Tertiary Source

Vaccine fears and risk tradeoffs

2008-12-26 11:28:25
This weekend's This American Life included interviews with some of the participants in this summer's measles outbreak. I learned about the outbreak from a somewhat overblown reaction from Phil Plait. From memories of Plait's older material, I expected a little lesson in conditional probability. Not finding one, I did an analysis of my own. I reached the surprising-to-me conclusion that, even with this summer's outbreak, the risk tradeoff between measles exposure and vaccine side effects is not totally unbalanced. My writeup at the time got lost in comment noise, so I'll condense it again here.

Data on infectious diseases, including measles, are compiled by the CDC. An update in August in the CDC's Morbidity and Mortality Weekly Report, coupled with activity from the CDC press room, seems to have prompted coverage from the Associated Press and other mainstream outlets, which trickled in turn to weblogs, which trickled in turn to me. One problem with blaming "antivaxxers" for the outbreak becomes apparent on reading the paper: only sixty-three cases, about half the 123 reported infections in US residents, occurred in people who were unvaccinated for "philosophical or religious reasons." At least a quarter of the infections occurred in people following the CDC's recommendations for vaccination. An effective vaccine reduces the risk of infection. Prevention can make risks negligibly small, but no process can completely eliminate risk.

Let's do some estimating. Measles seems to mostly infect people under twenty, and there are about eighty million people under twenty in the US. Of those, at 2007 incidence rates, about one in 150 will be diagnosed with autism-spectrum disorders, a rate of about 25,000 new diagnoses per year. The news in mid-2008 was that the annualized rate of measles infections had quadrupled, to 1% of the autism rate. (Not having heard of another outbreak since, I suspect the second half of 2008 had a lower-than-average measles incidence; this sort of error happens when you slice data too thinly. I have not found final numbers yet, though.)

I'm not terribly familiar with the autism-vaccine argument; my wife and I satisfied ourselves that we ought to vaccinate our children, and we did. But in my little corner of physics, people try hard not to say "there is no effect"; instead we say "we looked so many times and didn't see anything, so if there's an effect, we have such-and-such confidence that it's smaller than something." The reasonable-looking literature review linked by Plait highlights two studies in particular, one of which (Taylor et al., 1999) looked at 500 autistic children and one (Madsen et al., 2002) at 540,000 children total, all the children born in Denmark over eight years. The Madsen cohort contained 740 autistic-spectrum children. If those numbers follow counting statistics, where a measurement of N things has uncertainty ±√N, the observed division of 620±25 vaccinated autistic-spectrum children and 120±11 unvaccinated autistic-spectrum children does not differ from the division of 610 vs. 130 autistic-spectrum children expected knowing only that 80% of the children received vaccines and 0.14% received an autism diagnosis. A statistically significant effect would shift the split by fifty or sixty cases. So a concise summary of the Madsen et al. result might be:

If MMR vaccines do increase or decrease the chance of a subsequent autistic-spectrum disorder diagnosis, the risk changes by less than eight or ten percent.
At least 90% of autistic-spectrum diagnoses would have happened whether the MMR vaccine existed or not.
Either of these statements supports the hypothesis that vaccinations have no relation to autism, but not the somewhat stronger hypothesis that people who think differently live in an ignorant fairyland.

Let's give the antivaxxers the benefit of the doubt: suppose vaccines are linked to two or three percent of autism cases, a total of about 650 a year (in the US, at the 2007 rate). In that case, the roughly 8% of children who are unvaccinated would reduce the number of autism diagnoses by about fifty a year. During the period 2002-2007 there were forty or sixty measles infections each year. So a parent deciding whether to vaccinate his child on this information is choosing between roughly equal odds of rare events with very different costs:

  • A measles infection is dangerous, but also brief. Most infections last about a week; perhaps 80% have no side effects beyond the rash and fever. About 5% of infections lead to pneumonia, and somewhere under 1% lead to encephalitis or death.
  • A "triggered" autism diagnosis wouldn't present the same sort of straightforward danger. But autism is difficult. A very large fraction of autistic-spectrum children will require heroic care from their parents for their entire lives.
If those two choices were equally likely and not rare, choosing between them would be agonizing. Fortunately both are rare --- "triggered" autism is rare enough to generate serious debate about whether it ever occurs. In most cases, parents following whatever advice they stumble onto will deal with neither measles nor autism, and will feel justified in their decision.

So no [passive] participants in the vaccine-autism debate are acting unreasonably. Unfortunately, from a public-health perspective, the threshold where side effects make a vaccine "unacceptably risky" stiffens as the risk of exposure to the disease itself falls. The Madsen et al. study identified 120±11 unvaccinated autistic-spectrum children, and so could quantify the rate of autistic-spectrum diagnoses with a precision of about 10%. Improving this precision to 3% could rule out the scenario above, where the vaccination decision's positive and negative possible outcomes have roughly equal odds. But this precision would require identifying 1000±30 unvaccinated autistic-spectrum children. Using the numbers above, there are only about 2000 autism-spectrum diagnoses among unvaccinated children in the USA every year. Following this many children would be a huge undertaking. Would it ever happen?

There's a population dynamics question in here, which might or might not have a straightforward answer. If a population has some common and dangerous endemic disease, reasonable people might choose the protection of a moderately effective vaccine carrying its own risks (physical, social, financial, or otherwise). Technological advances typically reduce physical and financial costs over time; an effective publicity campaigns might adjust the social cost of a decision to vaccinate or not. How many iterations of safer/cheaper vaccines are required to eliminate an initially-common disease? Are there diseases that can't be eliminated from a population by vaccination alone, for the risk-tradeoff reasons I talk about here? And (most interesting from a public policy perspective) does the regulatory threshold where a treatment is considered "safe enough to use" change the answer?

Comment on Vaccine fears and risk tradeoffs
(I promise not to do anything unsavory with your contact information.)
You can also send regular email.

Recent questions


Older questions

Arguments about the safety of high-energy experiments sometimes cite the rate of high-energy few-particle collisions when cosmic rays hit the moon. What's the production rate for making transuranic elements from this process? What fraction of the universe's element 118 was made in earthbound accelerators?
2009-06-11 Thursday 15:34:41
Low-earth orbit has gotten full enough that collisions are a risk to consider when sending up a new satellite. How full are the Earth-Sun Lagrange points? How much could be put there?
2009-05-20 Wednesday 06:54:49
Venoms have evolved independently in several different vertebrate lineages: in snakes and lizards, and in the platypus, and in one other mammal. What are the transitional stages for venom to appear? How would the appearance go in, say, a population of people?
2009-04-01 Wednesday 17:41:46
Computers have fast storage with limited space (RAM) and slower storage with fewer overall limits. How could this set of constraints change and make computing fundamentally different? How would similes about how "your brain is like a computer" change? Is there a better model for the brain?
2009-02-23 Monday 15:23:33
Much of the work of digestion is done by bacteria in the gut. Could an appropriately engineered infection permit someone to extract nutrition from normally indigestible materials, like grass and wood?
2009-01-29 Thursday 19:37:59
There's a theorem in control theory that sets limits on how quickly the gain of a feedback system can change with frequency without driving oscillations. This is the logic behind using the integral and/or the derivative of the feedback signal in mechanized control systems. One factor in the current financial disaster is tension between short-term and long-term risk, a problem that also appears in smaller-scale "markets." Suppose this tension were reduced by, say, paying fund managers with investments less liquid than cash, in some quantifiable way. Are cash commissions guaranteed to have boom and bust oscillations? Do oscillation-free commission schemes exist?
2008-12-31 Wednesday 10:03:07
Yesterday's solstice was the day when the northern hemisphere gets less solar irradiance than any other. In most countries this is "midwinter," but in the United States it's "the first day of winter." When did this label change?
2008-12-22 Monday 06:58:50
Fresh Air interviewed Katharine Jefferts Schori, the primate of the US Episcopal Church, who has a doctorate in oceanography. Are advanced degrees in the sciences more common, or less common, in the clergy than in other nontechnical fields? How does the frequency change across different denominations?
2008-10-08 Wednesday 10:27:03
Political polls of a thousand people's opinions are reported with an uncertainty of 3%, which is roughly 1/√1000. Is this mostly Poisson counting? An election is just a larger statistical sample with a different set of biases. What is the margin of error on an election?
2008-09-20 Saturday 21:38:27
NPR has reported twice in the past couple weeks that NASA managers have expressed anxiety about the upcoming mission to service the Hubble telescope. Because the Hubble orbits further above the atmosphere than the ISS, where most shuttle missions have gone recently, the chance of the shuttle colliding with some space junk is "double" that on recent missions. Doubled from what? to what?
2008-09-20 Saturday 08:28:36