First, right off the bat, spoiler alert: my end conclusion here is going to be that we don't have enough data available to know whether getting most vaccines is harmful or helpful, specifically in 2014 in America, to either the individual or to society as a whole. It is neither pro-vaccine nor anti-vaccine, so don't get your bustle in a bunch just yet.
Edit: In terms of "so what?" the actual bottom line here is that
"people should stop being dicks to each other about personal vaccination decisions, when in reality, neither of any two people arguing about it has sufficient data to actually know who is making the correct choice, for themselves or society."Anyway, this is how people SHOULD be talking about vaccines and making decisions about them, in a rational, scientific world:
1. The simple method you should consider when deciding to undergo ANY medical treatment - risk vs. reward.I trust that this should be an uncontroversial starting point: You should undergo medical treatments that have a higher chance of helping you than they have a chance of hurting you.
Long version:Sum ((chance of each risk) * (magnitude of risk)) / Sum ((chance of each benefit) * (magnitude of benefit)) = risk/reward ratio.
If that number is greater than 1, you should undergo the treatment. If it is lower than 1, you should not undergo the treatment. This is as relates to an individual making a decision for him or herself. You can also ask the question about society in general. For most treatments, that's no different, although for vaccines it is, due to "herd immunity." I address this alternative way of looking at the issue in section #4 below, and conclude that no matter whether you take an individual or societal perspective, it doesn't influence the end result, given current data for people in the U.S.
Looking at death rate as a representative subset of total risks and benefits, and using measles as an example, the benefit to you over your lifetime of a measles vaccine in 2014 in America is in the ballpark of a 1/60,000,000 chance of it saving your life from a measles death.
Long version:It's fairly easy to quantify the benefits of vaccines. I'm going to look at things ONLY in terms of death, to keep the length of the post reasonable. You could add in other complications that vaccines save you from versus cause (and I have done this in the past), but it doesn't really change the conclusion, so to avoid too much text, I'm using this simplification here to make the point.
So let's take measles as an example case. What is the chance that a measles vaccine in the U.S. today will save a person from dying of measles over their entire lifetime?
a) How many people get measles in the U.S.? Over the last ten years, the average has been almost exactly 100 per year.
b) What is your chance of getting measles in your lifetime? If we project current rates out, you'd do (100*(life expectancy)) / (current population, since that's what the base rate cases are calculated from, i.e. it will scale automatically) = (100 * 78) / 309 million = 0.0025% Yes you would need to put a negligible adjustment in here for splitting out by vaccinated/unvaccinated, but at such small incidence, it's almost zero. Don't want to complicate things too much, and I outweigh this with two conservative estimates below.
c) What is the likelihood of dying of measles once you get it? For this, we look at 1960's death rates amongst infected, which were approximately 1/1,500. Today, the rates would be much better due to significant medical advances, but to be very conservative, I'll just use the 1960s rate. So 0.0025% to get measles / 1,500 = 0.0000017% to die of measles.
d) How effective is the vaccine? Estimates vary 90-95%, I'll be generous and just say 100% and not make any adjustment.
Conclusion: a measles vaccine has the inverse of the above percentage, or 1/60,000,000 chance of saving you from dying of measles in your lifetime, assuming current types of conditions.
We don't know, because clinical trials only use ~2,000 people at most for vaccines, which obviously can't tell you about hypothetical death rates in the neighborhood 1/60,000,000, and even giant observational meta-studies (setting aside inherent weaker causal claims) don't have enough participants, use odd statistics, and also tend to focus only on thimerosal and autism to the exclusion of what you should care about more, which is "all risks (including current example of death) from any causes."
Long version:To complement the above calculations, we need to ask "What are the chances of a measles vaccine killing you?" and if the answer is greater than 1/60,000,000, then taking the vaccine would be bad for you individually, or if lower than that, taking the vaccine would be good for you.
Well, which is it? NOBODY KNOWS. Clinical trials for vaccines are the gold standard, because they involve randomly assigned control and experimental conditions, usually double blind, and thus unequivocally test causality. However, the largest vaccine trials tend to have around 2,000 people, which is obviously mathematically incapable of detecting, say, a 1/50,000,000 chance of death, if it exists. So they simply don't tell us what we need to know one way or the other.
In lieu of clinical trials, we can turn to lesser data, like cohort or case-control studies. However, there are several issues with these:
* Most of these studies focus specifically on thimerosal, mercury, or autism, which means that they aren't capable of telling us anything about any other potential risks that would probably be way more likely anyway, such as side effects from the antigens themselves i.e. rarer versions of that disease's side effects, anaphylactic shock from non-mercury allergens in the vaccine recipe, or possibly fatal immunological weird side effects from the body responding to antigens mysteriously appearing in muscle, etc.
* The largest meta studies I've seen on this issue tend to only have 1-2 million subjects, which is also simply incapable of detecting anything approaching a 1/60,000,000 event.
* Every meta study I've seen has ALSO included component studies that look specifically at thimerosal, mercury, or autism. This dilutes their subject pool even more if you care about all risks in general, and also makes the final statistic impossible to interpret without contacting the author and having them re-run with only general risk studies.
* Nearly all the studies (autism or otherwise) use odds-ratio statistics in a way that is inappropriate for the issue by defining a "significant result" as one that is significant with regard to the base rate of whatever threat is being measured. In layman's terms, the studies are testing for (depending on specific maths used) either "Are vaccines the SOLE cause of [insert risk]?" or "Are vaccines a significant contributor to [insert risk] as compared to whatever else might be a cause?" Neither is the correct question, since what we need to know to make a decision about a drug is the ratio of risks versus benefits of that drug, NOT whether some unrelated thing out in the world happens to be even riskier or not.
You simply have no way to know with current data. Knowing benefits but not risks is equally as useful as knowing no data at all. Therefore, the only way to make a decision is gut instinct or intuition, and I see no scientific basis for telling yourself or anybody else that they are correct or incorrect about their decision in any objective sense. At this time, in the U.S.
(We BARELY even have enough data to be sure that current measles vaccines help more than they hurt even if we had the same infection and death rate as in 1960 pre vaccine!)
5. What about herd immunity? I.e. calculating based on societal risk/benefit?Short version: One, this is a pretty unethical basis for making policy. Two, even if we ignore that, we don't have enough data anyway to know whether the benefit to society is greater than the risk to society.
Long version:First of all, I find it highly morally questionable to even really consider this question, because
People should never be legally or morally obligated to give up their own bodily integrity. In America, we have strong precedent that citizens have a right to their own bodily integrity despite potential costs to society.
Roe v. Wade establishes a woman's right to bodily integrity even if a potential child might incur significant societal financial strain, for example.
McFall v. Shrimp establishes it is unconstitutional to be forced to donate bone marrow even if you are the only viable donor and death is certain without it. The logic here is no different, nor the relative magnitudes of risk/reward even significantly different.
But let's set that aside for a moment, and consider this anyway, as if bodily integrity were not a thing. What herd immunity means is that basically, the benefit of a vaccine goes up the fewer the people who are vaccinated. The very first person to be vaccinated provides benefit to himself in avoiding disease (which is maximally high among an unvaccinated population), but also the full possible amount of benefit of one potentially contagious person to ALL of the people he knows and contacts. The very last person being vaccinated provides ONLY their own personal benefit (which is maximally low, since only people who had unsuccessful vaccinations are potential threats and epidemic rates are lowered), and almost zero societal benefit, since everybody else is vaccinated already and doesn't really need to worry if that last guy is sick or not. The only reason the marginal benefit isn't literally zero is that vaccines are not always effective.
Risk to society, however, from each dose is basically flat no matter how many people are vaccinated. Overall, what you get is something like this:
Graph of marginal benefit and risk for each additional vaccinated person
Since we have almost no idea where the red line is, we don't actually know whether the optimal vaccination level is 0%, 100%, or anywhere in between!
And even if I throw you a bone and say "okay let's just assume it's not the highest red bar, and that it's at least lower than the highest benefit" (which is btw reasonable if you assume 1960's healthcare, just barely. Probably not reasonable to assume today) This STILL tells us nothing very useful, because the optimal vaccination level could still be anywhere from 1% to 100%, it might be higher or lower than our current vaccination level at any time.
Author
Topic: Vaccine risks vs. benefits, a thorough mathematical consideration (Read 35737 times)