Orac highlighted here a post over at Vox Populi which doubted the effectiveness of the mumps vaccine, in light of the recent epidemic in Iowa. I was prepared to write a whole post on the math of it, but Mark at Good Math, Bad Math saved me some work. Nevertheless, I have a few things to add after the jump.

As has been mentioned, the given efficacy rate for the mumps vaccine is 95%. This is actually likely a bit high; previous outbreaks have suggested it’s more like 85-90% effective, so that as many as 15% of the vaccinated population won’t actually be immune. The key to telling whether the vaccine is helpful, then, is to look at the attack rate–the percent of the population that develops disease–in the vaccinated versus unvaccinated population. So, some more math to follow.

For the sake of simplicity, say you have a population of 100,000 people. Vaccination coverage in the population is 95%, meaning that 5,000 will be unvaccinated and lacking in immunity. Additionally, let’s say the vaccine is only 90% effective. So, of your vaccinated population of 95,000 people, you’ll have 9,500 people who remain susceptible–”vaccinated but not effectively so,” let’s call them.

Now let’s assume, again for the sake of simplicity, that susceptible people are equally likely to become infected with mumps, whether they’re in the “vaccinated but not effectively so” or “unvaccinated” group. (Real life is actually messier, leading to a skew in one group or the other, but we’ll ignore that for now). Therefore, if you have an outbreak of 500 cases–roughly the size of Iowa’s right now–in an ideal world they’d be divided randomly between the two groups. The “vaccinated but not effectively so” group is roughly twice as large as the “never vaccinated” group, so figure they get 333 of the 500 cases, and the remaining 167 cases are in the unvaccinated population.

Still following? Now it’s time to calculate the attack rate. In the vaccinated population, we ended up with 333 cases of disease in a total population of 95,000. So, the attack rate = 333/95,000 = .35%

In the unvaccinated population, we ended up with 167 cases of disease in a total population of 5000. So, the attack rate = 167/5,000 = 3.34%: TEN TIMES the rate of the vaccinated population.

This is the key to the whole thing. Yes, there’s disease in the vaccinated population. Of the cases in this little hypothetical, by the numbers alone, 66% were vaccinated–lower, but similar to our numbers here in Iowa. Yet as you can see, this doesn’t mean that “the vaccine isn’t working:” in our scenario, it means it’s working at a 90% effectiveness rate, which is pretty good. The unvaccinated population acquired disease at 10 times the rate of the vaccinated population overall, so while being vaccinated was no guarantee of protection, it’s a damn good gamble.

Now, as I mentioned, real life is messier. It’s unlikely that the spread of disease is completely random. For example, most of the cases thus far have occurred on college campuses, which are very highly vaccinated populations. As such, it’s more likely that there will be more of the disease in the “vaccinated but not effectively so” population than the “unvaccinated” population, simply because there is less assortment with the unvaccinated folks. And this is what we’ve seen–instead of the 66% of cases that were vaccinated, up to 80% of the mumps cases here in Iowa have received at least one dose of vaccine. I’ve not crunched the actual numbers, but this would mean that in our real-life outbreak, the difference in attack rate in vaccinated vs. unvaccinated would be less than a factor of 10–perhaps 7, or 5–but still significantly better than not having the vaccine at all.

Soooo, next time you read stuff like this:

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?

…ask them if they know what the difference in the attack rate is between the two populations. If they don’t know, educate them. (But if it’s Vox, don’t bother to point them here…apparently, being XX disqualifies me from having a say in it).

Comments

  1. #1 Mark Paris
    April 13, 2006

    Vox, which I do not read, demonstrates the danger of talking on the record about things about which you know little or nothing.

  2. #2 Kristjan Wager
    April 13, 2006

    Mark, to be fair, if he only talked about stuff he knows something about, his blog would be awfully empty.

  3. #3 Mark Paris
    April 13, 2006

    Ahh, Kristjan, you slipped that one right up next to me before I realized it.

  4. #4 wheatdogg
    April 13, 2006

    Being XX and an epidemiologist makes you unqualified? THis guy is really OTL. (I confirmed this hypothesis by reading some of his blog posts.)

    Many lay people (I think) do not understand that vaccination reduces the chances of contracting a disease. It does not eliminate the possibility. Flu vaccines are an obvious example. So it’s entirely possible that a few children who got the MMR vaccinations might in fact get the mumps. If the MMR were not required, the number of infections would be much higher.

    The antivaccination crowd do not appreciate what life was like before mandatory vaccinations. I’m an amateur genealogist. Walking through cemeteries and finding scores of markers for very young children should give anyone a gut sense that vaccinations prevent a lot of heartbreak. Child mortality was much higher before vaccinations than it is now. It was not uncommon for mothers to give birth to as many as 10 or 12 children, only to have half of them die before age 6.

    On a similar note, I learned today from a student’s senior exit project that one of our children’s homes here was founded after a cholera epidemic left many children with no family. There’s a telling anecdote.

  5. #5 Julie Stahlhut
    April 14, 2006

    Count me in as someone who has both logical and anecdotal reasons for being a big fan of vaccines. The logical justification: I can do the math (as Tara has done and explained so clearly above). The anecdotal justification: My grandmother gave birth to 10 children between 1908 and 1925, before vaccines against “childhood diseases” were available. Whooping cough killed one child and permanently disabled another, in separate outbreaks more than 10 years apart. Diphtheria killed another child and sickened yet another for weeks. This all happened not among desperately impoverished or neglectful people, but in a loving, attentive, working-class family in a small town in New England.

    I recently got vaccinated against typhoid, yellow fever, and hepatitis A in preparation for upcoming fieldwork in Central America. All of these vaccines are recommended but not required for the sites that I’ll be visiting (many of which should have near-U.S. quality sanitation anyway). I chose to receive the vaccines, although my chances of exposure to those diseases will be, for the most part, low. And, you can bet that I’ll still be careful about avoiding insect bites and dubious food and water sources, since the vaccines are less than 100% effective (and carry no protection at all against different water- and arthropod-borne diseases).

    Two of the hardest things for the general public to understand, IMO, is that (a.) all medical treatment has risks, and (b.) no medical treatment is perfect. Given that uncertainty, we still have to balance risks and benefits when making health care decisions for ourselves or our dependents.

    (Hmmmm, to tie all of this in to a thread on PZ’s blog a couple of months back: I wonder if the ability to integrate all of this information is correlated with one’s grades in Algebra I?)

  6. #6 JL
    April 14, 2006

    Is there any correlation to mumps cases in the population that is not born in the US and those that are?

  7. #7 Tara
    April 14, 2006

    JL, you mean, here in Iowa?

  8. #8 K
    April 22, 2006

    Hi coming out of lurkerville.

    Can you please crunch the numbers for the Iowa outbreak?
    The said efficiency rate is not 95% so what is it, 85-90%?

    PLease specify the unvaccinated vs vaccinated attack rate in this outbreak.
    Also where is the cross protection with Iowa’s high MMR vaccine coverage?
    Thanks

  9. #9 Courtney Gidts
    May 16, 2006

    I’ve managed to save up roughly $71765 in my bank account, but I’m not sure if I should buy a house or not. Do you think the market is stable or do you think that home prices will decrease by a lot?

  10. #10 lissa
    February 27, 2007

    “Additionally, let’s say the vaccine is only 90% effective”

    how would your scenario work out if we said it was 0%?

  11. #11 lissa
    February 27, 2007

    The pertussis vaccine is estimated to be 63% to 94% effective in the DPT shot and 59% to 90% effective

    WOW. that’s pretty close to 0 in my book. (or maybe more along the lines of I don’t know but I gotta say something to sell all these vaccines I bought)

    I don’t know about mumps but I won’t be surprised when polio resurfaces.

  12. #12 lissa
    February 27, 2007

    Correct me if I’m wrong but you seem to be relying upon the presumption that the vaccine is at least 90% effective from the gate.

    And you follow that with the presumption that only 9500 vaccinated people will be susceptible to infection.

    What kind of nonsense is that? Today it might be 95 tomorrow 80 the next day 60 or maybe it was never effective at all and the disease just took a break (like polio did years ago BEFORE a vaccine was thought necessary because it came back)

  13. #13 lissa
    February 28, 2007

    forgive the numerous posts but:

    I don’t see how 80% of people infected with mumps being vaccinated shows the effectiveness of a vaccine, regardless of whether they might fall into a so-called vaccinated but not effectively so group or not. 100% of other people vaccinated might fall into that group for all I know and they were lucky enough not to ever be exposed to the virus(of course the authorities say that’s an unpredictable thing within ANY group of people, conveniently so I guess).

    I really liked that show I watched the other day blaming epidemics on the people who don’t get vaccinated. That’s about as stupid as it gets and the hokiest propagandatizing I ever heard of when most of the folks are vaccinated(of course they forgot to mention that part). As if the virus can’t find a way to infect people no matter how many people get vaccinated.

  14. #14 Sullivanthepoop
    March 21, 2014

    Since when is 63% or 93% zero in anyone’s book. If I a choice between two treatments for a fatal illness and one gave me a 63% chance to live and one gave me a 0% chance to live is that even a choice?

    Polio did not take a break. Where do you pull these ideas from? There were no known large scale epidemics of polio until the late 1800s. Then it came in ebbs and waves for a variety of reasons. One, it requires warm weather for effective transmission so cold years could disrupt it. Two, catching it causes effective long-term immunity. Three, it is a gastrointestinal infection which produces copious amounts of IgA antibodies. IgA antibodies are readily passed through breast milk. Doing the same ebbs and waves it had done for the previous almost hundred years is not taking a break.

    The mumps vaccine is 90% effective in 95% of the population after 2 MMRs. Luckily in me it is better than that after 1 MMR. I just had my titers checked last year.

    It is the people who don’t vaccinate who are responsible. Though, in the case of pertussis at least they showed us we need a new vaccine. 90% is plenty enough to protect everyone if everyone who got vaccinated could or if no one who is unvaccinated left the country. Even if the vaccines are not as effective as hoped, we wouldn’t have known if there were not patient zeros who travel unvaccinated and if there were not large concentration of unvacinated people to drive outbreaks.

  15. #15 Sullivanthepoop
    March 21, 2014

    Oh, and if the effectiveness was zero than the same percentage of vaccinated people would get it as under vaccinated and unvaccinated. That has yet to happen in any outbreak.