When Can We Say The Swine Flu Isn’t As Bad Here As There
When I first started writing for TMV, I meant to have a few posts pointing out how a basic ignorance or misunderstanding of statistics clouds our political discussions and news stories. I got distracted with all the happenings in the world, but this outbreak sounds like a good place to start.
So far there have been 103 deaths in Mexico out of 1614 suspected sickened. This is a fatality rate of about 6%, which is very high for flu — even the Spanish Flu only had a rate of 2.5%. That shouldn’t be taken to mean that this flu is much worse, because hundreds of millions had the Spanish Flu and the huge infection rate surely brought down the fatality rate. Still, it is very concerning.
Yet thus far, there hasn’t been one death in the US or Canada out of the confirmed cases which is leading to news stories suggesting that there might be something different here that makes it less dangerous. Obviously I don’t know all the symptoms of the infected here versus there, so I can’t generalize about severity of people that don’t die, but I am kind of taken aback by the reporting that is focusing on deaths. I’ll explain why.
Between here and Canada there have only been 26 confirmed cases. This means that the number of expected deaths is 1.56 (26 cases multiplied by 0.06 probability of dying). Thought about that way, it no longer seems very odd that no one has died here, since the virus could have the exact same fatality rate and we’d expect to see only one or two deaths. There is a way to calculate the chance that zero people would die, which I’ll briefly explain now.
In statistics there are two types of outcomes that a question can have. One is called continuous, and that’s what we are talking about if we’re looking at IQ scores or height or weight, or any sort of variable where there can be a range of values and we want to see how a value compares to what’s expected. The other one is discrete, where they can only be a few values — the classic is having colored balls you are picking out of a hat — and in this case I’m going to talk about only two outcomes: sick but hasn’t died or sick but died. The best way to calculate probability for this instance is using something called the binomial distribution, binomial meaning that there are only two possibilities.
This page explains the math and has a calculator that can be used. For the calculation, there are three things that must be entered: the number of trials (n), the number of “successes” (k) and the probability that a trial will be a success (p). The classic example is the coin flip. Let’s say that you want to test whether a coin is weighted. The idea is that either heads or tails will pop up a lot more than is expected, and so if you flip it enough times, you can show whether it’s reasonable to suspect that the coin is weighted.
For instance, if you flip a coin 100 times and get 44 heads. That’s less than 50 that is expected, but is it abnormal? A coin has a 50% chance of coming up heads, so p = 0.5, n = 100 and k = 44. The calculator says that the probability of getting 44 heads or fewer is 0.13. This means that if you flipped a coin 100 times and did the calculation, then flipped it again 100 times as a new experiment and then did the calculation, etc. several times, that 13% of the experiments you’d get 44 or fewer. The definition of whether this qualifies as “suspect” is based on your viewpoint. In biological sciences we want it to be less than 5%, so you wouldn’t say that statistically speaking we would have reason to think the coin is suspect (however only 40 heads gives less than 3% chance, so we’d definitely want to repeat the 100 flips and see if it occurs again). On the other hand, if you were gambling at a speakeasy, then you’d probably have a lower tolerance and may be suspect.
As for the number of deaths? Well, in the US/Canada there have been 26 cases (n = 26), fortunately zero deaths (k = 0) and we’ll use a p of 0.06 because we are asking how sure we can be that there is something different between here and Mexico.
The calculator shows that there is a probability of 0.2 for this occurring. That is obviously less than a coin flip of 50/50, but still, a 20% chance that something happened purely by chance is pretty high for someone to conclude that it means there is a reason behind it. After all, if you flipped a coin 100 times and got 44 heads, intuitively you wouldn’t think much of it, but that is less likely to happen than the fact that no one has died from the flu here.
And that’s assuming that the p of 0.06 is correct. I would argue that it’s much more likely that people will be diagnosed here because there is a natural screening process that few people satisfy (flu symptoms and visited Mexico recently) while in Mexico, there will be much less reason to suspect that people have it instead of another disease. If the flu does have a fatality rate more similar to the Spanish Flu, and we just haven’t seen it yet because it’s so early in the process, then that would mean that the probability for no one dying here would be 0.51…or in other words, there would be no basis at all for thinking that something is different here.
This turned out a little longer than I anticipated, but it is a very clear example of poor reporting and speculation. It’s obviously not wise to panic, but on the other hand I think it’s also a bad idea to start a meme that could quickly turn. As more people start getting sick, there is a good chance that deaths will happen, possibly in rapid succession and it’ll be important to keep a cool head and not assume that something drastic changed. For instance, after the next 26 people
die (huge typo, I meant get confirmed diagnosis), then there is a 60% chance that 3 or more people will have died if it has the same fatality rate thus far observed in Mexico. There’s even a 10% chance that 6 or more could die…yet if 3 out of the next 26 die I guarantee there will be sensational headlines and if 6 out of the next 26 die there will be panicked ones — all prematurely. On the flip side, if still no one has died, then that’s only a 4% chance, so it suggests that perhaps something really is different here (assuming that the fatality rate stays constant in Mexico).