Autism-Vaccine Link? Thousands of Coincidences might Still Mean No.

Autism Caused by Vaccines?
Autism-vaccine controversy has lately captured (more of) my attention. You can’t search for “autism” or “vaccine” even separately on Google without stumbling across a dozen blogs dedicated to this subject¹. This is obviously an area of  high passions. People’s children are being diagnosed with very scary, fundamentally unsettling disorders at increasingly high rates (although the rate of increase of the rate seems to be slowing down, a fact cited as support by both sides of the debate), and nobody has any solid answers about what causes this, or how to fix it.

Though of considerably lesser consequence, epidemiologists’ competence is also being called into question. I’m sure this has at least something to do with the drama.

It seems  that the “vaccines cause autism” side of things is being driven largely by reports of people whose children have received vaccines and then been diagnosed with autism, countered by a boatload of empirical studies suggesting the there is no link. Personally, I think the studies so far still leave room for a possible association (perhaps only for a few individuals?), but this would not be the broad-strokes disease model suggested by the so-called “mercury militia.” If vaccines imparted a general, across-the-board risk for autism — even a fairly small or inconsistent one — it would almost certainly have shown up in spades by now. It hasn’t.

The Null Hypothesis
Whether vaccines cause autism or not, the discussion illustrates a sinister mental error we humans make. Well, more than one, actually². The null hypothesis can help illustrate the concepts here³. The null hypothesis is a fairly simple and logical concept, yet we so rarely apply it. It is simply the question,

“What would I expect to see if my suspicions weren’t correct?”

See how insidious that is? Nobody likes to sit around and seriously consider the possibility that they may be wrong⁴. So, let’s look at this possibility, as much as a lazy sometime-blogger can, within a limited amount of time and not being paid to do this.

In case this is not clear by now, I think people may be tempted to assume (especially if they never stop to think about it carefully) that a lack of association between vaccines and autism would mean that nobody ever had the experience of autism being diagnosed fairly soon after a vaccine. However, I will show that this is not the case at all. In fact, if there’s no association, we should still expect to see quite a number of cases like that.

What Should We See if Vaccines Don’t Cause Autism?
I’d like to see how many children should, statistically, be diagnosed with autism relatively soon after a vaccination, if in fact there is no association whatsoever between vaccinations and autism. Importantly, if the two things are totally independent of each other (i.e., if vaccines don’t cause autism), there will still be some overlap, right? By pure coincidence, some children will be diagnosed with autism right after a vaccination. How many children would we expect to fall into that category?

An hour or so on various government and consumer health/disease stats sites has shown me a few facts that should help, at least for demonstration purposes:

1. The CDC currently estimates between 2 and 7 per 1,000 children may develop autism (holy cow!). For our purposes, let’s take a middle estimate of 5 children per 1,000⁵.
2. Some data suggest roughly⁶ 60% of autistic children are diagnosed between ages 4 and 6. Other sources also suggest that this is when an awful lot of children with autism receive their first diagnosis, so let’s work with this age range as our target.
3. In California⁷, about 39% of children have had 2 or more vaccinations by age 6.
4. Some interpolation⁸ of age-range figures from the 2006 U.S. Census, suggests there were just over 12 million children in the country that year⁹.

For this thought experiment¹⁰, we will ask, “If none of those autism cases were caused — or even influenced — by vaccinations, then how many cases of autism per year should we expect to see popping up right after a child is innoculated?”

The Setup
We need to define after (as in, “my child got autism after he got his MMR shot”). How large is the post-vaccination window during which parents of newly-diagnosed autistic children will conclude that the vaccines were the cause? That, to me, is a very interesting question, but let’s just say a year. I dunno. It’s a nice, round number.

If 39% of the 12-million-odd young Americans got vaccinated by the time they were 6 (just like in California), that’s about 4.7 million.

Some children might have gotten their vaccinations before age 4, so let’s arbitrarily assume that only 75% of children got a vaccination from age 4 to age 6. That leaves us with about 3.5 million children in our target group.

Let’s say those 3.5 million kids’ vaccinations are evenly spread out over the 4 to 6 age range. That’s about 1,175,000 children getting vaccinated per year.

The Fun Part
Our estimated lifetime prevalence rate for autism is 1/2%, or .005…
60% of those cases appear from age 4 to age 6…
That means .003 or about 1/3% of the U.S. child population will be diagnosed with autism during our target age range.

About 1/3% of those children, even if there is no relationship whatsoever between vaccinations and autism, should coincidentally be diagnosed with autism within a year after receiving their vaccinations:

1,175,000 x .003 = 3525.

That means we should expect to see about three thousand five hundred children develop autism symptoms and receive a diagnosis, per year, within 12 months of receiving a vaccination. Even if there is no link at all between vaccines and autism spectrum disorders.

Conclusion
This does not prove there is no causal connection between vaccinations and autism. It does, however, demonstrate that it’s entirely plausible that there might be no association. I am guessing that this demonstration is not far off from what actually happens in the U.S., though I suppose I should look for some data. How many parents have the experience of vaccination –> autism every year?

To the extent that the numbers I’ve used in this demo are correct¹¹, there could be tens or even hundreds of thousands (3500 per year, for how many years?)) of people who are convinced they’ve actually seen vaccines cause autism, but that would not demonstrate any association, much less a causal association¹².

I’m a little nervous about the idea of giving my children multiple mercury injections, but if I’m asked about my position on this, my answer will be what I think a good scientist’s answer would be: look at the research.

1. The blogs tend to be written by nonscientists interested in asserting that vaccines cause autism, whereas the scientists don’t usually have blogs arguing back [↩]
2. Repeat after me: correlation cannot prove causation [↩]
3. Despite its sullied reputation in peer-reviewed research [↩]
4. Did I mention the scientific method? It can help with this kind of stuff [↩]
5. This may actually be a bit low, it turns out [↩]
6. I had to infer from program enrollments; I couldn’t find any incidence rates broken down by age… the aforementioned laziness took over, at this point [↩]
7. I was too lazy to find national estimates; besides, California seems to have the best data anyway [↩]
8. Linear… I don’t know enough about census data to try anything else [↩]
9. Note on my rough estimates: I am just trying to demonstrate a concept, not calculate specific incidence rates… [↩]
10. If you see errors, omissions, or have suggestions, I’m quite open to them; this is seat-of-my-pants stuff, and it would be interesting to make it more valid [↩]
11. I know they’re not totally correct, but I based them on real values, so I suspect they’re not too unrealistic [↩]
12. Note: it would also not prove a lack of association [↩]