In a recent comment posted on the Australian Vaccination Network blog, Meryl Dorey linked to a news article about Whooping Cough vaccination rates in California. Dorey noted that she'd also posted a comment on the news website and she included the following statistics...
There are 10,000 unvaccinated children in California – a state with a population of over 36,000,000. That means that less than .03% of California’s population is opting out of vaccination.
Dorey goes on to argue that the numbers of willingly unvaccinated children is so low as to be trivial compared to the numbers for whom vaccination is ineffective. But was she using statistics correctly this time?
As I've mentioned before, I'm so scientist or statistician so I welcome corrections in either calculations, data or approach. What I provide here is a layman's summary.
My first instinct was that Dorey had made a glaring error by conflating two entirely different data sets - unvaccinated children vs entire population - at the very least because she'd failed to supply data about the known vaccination status of those who aren't "children".
With her 0.03% statistic, she'd effectively said that those 10,000 kids were the only unvaccinated people in the entire state of California.
You cannot simply take one figure showing childhood vaccination numbers and then draw a whole-of-population statistic from it. It would be like saying - if there are two black rabbits at the zoo and there are 10,000 animals in total at that zoo, then only .02% of the zoo's animals are black. But the first statistic tells us nothing about what other animals might also be black. What about the panthers and monkeys and seals and yaks? And how many rabbits are there altogether? What percentage of the rabbits are black? That's something we might like to know but we can't calculate it without more information.
For her "10,000 children" figure to be of any use, we need to know how many "children" (of similar demographic) there are in California, not how many people. Using "under fives" as my starting point, since we're talking vaccination, I found a few websites that suggest the number of "children" in California is around 3 million. That's much less than the 36 million that Dorey used. So immediately we can see that her calculation was out by around a factor of 10 (ten).
At this point I still hadn't read the article Dorey had linked to, I was just running numbers based on what she'd written in her comment. When I did read the news item, the statistical murder scene looked much worse.
From the article (my bolding)...
Our media partner, the Watchdog Institute, crunched the numbers for kindergartners entering California schools in 2009. The number entering kindergarten with so-called “personal belief exemptions” against vaccines hit 10,280 last year.
I'll forgive Dorey the rounding-down since the additional 280 kids wouldn't make any real difference to the calculation she was doing. But what is really important is what data set was really being measured in the article - and that was "the number [of children] entering kindergarten... in 2009".
Kids entering kindie in one specific year is a much smaller number than all kids under five. With this new information, it was clear that even my calculation was going to be far too generous in favour of unvaccinated kids. At a wild guess, I'd have to assume that around one fifth of kids aged five and under would be entering kindergarten in any given year (and that's assuming all kids of eligible age go to kindie in California).
So from our figure of 3 million kids under five, we should only be expecting around 600,000 of them to be old enough for kindergarten. With just a tiny bit of effort, and correct reading of the text in question, I've slimmed Dorey's population figure by a factor of 35,400,000 people. That's over 35 million people that should not have been included in her "calculation".
With our new information we find that those 10,000 unvaccinated kids represent around 1.5% of kids of kindergarten age in California. That's 50 (fifty) times higher than the rate Dorey "calculated". We could probably extrapolate this to suggest around 1.5% of all kids under five are likely to be unvaccinated.
So, is that as bad as it gets? Of course not.
Firstly, the news article also noted that the "exemption" rate was as high as 50% of kindie kids in one school and 45% and 39% in two others. If your kids were in those classes then whole-of-population vaccination rates are meaningless - your kids are at serious risk. But I'll ignore that for now, just as Dorey did.
Just before I hit POST, I thought I'd take a look to see if kindergarten is compulsory in California. Since I've mentioned it, you can probably guess the answer - no it isn't compulsory.
Given that, we can make a (fairly safe) assumption that a percentage of those kids who don't attend are also unvaccinated. That means the real number of unvaccinated kindie-aged kids in California is likely to be much higher than the 10,280 mentioned in the news item.
Considering that up-to-date immunisation records are required for entry to California kindergartens, I think we can safely assume many parents of unvaccinated kids just wouldn't bother with it.
If we also consider that a good percentage of those parents who seek a "conscientious objection" to vaccination seem also to believe in conspiracy theories in which the world's governments are hell-bent on making our children sick for the sake of pharmaceutical profits, you might wonder if they'd risk sending their kids to kindie when it's not compulsory. I suspect that 1.5% figure for unvaccinated kids probably pales in comparison to the reality.
This got me looking still further and with one search I find that the California vaccination rate in children is probably closer, on average, to 76%. That would mean 24% of Californian kids are not vaccinated for one reason or another - that's 800 times greater than Dorey's suggested figure. Some of those kids will have legitimate medical reasons, some others will have parents who think health is delivered by magic and taken away by lizard people with microchips.
Once again, I'm not a statistician. It's also late. If I've made an alarming error, please point it out so I can fix it asap.
UPDATE:
It appears the actual numbers for kindie attendance in California are closer to 430,000. That increases my 1.5% figure to 2.3% (76 times Dorey's figure) and that still doesn't tell us anything about the rate of "personal belief exemption" outside of kindergarten. No matter how you look at it, Meryl Dorey's 0.03% figure was beyond incorrect. For someone who does claim to be able to crunch the numbers to the extent that she can supposedly re-interpret scientific papers and draw conclusions different to those drawn by the experts who wrote them, it is unforgivable that she puts such nonsense out in public then claims to be offering parents information they can use to make a decision on vaccinating their kids. Such "information" is dangerously misleading.





