Risk Analysis of the Moderna and Pfizer Vaccines, part 1

There has been some push-back against the call to get vaccinated against Covid-19.  I've heard claims that the vaccine itself is more dangerous than the disease it protects against; I've heard claims that the safety of the vaccine hasn't yet been established sufficiently.

I'd like to think through the relative risks involved here, and will do so over a small series of posts.  I'm going to begin by going over what I consider to be the easier odds to calculate, based on just top-line data points without looking in the details of the vaccine trial data--that will be this post.  Then after establishing a sort of odds baseline, I'll go into more detail on the harder parts of the risk analysis, dealing as it does with more unknowns (risk of serious reactions to the vaccine, possibility of long-term complications from the vaccine vs. possibility of long-term complications from Covid, etc.)

At the end of this series of posts, the result will be a spreadsheet that breaks down risks of death and severe health effects based on whether you take the vaccine or not.  I will put all of the more arguable factors of my calculations as parameters in that spreadsheet, so that anyone who disagrees with my estimates can enter his own numbers to see how much that affects the bottom line.

Note: I will be only be looking at US numbers throughout, on the assumption that the bottom line should be roughly transferrable to other nations.

Risk that you will get Covid 

First, what is the chance that you will get Covid-19 at all, with or without the vaccine?  This is a difficult question to answer, for three reasons:

1. It has been difficult to ascertain the true infection rate of Covid in the general population due to mild and asymptomatic cases not all being identified and tracked in the official numbers.
2. It is very difficult to say how the epidemic will act going forward.  Are vaccinations currently going out going to drastically and suddenly cut down on the number of infections?  Unknown.  Is the virus quickly going to become self-limiting because it will run out of the most easily infectible people and we will rapidly get to herd immunity?  Unknown.  Will a new, more infectious strain emerge and suddenly drastically raise the percentage of people who ultimately get the disease?  Unknown.
3. Even if you came up with a good *average* answer to this question, the specific answer for an *individual* depends highly on his own behavior.  If you can seal yourself away from most interaction with society and if you are highly paranoid about those interactions you do have, it is theoretically possible to be very sure you will not catch the virus.  On the other hand, if you have a job in a very crowded indoor facility full of irresponsible people (prison guards, for example, or pastors of a church whose parishioners think face masks are an anti-religious conspiracy), your chances are likely to be much higher than average.

Let's deal with these factors in a broad, estimating way for the sake of argument:

1. Let's assume that one third of all Covid cases are actually reported.  The very first studies on Covid-19 spread estimated 50% based on a couple of different factors, and this number corresponds roughly with what was found for the swine flu back in the day.  Some people vehemently argue for a lower number, so let's go 33% instead of 50%.
2. Let's assume we've only got another couple months of pretty bad Covid spread.  I myself am optimistic that the vaccines will have a dramatic impact on the spread of the disease *fairly* soon, but I admit I am *more* optimistic in this respect than the national experts have been publically.  Certainly we aren't going to be able to have complete vaccine coverage until almost half-way through 2021.  So let's say that the virus is going to run rampant at least through January and February, though maybe not quite at the current levels of spread, which might be peaking (I hope, although I expect there will be a post-Christmas bump unfortunately).  Let's discount the chance of catching the disease in all the months after that (March through to the end of the year) so that all combined they only equal the chance of catching the disease in the next two months.
3. Let's ignore the question of individual risk and go for an average number.  Whatever risk factor we end up with, then, a particular individual can adjust depending on his own behavior.

Risk without the vaccine

Yesterday (December 23rd), there were about 216,665 new cases of Covid-19 reported in the US (7 day moving average from here: https://www.worldometers.info/coronavirus/country/us/).  Assuming only one third of actual cases were reported, you would triple that number to get the actual cases.  But then let's assume that this rate won't quite hold for the next 60 days because we're at or close to a holiday peak.  So let's get an average rate by halving this number, so we arrive at about 325,000 new cases per day for the next 60 days.  That's about 19 million new cases over the next 60 days, out of a population of about 298 million people who haven't already gotten the disease.  This means that there's about a 6-7% chance the average person in the US will come down with the disease in the next 2 months; which means we finally arrive at an 12-14% chance of catching the disease at all in the next year.

Risk with the vaccine

The Moderna and Pfizer vaccines have very similar effectiveness rates, right around 94.5%.  This is for a complete prevention of the disease; there is also good indication that if you *do* get the infection after being vaccinated, it will significantly reduce the severity of the disease.  However, there is not yet enough data to really show how significant this effect is yet.  So let's just round the vaccine effectiveness rate up to 95% in order to give a slight nod to this effect; this is *probably* significantly underplaying the effectiveness of the vaccine.

This means that the chance for the average vaccinated American to get Covid-19 is 0.6-0.7%.

Risk that you will die if you get Covid

This risk varies *heavily* with age, and secondarily also with other pre-existing risk factors you might have.

The percentage of people who have been reported to have Covid in the US who have then died is around 3% (https://www.worldometers.info/coronavirus/country/us/).  Given our assumption that 2/3 of people with Covid never get reported and assuming none of those people died (reasonable given these are going to be mostly mild cases), then the average risk of dying is about 1%.

If we are wrong about that 66% factor, then the death rate will go down--but then also the risk of getting Covid that we initially calculated would go *up* because the total number of people being infected will be even more underreported--so things partially balance out from a risk assessment standpoint.  

Another factor to consider here is that a certain amount of that 3% of people who have died did so in the earlier phase of the pandemic.  To at least a certain extent, we know more about the course of the disease and are better able to treat severe cases now, compared to at the start.  On the other hand, it is also true that there are currently a large number of people in the hospital who recently got Covid who have not died yet, but will.  This would tend to increase the calculated fatality.

I am going to add a "fudge factor" to my calculation here to account for the likelihood that the 3% fatality rate is over-estimating the true risk of death from Covid even *after* you account for the underreported cases.  I'm going to arbitrarily reduce the risk of death from Covid by 20%, resulting in a risk of death from Covid (if someone comes down with it) of 0.8%.

Now, this is an *average* to be certain, and it's an average that conceals a huge range of variability.  If you are young and healthy, your chances will be much, much lower, and if you are old and frail, your chances will be much higher.

Risk that you will pass on Covid to someone else (without the vaccine)

If you get Covid, the health issues are not confined to you alone.  You are likely to pass the disease on to someone else as well.

This is a difficult risk to quantify, because not only can you pass on the disease to other people, those people also can pass the disease to more people, and so forth.  You can be personally responsible for a long and growing chain of sick people.  How will we quantify this responsibility?  Let's think through this:

Currently, there are 7.7 million known active cases of Covid-19 in the US.  Keeping in mind our "66% invisible cases" factor, that's about 23 million total cases.  We projected that there would be 38 million new cases generated in the next year (19 million in January and February and then the same amount for the rest of the year).  All of these cases will be caused by the people who are currently sick right now, because that's how disease spread works.

Further, however, we know that not all of the current sick people are equally contagious.  With Covid, there is an initial spike of high degree of contagion, followed by a longer period of much lower contagion  (https://www.cdc.gov/coronavirus/2019-ncov/hcp/duration-isolation.html).  Therefore it is likely that the bulk of infections that will occur is due to a *portion* of the current sick population, and not all of them.

What we can do is take the average length of time one is contagious with Covid and divide it by the average length of a Covid infection.  Roughly that proportion of the currently sick will be actually contagious.  Looking at the CDC for this information (https://elemental.medium.com/from-infection-to-recovery-how-long-it-lasts-199e266fd018), I see both numbers vary based on infection severity.  If I apply the numbers for "mild" cases to the "invisible 66%" and the numbers for the "severe" cases to the rest, I find that roughly a quarter of the currently sick should be responsible for the bulk of the infections going forward.

This means that the average person who gets sick *right now* will be ultimately responsible for about 6.5 additional cases of Covid-19 besides his own  (1/4 of 23 million people causing 38 million new cases ultimately).  This number will drop over time, however--the later you get Covid, the fewer people remaining to get the disease will be available and the fewer instances of disease will be your fault, all the way down to almost zero at the end of the pandemic.  So let's take the average of 6.5 and almost zero and say that if you get Covid, you will be responsible for 3.25 other people also getting Covid.

Risk that someone else will die if you get Covid

Here I think we can't do anything much aside from take the average death rate, which we're saying is 0.8%, and multiply it by the average number of people you will infect.  This is because the list of people to whom you pass on Covid is not confined to your immediate "victims"; you might only pass on Covid to young and healthy people, but one of those might have a nurse for a mother, and that mother might work at one or more nursing homes, etc.  The possible combinations of infection paths through a society are near countless.  I think we just have to take the population average death rate to assess this risk.  I guess if you know that you interact directly with a lot of vulnerable people, you can bump this up and if you know you're never around anyone who interacts with the elderly at all, you can bump this down.

But on average, this chance will be something like 0.8 * 3.25 = 2.6%.

Combined risk that either you or someone else will die if you get Covid

This is then a simple calculation of 1% + 2.6% = 3.6%, on average.  Note, though, that here the number doesn't vary as much on an individual basis as the chance that you yourself will die from Covid.  You might asses that because you are young and healthy, *your* chance of dying from Covid is closer to 0.05%.  But the chance that *someone* will die from Covid because *you* came down with it is still in that case more like 2.65%.  This effect is a lot more important for the young and healthy, though, because for the most vulnerable elderly, the first term of that calculation is more like 15-25% chance of dying, so the additional 2.6% doesn't matter so much.

Next Time

The next question I would like to address is, how much does taking the vaccine drop the chance that you will infect someone else?  This turns out to be not a simple question to answer, so I will have to address some necessary medical science first.

After that, we can turn our attention to risk of death from the vaccine, then finally to risk of severe medical issues from either the virus or the vaccine.