sex. The differences will not be sufficient to change the logic presented. Individuals 20-29 years of age make up roughly 16% of the United States population, or about 54 million individuals. In that age group for the year 2021, there have been 2,140 fatalities due to COVID or roughly 1 death for every 25,289 people in that age band. For extreme calculation purposes, we will lump all six females that had the Johnson & Johnson vaccine and subsequent cerebral venous thrombosis into that limited age band and further assume all six will ultimately be fatal. For a vaccine to be considered effective therefore in this population, you must save more lives from vaccination despite the potential side effect compared with foregoing vaccination.
What was not released in the Johnson & Johnson data that I was able to find is how many of the 6.8 million doses were administered to females between the ages of 20 and 29. For the vaccine to cause the death at a rate higher than 1 in 25,289 with the assumptions above, it would need to be administered to 151,738 such females or 1 in 44.8 of all the Johnson & Johnson vaccines given. As this may well be the percentage of the vaccines given to the age group, there is legitimate to question use in that age group when alternatives are present. Granted, every assumption taken to come to that conclusion was the most extreme possible. If four of the six affected females recovered fully, the scales tip significantly. Same if one of the remaining two was 40 years of age. We also permitted in calculations the assumptions that nobody in that age band would have gotten a cerebral venous thrombosis for any other reason. It’s only a toss up decision in a small age band if everything went the worst way possible.
For those outside that particular subset of the population, the risk of dying from COVID is much higher than the risk of getting the Johnson & Johnson vaccine based on the data released to date.