Risk Analysis of the Moderna and Pfizer Vaccines, conclusion

The bottom line

Taking all of the risks I determined / decided upon above, I put them into my spreadsheet, available here: Vaccine Risk Analysis.  I decided to calculate the risks for an average adult--meaning I don't use the average Infection Fatality Rate of 0.8%, which includes all of the vulnerable and elderly.  Instead, I put in an "individual fatality rate" of 0.1% for the purpose of the bottom line.  So this would be approximately the risk for a regular adult, not an elderly person.

I think it is worth looking at these "bottom-line" risks from two different aspects: relative risk and absolute risk.

Relative risk

 The question we are asking here is, "how many times more likely is it that something bad will happen to me if I decide not to take the vaccine, as opposed to taking the vaccine?"  The answer my assumptions produce is that there is roughly 16x the risk of death, 14x the risk of serious permanent injury, and 24x the risk of serious temporary injury.  This includes only the risk to oneself, not considering the risk to other people as well.

Note that this answer is not the answer to the question, "how much more risky is it to get Covid than to get the vaccine?"  I am including in the above risk factors the possibility that you will not get Covid at all even if you don't get vaccinated.  To get the comparative risk of getting the vaccine vs. getting Covid, you have to multiply all of those numbers by 7 or 8.  Oh, and in case it wasn't clear, the above multipliers also take into account the chance that you get the vaccine, but get Covid anyway and so have both the risks for the vaccine plus the risks for Covid (mitigated somewhat by the fact that the vaccine should reduce disease severity).

Absolute risk

The relative risk seems very clearly in favor of getting the vaccine, but it isn't the only important answer: we don't always care about relative risk.  After all, the risk of getting hit by lightning if you go hiking five times per year is about five times greater than the risk of getting hit by lightning if you go hiking only once per year, but we don't let that factor determine our vacation plans.  Five times a tiny risk is still discountable.  So what are the absolute risks here?

Again using the risk numbers for an average adult, I took the chances of a bad outcome for the "with vaccine" scenario and subtracted them from the chances of a bad outcome for the "without vaccine" scenario.  This gives us how much more likely a bad outcome is to happen if you forgo the vaccine compared to if you take it.

The results are that if you don't take the vaccine, your chance of death increases by 0.01%, your chance of serious personal injury increases by 0.06%, and your chance of serious temporary injury increases by 2%.  How significant these risks are will depend on your own personal risk toleration threshold, I suppose.

However, the absolute risk to other people must also be noted!  The chance that someone else will die because you forgo the vaccine is 0.3%, that someone else will suffer serious personal injury is 0.2%, and that someone else will suffer serious temporary injury is 5.5%.  Again, these chances would have to be multiplied by 7 or 8 if you wanted to know what the chances are to hurt someone else if you actually get Covid.

A 3 in 1000 chance of causing someone else's death, in my opinion, is a number that should give one pause.  It is, honestly, higher than I was initially expecting it would be and was one of the surprising things I discovered from doing this analysis.

How much stock should we put in these numbers?

It should be made quite clear that all of these numbers are ballpark estimates; the spreadsheet has all sorts of misleading significant figures in it, but that's just because it's formula based and those should all be ignored for the result portion.  I will note again here that I have biased my guesses in a number of places against the new vaccines; I have intentionally chosen what I considered worst-case scenario numbers for those risks, whereas I never did for the Covid risks.

It should also be made clear that the separate risk numbers are not all equally dependable.  In the case of fatality, we have a lot of hard numbers that can give us very reasonable estimates.  All of the online drama fighting over exactly what the IFR of Covid is and what exactly is a death "with" Covid instead of "from" Covid--that enters into these calculations as something that is at most about a factor of 1.5 or 2.  That barely matters for the sake of this analysis and it doesn't really change the bottom line at all.  I'm personally quite comfortable with the fatality risk numbers as good estimates.

In the case of the long-term risk, however, there was a lot more bald guesswork going on than with the fatality rates--both on the vaccine side and on the Covid side.  In this case, I still think it was a valuable exercise to go through and try to rate the risks as fairly as possible, but the end result should be treated as something like a Fermi Estimate (explained in this article: Fermi Estimates).  Fermi estimates have a long tradition in physics and have proven to be very useful in dealing with a lot of unknowns. With a Fermi estimate, you build up from a lot of informed guesswork (as I have attempted to do with these long-term risk estimates), and in the end, you hope your end result is accurate within an order of magnitude.  

On this basis, I think it's fair to say that my analysis indicates that getting Covid is roughly two orders of magnitude more dangerous than getting the new vaccine, and that since your chance to get Covid is roughly 10% if you don't get the vaccine, it's roughly 10x more dangerous not to get the vaccine than it is to get the vaccine.

I think this is a clear enough result that you can confidently base decisions on it.

Final words

Here at the end, I'd like to make one final point.  I think there is a category of risk that I have been completely ignoring that is worth discussing here, which is that if enough people decide not to take the vaccine, the pandemic could last considerably longer and more total people will eventually get infected.  I have been considering only the individual health risks so far, but there are serious societal risks as well.  There are many, many social evils associated with the pandemic continuing on for another year, or more.

I'm not here going to try to quantify these risks, and try to assign some portion of blame to an individual decision to not get vaccinated (like, maybe assign a fraction of a day of continuing societal ills to each decision?).  Firstly this is not appropriate because of how herd immunity works: you can tolerate a certain percentage of the population not being vaccinated and still get enough immunity to eliminate a disease.  Secondly, right now the vaccines are being applied as quickly as we can get them out the door, so this is a moot question.

However, if at some point the production and distribution of these vaccines outpaces the willingness of people to take them, then we will need to revisit this point.  I don't think anyone would argue with the extreme good of ending this pandemic as quickly as possible, and we need to realize that the vaccines are going to be the principle way in which we do that.

Risk Analysis of the Moderna and Pfizer Vaccines, part 5

Risk of non-fatal, serious side effects from Covid

When most people claim that the vaccine is more dangerous than the disease it is protecting you from, they will typically discuss only the fatality rate of the disease.  This rate has been very much discussed and has a lot of literature around it, so this is excusable.  However, while the rate of serious non-fatal side effects from Covid is less well discussed, it certainly can not be neglected.

For one thing, even if we didn't have some hard data on nasty but non-fatal effects from Covid, there is a lot of inherent plausibility to this sort of stuff happening with Covid that is not true of the vaccine.  Aside from allergic reactions (which can happen because of any random type of foreign material you inject into the body if your immune system happens to take a disliking to it), there isn't a readily available mechanism from the vaccine that would explain bad reactions.  Everything about the vaccine was chosen because it was seen as harmless or helpful.  On the other hand, the virus (as we have already seen) attacks any organism in the body containing cells with ACE2 receptors.  This includes vital organisms made up of cells that do not regenerate over time (neurons) or which barely regenerate over time (heart tissue).  The potential for long-term damage to the system from Covid is therefore obvious.

What effects have already been seen?

This Mayo Clinic has a good summary of lingering / long-term effects here. Here are the things we have definitely seen:

• Fatigue
• Shortness of breath
• Cough
• Joint pain
• Chest pain
• Muscle pain or headache
• Fast or pounding heartbeat
• Loss of smell or taste
• Memory, concentration or sleep problems
• Rash or hair loss
• Heart tissue damage
• Lung scarring
• Strokes (which have follow-on long-term effects)
• Guillain-Barre syndrome

Problems that are represented as possible, but not seen for sure yet:

• Chronic fatigue syndrome (deduced as possible because SARS CoV 1 causes it)
• Parkinson and Alzheimer's disease (the article says Covid "may" increase the likelihood of these)
• Long-term leg, liver, or kidney damage due to blood clotting

What are the frequencies of these effects?

It's obvious from an initial searching around and reading that we really need more studies on this.  There's a lot of data from the field, but it's a lot harder to parse and evaluate data from the field than from studies that are set up ahead of time to give us specific answers.  Let's try to find current "best guesses" and derive some risk numbers from them.  I'm going to focus specifically on two of the most concerning known issues: heart and brain problems.

Heart Problems

Here is a summary of some recent thinking on Covid-19 and heart problems.  And here is another study pointing to high levels of heart damage in Covid patients.  Here are some key facts:

• In a study of people who recovered--some months prior--from Covid (2/3 had a mild form and recovered at home and 1/3 had been hospitalized), 78% showed signs of heart damage and 60% proved to have continuing cardiac inflammation.  This study of 100 people has some possible selection bias in that there were a few people in the study who were having continuing symptoms and may have therefore self-selected for the study to find out what was going wrong.
• Post-mortem examination of 39 people who died from Covid showed 41% of them had significant infection in the heart even though they had not been diagnosed with any heart-related issues before they passed away.
• In another study, about a quarter of those hospitalized with Covid "experienced myocardial injury".  This may have been only the most obvious patients, however, as this result was from a retrospective study and therefore was only looking for patients diagnosed with these issues.  The median age for this study was 49 years old.

So we see a high percentage of issues here, frequently not obvious and therefore probably underdiagnosed, and not limited to either the most severe cases or the elderly.

On this basis, I am going to assign a relatively high risk to this factor.  I'll put this at a risk of 25% of a serious problem if you are actually diagnosed with Covid and 10% if you are one of the "invisible 66%".

Nervous System / Brain Problems

Here is a decent summary of the uncertain state of affairs regarding brain damage from Covid from Nature.  It only vaguely guesses at prevalence of nervous system issues by comparing with other coronaviruses: 0.04% for SARS and 0.2% for MERS.  This article, on the other hand, states that about a third of Covid patients will experience some neurological issues.  Probably the discrepancy is due to the surprising and not-very-well-understood symptom of anosmia, which turns out to be super-common in Covid for some reason.

This meta-study analysis is the best information I have found so far, combining multiple studies that covered a total of a bit over 11,000 patients.  If we restrict ourselves to looking at the more serious neurological problems, we find a 3% chance of acute cerebrovascular disease and a 2% chance of impaired consciousness.  I am therefore going to go with a 5% chance of serious nervous system problem.  To account for the fact that these studies were probably only looking at diagnosed cases, we will apply this only to the 33% diagnosed cases of Covid.

What percentage of these effects will be permanent / long term?

This is obviously as-yet unknown, since we don't have long-term data for Covid yet.  Both cardiac tissue and nerve cells, though, essentially do not regenerate (cardiac tissue does so very slightly, but unless you're quote young, you can count on the damage being roughly permanent).  We know for certain that some of these issues will be permanent, because we have seen irrecoverable tissue scarring and cell loss in some people.  So it is very difficult to discount this as a risk.

"Long hauler" Covid (Covid that just lingers and lingers and takes forever to go away) has been estimated to happen for about 10% of Covid patients, so this may give us some ballpark figure for how often Covid symptoms will be long term.

Using this as a guide to rough order of magnitude, but decreasing it by one order of magnitude to translate "months" to "years", I'm therefore going to put the risk of this heart or nervous system damage being long term at 1 in 100 if it happens.

What about as-yet unknown long term effects?

With the vaccine, I answered this question by looking at a survey of vaccines in the past that had proven to have unintended side effects, and picked the very most dangerous one I could find as a baseline.  Let's do a similar exercise here, though I will instead pick the most similar virus we know of rather than the most dangerous one. 

For another coronavirus, SARS, there was a 3.6% chance of serious long term lung damage many years after recovery.  Now, SARS had a fatality rate roughly 10 times that of Covid.  So then I think it's fair to give Covid a 0.36% chance of having some serious long-term issue for people beyond just the heart and brain issues I've already discussed.  We'll again apply this risk only to the 33% of diagnosed individuals.

I think this is fair, given just how many different systems Covid can attack.  There are many, many plausible ways that Covid could create serious long term issues that might be overlooked currently.  Furthermore, there are some risks here that we haven't even considered yet, because they are only indirectly linked to the virus itself.  For example, supposing you are hospitalized with Covid.  One thing you can expect to happen is that a bunch of drugs will be given to you.  If you are concerned with possible unknown side effects of the Covid vaccine, shouldn't you also be concerned with possible unknown side effects of all the drugs they will give you to treat your Covid, should it come to that?  This has been known to kill at least one woman, and I'm sure many others as well.

This starts getting really hard to quantify, so I'm just going to roll that type of risk into my 0.36% risk here, which is a guestimate anyway.

Risk Analysis of the Moderna and Pfizer Vaccines, part 4

Health risks of the Moderna and Pfizer vaccines

At this point, I know of three sets of concrete data that can help us determine risk factors here.  First, we have the results of the human trials from both Moderna and Pfizer, which the FDA has made available:  Moderna's Data,  Pfizer's Data.  Together, these trials give us data on about 33,500 people who were given the vaccine (both shots) and the same number who were given a placebo.

I have read through both documents rather thoroughly and believe there is enough similarity between the results of the two trials to combine those results and treat them as if they were the same vaccine for the purposes of risk analysis.  The mRNA technology they both use is close to identical; Moderna's side-effects seem slightly steeper than Pfizer's, but they also chose to go with a larger dosing, so that makes sense.

Second, I'm aware of an initial report on anaphylactic shock from the initial wave of vaccines, hosted by the CDC here: https://www.cdc.gov/vaccines/acip/meetings/downloads/slides-2020-12/slides-12-19/05-COVID-CLARK.pdf.  This report covers a dataset of 272,001 additional doses beyond the vaccine trial doses.

Third, we also at this point have very broad short-term data from the fact that we have now been vaccinating people as quickly as we can and so have given the *first* shots to more than 1.9 million people at this point: https://www.nytimes.com/interactive/2020/us/covid-19-vaccine-doses.html.  That number will become out of date very quickly, but it is a minimum that we can use for now.

Types of health risk

Both of the data sheets from Moderna and Pfizer split possible side-effects from the vaccine into two categories: side effects related to immune response reaction and side effect unrelated to immune response reaction.  There is a very good reason for this: the way a vaccine works, fundamentally, is to provoke an immune response from your body in such a way that it learns to produce antibodies against the desired antigen.  You trick your body into thinking it is infected with a certain disease, so that it fights against it.  Having an "allergic reaction" to a vaccine is therefore not really a side effect--it is the whole point of a vaccine that this should happen.

So these studies recorded every adverse medical event that happened to both the vaccine group and the placebo group, and categorized them into immune response related or not, and then compared how much each type of adverse event happened in the vaccine group compared to the placebo group.  If something was happening more often in the vaccine group, this was counted as a "significant adverse effect".

Actual significant adverse effects they found

What the studies found were essentially no significant adverse effects outside of the expected immune system responses to the vaccine: fever, chills, achiness, etc.  Both studies noted some adverse effects that happened a little more than you might expect in the vaccine group and some adverse effects that happened a little more than you might expect in the placebo group.  This is actually expected: in true random samples, if you look at all data you're going to find things that don't break down evenly just by chance.  Since even the slight amount of difference from even that was seen in some adverse effects was balanced between things that happened more often for the vaccine group vs. things that happened for the placebo group (that is, neither group saw this with more dangerous effects or more often than the other group), we can just ignore these from a risk analysis perspective.  Aside from the immune response reactions, it's a wash in safety between taking the vaccine and not taking it.

The only possible exception to this is a small number of extra cases of Bell's Palsy that occurred in the vaccine groups in both studies at a more elevated rate than the other adverse effects.  This still happened at a low enough rate where it could just be a coincidence, and also this is not a very serious condition that clears up on its own over time.  So I'm not going to bother including it in the risk analysis.

Immune response risks

So what are the actual immune response risks?  Mostly, just the standard "feels sick" symptoms of your immune system working which we've already discussed.  Typically these were mild, frequently they were bad enough to cause a couple days off of work, and rarely (11 cases) they were severe enough to last for a week or more and merit an emergency room visit.  No deaths or lasting effects were discovered from these side effects. 

During the trial, no instances of acute immune response side effect (also known as an allergic response to the vaccine, or anaphylactic shock) were observed.  After the trials, once the vaccine was beginning to be administered in bulk, we did begin to observe some instances of anaphylactic shock: about six in 272,000 doses, which makes sense if the likelihood of acute allergic reaction were just beyond the threshold of being likely to occur in the 33,500 trial cases.

This rate is quite a lot higher than the typical rate for other vaccines: other vaccines in the standard roster have about a 1 in 1 million rate of anaphylactic shock, so this is 22 times more common than seen with vaccines we ordinarily administer.  This has led some people to speculate that one of the materials used to stabilize the microscopic packets of vaccine (polyethylene glycol, or "PEG") is causing an allergic reaction in some people (a theory covered in this article.)

This is one theory, but there are other possible reasons for the high rate of anaphylaxis.  First, most people with severe allergies are told to avoid vaccines, precisely because of the innate tendency of all vaccines to cause allergic reactions.  However, due to the high profile of Covid, many people even with severe allergies are getting this vaccine anyway--in several of the cases of anaphylaxis we have seen, the person had a history of severe allergic reaction to vaccines.  This might be artificially inflating the rates (we do, after all, have only 6 total cases of anaphylactic shock to go off of here--it's entirely possible that 6 severely allergic people decided to be heroes in order to be early testers of the vaccine).

Another possibility is that Covid itself has a higher tendency to provoke an uncontrolled allergic reaction.  The vaccine causes human cell muscles to replicate *part* of the virus--just the spike protein part, not the rest of it.  Although the majority of cases of Covid follow a certain pattern, we have seen a persistent subset of the fatal cases in which the patient seems fine and then goes suddenly and almost inexplicably downhill and dies.  This has led to the theory that cytokine storm (being essentially an allergic reaction) is a key mechanism by which Covid can kill people.  It is therefore also plausible that the spike protein itself has a tendency to provoke an out-of-control immune response in some people.  

Regardless of the cause, it is important to note the allergic reaction as a possible risk.  It is also important to note that this risk can be mitigated.  When the FDA advisory committee was reviewing Pfizer's data, the question of allergic reaction was discussed rather vigorously (8 hour video here if you have the stomach for it).  In the end, it was pointed out that all vaccines have a risk of allergic reaction, and that it is already the case that vaccines are administered in locations with ready access to epinephrine injections and other means of emergency treatment for just such scenarios.  

This risk mitigation factor should also be kept in mind in case it is the spike protein itself that tends to cause an allergic reaction.  If this is the case, then either Covid or the vaccine could produce an allergic reaction, *but* the virus would tend to cause that reaction at your home (which is where you are told to sit and wait out the milder forms of the disease), whereas the vaccine would cause the reaction in a location where they can do something about an acute problem.  Earlier, we estimated that none of the milder, unreported forms of the disease were causing deaths.  However, if a small percentage of these sorts of infection are causing people to drop dead from anaphylactic shock, it may well be that these deaths are not being counted as official Covid-caused deaths, there not being any good reason to test these people for Covid after death.

Quantifying the immune response risks

When the first person to get one of the vaccines had an anaphylactic reaction, this was instantly a news story.  I'm therefore confident that no one so far (at least as of a few days ago) has died from administration of the vaccine.  This means we can confidently put the risk of death at about 1 in 2 million per dose at the worst.  Since you need 2 doses to get the full vaccine, we'll call this 1 in 1 million.  This number is likely to improve with time as we vaccinate more and more people.

The risk of an acute attack and therefore a stay at the hospital of a few days should be put at 6 in 272,000, keeping in mind that this could be an overestimation and that I'm ignoring the possibility that some of this risk could be offset by the counter-balancing risk of allergic reactions to Covid itself.

Unknown risks

This now suffices for all the *known* risks of the vaccine.  There are now two categories of risks from the vaccine we can still talk about: short term risks that are too rare to have shown up in the data so far, and risks for adverse effects that don't show up until the long term, beyond the experience we have so far.

Rare short term, serious but non-fatal risks

Here we are limited by the vaccine trial data.  Since they were looking at all adverse health effects, we know that anything that is more common than about 1 in 33,500 would have been caught. I am inclined to put any risk here into an even lesser frequency on the basis that there isn't a lot new about these new vaccines.  The real novelty of this approach is the delivery of a much smaller genetic load than the typical vaccine.  It is thought that this approach is inherently safer than using a full viral gene sequence that has been neutered somehow, and which can very rarely therefore cause an actual infection (for example, as in the small pox vaccine, which has about a 1 in 1 million chance of doing that.)  Aside from the smaller genetic load, it is packaged in known safe materials that are used in a lot of other common drugs and consumer goods.  The PEG issue was discussed already and is dealt with under the immune response risk.

I will therefore assign a risk of 1 in 50,000 to the possibility that there will be some rare short-term complication caused by the vaccine that hasn't been recognized yet.  This would be, by the way, worse than almost any modern vaccine, including some vaccines that have been recalled by the FDA for safety records that were better than that (see this article).

Unknown long term risks

Some people are concerned about the possible long term effects of the vaccine, due to the rapid way in which it was developed.  There are a few reasons to discount this fear.

First, the vaccine was really in development for a significant portion of its early stage before Covid.  This is not the first coronavirus to emerge and endanger the world, so people were already working on isolating the specific genetic code for the spike protein for a while: see this interview with one of the vaccine inventers for more details.

Second, there are some reasons that vaccine development takes longer typically that don't apply to the Covid mRNA vaccines.  Many vaccine trials take some time before they can recruit enough people, whereas due to the urgent need for a Covid vaccine, both trials easily recruited about 10 times the typical size of a normal vaccine trial in record speed.  Further, a significant portion of the time taken to complete a vaccine trial is to wait for enough people to get sick so that you have statistically significant data with which you can compare effectiveness between vaccine and placebo groups.  The rapid and widespread multiplication of Covid in various places which began this Fall is sad otherwise, but had the beneficial side-effect of causing the correct statistical milestones for these trials to be crossed quickly.  Finally, there is a lot of just administrative cruft in a typical vaccine approval process that was burned through quickly this time because of the perceived urgency.

The third reason to discount the risk of unknown long term effects is how rare long term side effects of vaccines are, if they do not also cause a short-term problem.  As was pointed out in the FDA deliberations, long term effects from a vaccine after 2 months of no short term effects are currently essentially unknown.  If that were to happen with these new vaccines, it would be essentially the very first time.

How I will score this risk, then, is to rely on this article which summarizes the health risks of problematic modern vaccines that did make it through an initial approval.  Of its various examples, the worst case it contains was the yellow fever vaccine which ended up having about a 1.5 out of 1,000,000 rate of unexpected serious side effects.  This is not an example of a long term side effect, but is about the worst plausible "surprise factor" I could find from that article so I will use it here.

Risk Analysis of the Moderna and Pfizer Vaccines, part 3

What is the risk I will pass on Covid even if I get vaccinated?

At first this seems as if it should be an easy answer: it would be the risk of passing on Covid if you get it, multiplied by the risk of the vaccine not protecting you from getting Covid (5%).  But now we can see there are two complications with that simple formula.

Why this is a hard question

First, even if the vaccine doesn't protect you from Covid entirely, it might reduce the severity of the infection and therefore reduce the amount of viral shedding.  Given how few people actually got Covid who were given the vaccines, there is simply not yet enough data to prove that the vaccine reduces the severity of the disease if you get it.  There are some early indications that this might be the case and it is very reasonable to think it might be the case, but it is not yet medically proven.

Second and more worrying, however, is that we don't know for sure that if the vaccine keeps you from getting Covid (the disease) it also keeps you from spreading the disease.  The way they tracked people in the trials for both vaccines, is that they tracked all symptoms that people had, and then verified the presence of the virus in people who reported the right symptoms.  This leaves open the possibility that many vaccinated people caught the virus, that the vaccine made them asymptomatic, but that they were still contagious even though they showed no symptoms.

It should be noted up front that this is a *possibility*. Some people have erroneously heard about this possibility and concluded that we know you can still transmit the disease even after being vaccinated.  We don't know that this is the case; in fact, it could well be that the vaccination as effective at preventing the transmission of the disease as it is at preventing its symptoms.  I believe this to be the more likely scenario, in fact.  But this is not proven one way or another yet.

How to estimate an answer

This being the case, we have to come up with a way of getting a reasonable estimate of the likelihoods here in order to build a risk assessment.

I think the most useful study to use here is this one (https://www.nature.com/articles/s41591-020-0869-5), which looks at the percentage of transmission that occurs before onset of symptoms: 

The useful thing about this study is that they looked at things from the perspective of timing of the viral load, but they also cross-checked with studies that looked at transmission in countries where extremely careful contact tracing was happening and which were deducing from that data how much spread was happening before symptom onset.  This two very different ways of looking at things came up with very similar answers: somewhere around 40ish to 50 percent of transmission happens before symptom onset--say 45% to take an even number.  This answer would include both asymptomatic and pre-symptomatic transmissions, which means that an absolute minimum of 50% of transmission happens in conjunction with some symptoms--more, almost certainly, because this number includes transmission that happened just before symptoms started.  Since the vaccines are 95% effective in preventing the disease to the extent where no symptoms ever show up, we can say that it's likely at least 49.5% (say, 50% rounding off) effective at preventing transmission.

The next question is, what percentage of that ~45% of transmission that is happening before symptom onset is truly asymptomatic and what percentage is pre-symptomatic?  I have been unable to find really convincing answers here, but the sense I get from the research is that this split is heavily weighted towards the pre-symptomatic--say, 80/20 in its favor.  So I would personally bump up the likelihood that the vaccines protects from passing on the infection from 50% to about 65% based on this split.

But it gets better than this.  Recall that what is happening at least some of the time with asymptomatic individuals is that their immune system is fighting off the disease by producing antibodies, just not by also ramping up on the other general disease-fighting mechanisms which create all of those typical illness symptoms: fever, congestion, aches, etc.  

While the vaccine trials did not do routine testing for the virus in all of its participants, they did do testing on the antibody production which the vaccine generates, and we do know that it causes antibody production in its recipients equal or greater than we see in those who have cleared the virus from their systems naturally.

Recipients of the vaccine are therefore in a situation after having been vaccinated that most of the asymptomatic infected people are not in until after they have cleared the disease.  What this means is that however much asymptomatic transmission happens because of this time period before antibodies are generated, that much transmission will also be blocked by the vaccine.

Conclusion

Therefore I think it is reasonable to bump up the percentage likelihood that the vaccine will prevent you from transmitting the disease even further--let's say, to 80%.  Personally, I think this is conservative and that the true number will be closer to 95%, but I'm fine with using the 80% figure for risk estimation.

(EDIT 1/11/2021) Update

There was some important data I missed for this section of the series.  There is actually some data from the Moderna trial specifically which gives a good early indication that we are seeing that protection from transmission from the vaccine.  This link: https://twitter.com/EricTopol/status/1338872330538237955 points out a part of the FDA briefing document that I had missed, which indicates approximately a 75% reduction in transmission of the virus after a single dose of the Moderna vaccine.

I think this is very encouraging because this would include a time range during which the vaccine doesn't have much effect at all (the first couple of days), and a longer time period during which your body is ramping up its immune response.

So if just the first dose confers a 75% reduction in asymptomatic spread, I would expect the full two doses to be closer to my hoped-for 90-95% effectiveness.  80% is still a good conservative estimate to use, so this data doesn't change my bottom line; it just makes it more reliable.

Risk Analysis of the Moderna and Pfizer Vaccines, part 2

Some background medical facts

I'd like to get to evaluating the risk that if one gets the vaccine, one will spread the disease anyway even though not getting it.  But this requires some understanding of the background science that not everyone will necessarily have.  So I'm going to make a couple of key distinctions in this installment.

Distinction between the virus and the disease

Medical science distinguishes between a disease and the virus which causes the disease.  The virus is the actual micro-organism that replicates in individuals: in the case of Covid, this has been named "SARS CoV 2" ("Severe Accute Respiratory Syndrom Coronavirus 2).  The *disease* is defined as the set of symptoms that infection with this microbe can produce, in this case named "Covid-19" ("Coronavirus disease that emerged in 2019").  Going forward, though, I'm going to call both the disease and the virus simply "Covid" as a convenience, unless necessary for disambiguation.

This distinction between virus and disease is important because the same pathogen can cause a variety of different symptoms depending on various factors.  The same virus can attack different parts of the body, it can replicate to various degrees of success, and the individual body which is infected can react to this infection in different ways.  Let's examine these types of variation in a bit more detail.

Variation by different body parts

Covid replicates by attaching to cells which have something called an "ACE2 receptor", entering them and hijacking the natural cellular reproductive mechanisms.  The mechanism by which Covid replicates means that it can attack any portion of the body containing cells which have these receptors, which (it turns out) is quite a large variety.  They are found in cells of the lungs, heart, blood vessels, kidneys, liver and gastrointestinal tract, and are also plentiful in neurons.  Blood platelets also have ACE2 receptors, meaning that Covid can cause system-wide blood clotting and can therefore damage any part of the body that is susceptible to capillary clotting.  Testicular cells express ACE2 and so the testes have been noted as a potential attack vector for Covid.  The uterus and placenta contain cells that express ACE2.

This wide array of potential cell targets for Covid at least partially explains the wide array of symptoms that have been associated with the disease, including (but not limited to) the following:

• Associated with cells of the nervous system:
• Anosmia (loss of the sense of smell / taste)
• Heart palpitations
• Brain fog
• Associated with epithelial cells in the lung:
• Pneumonia
• "ground glass opacities" in the lungs
• Associated with platelets:
• Blood clotting
• Associated with cells of the cardiac muscles:
• Damage to heart tissue
• Stroke
• Associated with cells of the intestinal lining:
• Nausea
• Diarrhea
• Associated with the liver
• Raised levels of liver enzyme
• At least temporary liver damage
• Associated with testicular cells
• Testicular damage
• Possible infertility
• Associated with cells of the uterus and placenta
• "Severe maternal disease" (not sure what that means)
• "Adverse pregnancy outcome"
• Infection of baby in the womb

Variation by replication amount

The severity of the disease may vary by how successful it is in replicating throughout the body.  There are various reasons why the disease may have different success rates in replicating in a particular individual.  One of the most interesting of these reasons is known as the "inoculum"--the size of the initial "dose" of virus that you get when infected.

There is research that strongly suggests that the amount of virus you are exposed to when you are first infected has an effect on how sick you ultimately become.  This is why, for example, they recommend that individuals who live with a family and are sick wear a face mask.  It might be very likely that they will infect their cohabiting family members, but by trapping a lot of the exhaled virus behind a mask, the amount of virus their family members will initially inhale will be smaller, and they are therefore likely to come down with a correspondingly milder form of the disease (one link here).

One of the theories behind this is that a smaller initial dose means that the virus takes longer to replicate up to very large numbers.  The longer that the virus takes to get up to full potential, the longer the body has to mount its own defenses and deploy them throughout the body.  By getting a jump on the virus, the body's immune system has a better chance of keeping it contained and under control before it gets out of hand.

There is some support for this theory by studies which show a large difference in the amount of virus shed between mildly ill patients and severely ill patients: a factor of 60 times larger according to some studies.  It should be noted, however, that the question of the relationship between amount of virus shedding and severity of the disease is not always clear cut and there are seemingly contradictory studies on this.

Variation by reaction of the body to the virus

The body can react differently to an infection.  There are a few important things to note here.

First, most of the most common symptoms of Covid, as with the cold and the flu, are actually caused by the body's reaction to the virus more so than the virus itself.  Extra mucus production is due to the ramp-up of white blood cells to combat infection.  This leads to congestion and headache.  Fever and chills are caused by the body raising the temperature in order to make a less hospitable environment for viral reproduction, leading in turn to muscle aches and fatigue.

All of these things aid in the body's fight against the virus, but are not strictly necessary to it.  It is possible for the body to produce antibodies and clear the virus from the body without doing these things.  This at least partially explains the phenomenon of asymptomatic infected individuals--people who become infected and even contagious, but do not seem to come down with the disease (i.e,, the symptoms).  This is a known phenomenon in a number of diseases sometimes called "subclinical infections".  

What I would like to point out here about subclinical infections is that there is a crucial point of ambiguity if we are talking about people who are infected but have little to no symptoms: it is possible either that these people have a very mild infection (as from the point above) or it is possible that they have a fairly respectably sized infection but are not exhibiting the classical symptoms that are caused by particular aspects of the body's immune response.  Or it could also be some combination of those two factors.

At the other end of the spectrum from subclinical infection is what happens when the body's immune response overreacts to the presence of the virus.  It is possible for the immune system to respond far to aggressively to a reaction, causing it to attack healthy cells as well.  In the extreme, this is called a "cytokine storm" and can be deadly.  It is thought that the Spanish Flu was particularly good at inciting a cytokine storm, and that was why it was able to kill so many otherwise healthy young adults.

The distinction between "asymptomatic" and "pre-symptomatic"

A key component to analyze the risk of spreading Covid is the phenomenon of asymptomatic spread.  At this point everyone knows that this is a major characteristic of Covid.  However, a lot of people are still not clear on what exactly this means.

A key point of ambiguity is, what is meant by "asymptomatic"?  Unfortunately, the term is used differently in different scientific studies, and the confusion over the term spreads out from there.  Sometimes, the term "asymptomatic" is used strictly for those people (mentioned above) who get infected but never show any symptoms over the whole course of the disease.  These people are obviously important from an epidemiological standpoint, because they have the capacity to be long-term unconscious spreaders of the disease.

Sometimes, on the other hand, some people will use the term "asymptomatic" also for the time period when a person is already infected but not showing any symptoms yet.  Every infected person goes through this phase, because there is always an incubation period for the disease of some length.  If a person is using the term in this way, then "asymptomatic transmission" can be used to describe someone who passes on the disease before they develop symptoms.

However, if someone is using the term "asymptomatic" more strictly, then the period of time before a person starts showing symptoms is called "pre-symptomatic" rather than "asymptomatic".  In this case, a true "asymptomatic transmission" would only happen from a person who never shows symptoms throughout the whole course of his disease, not when someone passes on the disease before then exhibiting symptoms.

As I said, the term "asymptomatic" is ambiguous and gets used in both ways.  You have to be careful to distinguish in which way it is being used when you read a particular study, and sometimes even when you read particular passages out of a single study.

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.