Pertussis: Misleading Statistics

So originally this graphic came from the CDC. It looked like this.

http://www.cdc.gov/pertussis/downloads/pertuss-surv-report-2013.pdf

It shows just what the CDC wanted to show, however useless it might be to the rest of us, it means something to them, I guess.

Then someone came along (I don't know the source of the beefed up graphic) thinking that it meant something it didn't (statistics are funny like that!), and tried to show that this vaccine doesn't work and you have a better chance of not getting it and reporting it if you're not vaccinated.

FALSE!

Enter a mathematician.

The original graphic from the CDC is showing a breakdown of the 6,235 reported cases in 2013. If you wanted to make the claims from the beefed up graphic, you'd need to look at the whole population, or take a sampling that included kids that did and did not get and report pertussis, including vaxers and non-vaxers, and you'd have to take a pretty large sampling for it to actually be an accurate statistic. 

So let's see if I can get a little more accurate view of what she's trying to show. There are 710 non-vaxed kids that got it, and 3,456 vaxed kids that got it. According the Census, there are 19,868,088 kids under the age of 5 in the US. According to the CDC 95.1% of kids entering kindergarten in the 2012-2013 school year had gotten the DTaP vaccine (the best number I could find, since before entering kindergarten vaccines don't have to be reported as received, but from other sites I've looked at, the non-vax rate is under 6%, so I'm thinking it's fairly close.) 

(This is where you should see a red flag go up... more kids have been vaccinated against pertussis, so there's more kids that could potentially get it. There's less kids that haven't been vaccinated against it, so there's a smaller population that can get it. So, it only makes sense that of the kids that got sick and reported it, fewer of them were un-vaccinated... there's just less of them to choose from!)

So with these numbers this is what we have...

With a population size of 19,868,088 and 4.9% not being vaccinated, that means that 973,536 were not vaccinated against pertussis. And 95.1% or 18,894,552 were vaccinated against pertussis.

Now, if we take the whole population of non-vaccinated kids and look at how many reported having pertussis (710 total kids that did not get any vaccination against it at all), we're looking at 0.073%.

Looking at the whole population of vaccinated kids and how many reported having pertussis (416 and 3,038 or 3,454 that got at least 1 dose of DTap), we're looking at 0.018%.

Both these numbers are incredibly small, yes. But it shows that the kids who did not get the vaccine were actually almost 4 times (3.984, to be accurate) more likely to get and report pertussis than those who were vaccinated against it.

Moral of the story: Don't let statistics scare you unless you actually understand them fully.