Uh Oh

FYI: I am like the most pro-vaccine person out there.

But, I also noted in COVID-19 coverage in class, and in the departmental seminar — both last February — that they've been working on a vaccine for the original SARS since 2003 and have not been successful. This is mostly due to side effects.

Which brings us to the third stage trial of the AstraZeneca vaccine against COVID-19 ... one of the best bets out there. It's trial was stopped about a month ago.

Why is that so?

Because in an 18,000 person trial there were two cases of transverse myelitis. Not to horrible a condition, but definitely worse than the typical side effects of "dry eyes, moist eyes, trouble sleeping, trouble staying awake, even numbers of arms, and so on." The thing is the incidence of that disease is 4 per million. †

This is a good example for students of how to get at probabilities of a certain sort. 

So, if 4 people out of a million get the disease, the probability of you not getting it is 0.999996. But what if you are just one of 18,000 people in a test? To get that, you'd need to raise that number to the 18,000th power. Good luck.

But there's an easier way. Take the figure 0.999996 and square it. That's the probability of having 2 people not get the disease. Square that to get the probability of 4 people not getting the disease, and so on. If you iterate that 14 times, you'll find that the odds of transverse myelitis not showing up in 16,384 (approximating 18K) people is 93.7%.

However, that doesn't get us the chance of getting two cases. Here's another trick: we can figure out the probability of getting exactly 1 case, and subtract both results from 1 to get the probability of getting two or more (figuring anything more than 2 probably has a probability really near zero). That's pretty easy to figure out. First, divide the 93.7% by the 0.999996 to get the probability of 16,383 people not getting it, multiply that by the (1-.999996) chance of getting it, and then by the 16,384 possible people you'd need to check, and you get 6.1%.

That leaves the probability of getting 2 or more in an 18K sample at roughly 0.2%. When I did that calculation and got that result, my first thought was: they're never going to re-open this trial. That doesn't mean there aren't other vaccine candidates out there, but it is the first sign that we're not going to get a vaccine on the optimistic timetables.

Why figure that out in a macro class? Because that's also the way that you figure out the bad effects of data mining when you subject your data to multiple tests. 

BTW: You could also approximate this with a Poisson distribution by estimating lambda as the expected number of cases, 4, times the sample as a fraction of a million (.018). Doing this gets you 0.24%.

† Of course, going on the basis of Wikipedia, perhaps the problem is that an effect of the side effect is "dysfunctional ... anal sphincter activities", and if they had to list that in a commercial's disclaimer I think they'd get some people's attention very quickly.