Good Math/Bad Math

Thursday, April 13, 2006

Vaccines and Geniuses

As Orac points out today, Vox Day, one of the most obnoxious assholes that I've encountered on the net, is an anti-vaccine guy, who's been using the recent outbreak of mumps in Iowa (discussed by Tara here) to argue that vaccines must not work.

It's quite sad in its way: Vox is a self-proclaimed genius and member of Mensa. And yet, this is typical of his idea of argument. The "math" is so poor that it's laughable, and the rest of the reasoning is no better.

So, here's Vox:

From the Star & Sickle:

A mumps vaccine was introduced in 1967. Iowa law requires schoolchildren to be vaccinated against measles and rubella, and the mumps vaccine is included in the same shot. The state's last major outbreak was in 1987, when 476 people were infected.

Of the 245 patients this year, at least 66 percent had had the recommended two-shot vaccination, while 14 percent had received one dose, the Public Health Department said.

"The vaccine is working," Quinlisk said. "The vaccine certainly was made to cover this particular strain, because it's a fairly common strain of mumps." Quinlisk said the vaccine overall is considered about 95 percent effective.

So, the question is this: if the vaccine, not improved hygiene or some other factor, is primarily responsible for preventing transmission of the disease it is supposed to prevent, how is it possible that 80 percent of the infected in this latest outbreak are at least partially vaccinated against it?

And isn't it at least somewhat doubt-inspiring that the health authorities continue to insist that the vaccine is working in the face of direct evidence that, at least in some cases, it is not?

So, Vox wants to argue that vaccines don't really work, because there's a mumps outbreak in Iowa. And 80% of the cases are people who received at least one dose of the MMR vaccine.

Let's look at some numbers, to get an idea of what the infection rates mean. We'll be charitable, and stack all of the numbers in Vox's favor - so whatever we come up with is going to make the infection rates seem much higher than they are.

So - let's start by coming up with an estimate of the number of people in the pool of potentially infectable. Playing the numbers in Vox's favor, we'll assume that all of the mumps cases came from people born in the same year. The birth rate in Iowa is is pretty consistent, acording to the official statistics: around 38,000/year. Of those, the number vaccinated is around 81%, again according to the official statistics. So, the pool of vaccinated people born in that year is around 30,700.

Now, the cited effectiveness rate of the MMR against mumps is 95%. What that number means is that 95% of the people who receive the vaccine will develop an effective immunity to mumps. So - the expected number of vaccinated people who would not be immune would be around 1500 people (rounding down).

There are 245 infections this year, according to the article Vox cited. That would mean that 15% of the non-immune population of vaccinated people had become infected. That's a damned high number, but not completely beyond reason for something as contagious as mumps.

But then, remember that all of the numbers are stacked heavily in favor of making the vaccines look bad: in particular, these numbers are based on reducing the pool of potential infectables by several orders of magnitude (because we assume all cases were born in the same year, and all of them were born in Iowa) - we find that the number of infections with mumps is entirely possible. It makes for a pretty serious outbreak for sure - but not something that calls into question the effectiveness of vaccines.

Now, to put the nail in the coffin: back to some official statistics. How many cases of mumps were there before vaccines became mandatory in Iowa? Official statistics are here: during the decade before mumps vaccines became mandatory in Iowa, the number of infections per year ranged from 2000 to 12000 per year. Now, during a dramatic outbreak, described as an epidemic, we've got a couple of hundred cases. Does that look to you like the vaccines are not working?

Nah. Me neither.


  • There's one odd thing, though. 80% of the (young enough) population have been given vaccines, and 80% of the listed cases have been given vaccines? Wouldn't you expect the 20% who didn't receive vaccines to be overrepresented among the mumps patients?

    Of course, it's likely that I've misread something.

    By Anonymous Anonymous, at 10:36 AM  

  • Not necessarily - since the disease spreads through contact, if people who were vaccinated (more affluent, educated people?) are more likely to interact with each other than with people not vaccinated (less affluent, educated -> not in college?), then given that the first case happens in someone vaccinated (but among the 5% failure group), it's probably not surprising that many of the other cases are also among the vaccinated.

    -- Steve

    By Anonymous Anonymous, at 11:12 AM  

  • anon:

    That 80% number is just an interesting coincidence.

    The thing to remember is that we're dealing with a very, very large number of people; the infection rate is extremely low. Remember, stacking the numbers to make vaccines look bad, we're looking at 250 cases of mumps over a space of four months in a population of 30,000 people.

    With a situation like that, the dominant factor in who gets infected isn't going to be who's vaccinated. It's who's in contact with the bug - more specifically, who's in contact with people who are either infected or carrying; and that means that social trends come into play.

    Remember that one of the major goals of vaccination programs is not just to reduce the chance of the specific recipient catching the disease - it's to create "herd immunity"; that is, to eliminate the carrier population. If the vaccine effictiveness is reasonably high, and it's universally given, then the population as a whole doesn't have enough people to be able to effectively carry and spread the disease.

    For mumps, in general, we've got really great herd immunity - the vast majority of people get the immunization, and so it doesn't spread easily. It only spreads by direct contact between succeptable people.

    The initial case in the Iowa epidemic appears to be a British exchange student; so the pool of people that are exposed are centered on the community that that student was in contact with; and that community very likely has a much higher vaccination rate than 80%.

    By Blogger MarkCC, at 11:37 AM  

  • NIS information (
    seems to indicate that the vaccine coverage rate in Iowa has been closer to 91-3% over the last ten years, in which case the unvaccinated are overrepresented among the infection cases. (Even ignoring the demographic factors other folks mentioned above.)

    Where'd you get the 81% number, Mark?

    By Anonymous Anton Mates, at 12:10 PM  

  • anton:

    I found the 81% figure in an Iowa state website; it was in one of the tables on the same site that I used to get the figures for births in Iowa. I suppose it should have occured to me to look at the CDC for that info :-)

    By Blogger MarkCC, at 12:23 PM  

  • It's quite sad in its way: Vox is a self-proclaimed genius and member of Mensa. And yet, this is typical of his idea of argument. The "math" is so poor that it's laughable, and the rest of the reasoning is no better.

    Given his choice of pseudonym, is it all that surprising?

    By Anonymous Anonymous, at 12:46 PM  

  • Vox is the MOST obnoxious asshole I have ever encountered on the net, but maybe I've just been sheltered. Ever seen the photo of him with a flaming sword? I apologize I can't seem to find it, but I think it was on his publisher's page about him, or something.

    But he is some piece of work, and not in a good way.

    By Blogger gravitybear, at 1:32 PM  

  • By Anonymous Sanguinity, at 5:27 PM  

  • Yes, but you don't have a Porche, recording career and can't get all the babes that you want, the way the Vox Day can.

    What a sad, sad little man Vox is.

    By Anonymous ArtK, at 6:25 PM  

  • Usually i tune out the moment someone says they are a member of MENSA.

    But that flaming sword picture is AWESOME. I mean come-fuckin-on.

    How can you question the arguments of someone with a +9 firesword against Goblins. I bet his THAC0 is like 2. And you could never land a blow yourself, I mean he doesn't even need armor his AC is so low.

    By Anonymous kyle, at 8:55 PM  

  • Uh, I believe it is "Porsche", not "Porche". That just shows how inferior you all are. And jealous, too. I mean, you are all obsessing over Vox talking about how smart he is, and how rich his father, uh, he is, and how many hot chicks he has f'd. I mean, so what if he talks about all that every other day; it shows everyone not to mess with him and that he is just über confident. Those numbers mean nothing. Vox is right because he has the confidence and Masculine Charisma to tell you he is right. Now I need to take that flaming sword picture to my bedroom along with some tissue...

    By Anonymous Derek, at 9:15 PM  

  • sanguinity:

    Thanks for the link to that picture. Totally made my day - I cannot believe that the moron actually had his *publisher* use that picture. I mean, it would be bad enough if he just used something like that on his trashy webpage; but to claim to be a professional writer, and use that instead of the typical authors headshot - that is just sad.

    By Blogger MarkCC, at 9:53 PM  

  • Flaming sword?


    Someone spinning a staff lit at both ends is a lot more impressive.

    Someone spinning chains with burning stuff at the ends while walking on stilts is a lot more impressive.

    I get to see more impressive fire things a couple of times a year. Flaming sword is really passé, unless you're in World of Warcraft or something like that.

    I also bristle at antivaxers -- my great-grandfather ended up as a public health doctor, I never knew one uncle due to his dying of polio, and I get very worried about the colletive immunity of the population.

    By Blogger Julia, at 10:52 PM  

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    By Blogger 10 325 rikon, at 4:07 PM  

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    By Anonymous ativan, at 12:17 PM  

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