Bad Math from Anti-Vax Comments

In following the Disneyland Measles story, I am finding interesting comments from anti-vaxxers about the articles. One that keeps resurfacing is something similar to this:

"If vaccines are so effective, why is it that 5 people that got infected were vaccinated? Out of 20 people, that makes 25%."

I am not good at math. But even so, this looks like a huge fallacy to me.

I find this comment interesting because even as bad at math as I am, I understand a few principles that show how flawed their reasoning is. The most important of these is that the vaccinated population is MUCH higher than the non-vaccinated population in the United States, therefore, even if the amount of people that got infected was exactly the same, or a bit higher, it is still way less likely to contract the disease if you are vaccinated vs. being unvaccinated.

Keeping in mind that to get an accurate estimate, I would need figures of the percentages of vaccinated vs. unvaccinated people at the park during that time frame, and that those figures are unavailable, here's the best with what I can do.

(If I wanted to approximate those figures, I could possibly come up with a reasonable ratio by figuring how many people from which states and countries attended and what the vaccine rate is from each of those areas. Alas, I'm not dedicated enough to actually go looking for this information, and I'm not sure the percentage of Disneyland patrons is available by where they're visiting from anyway.)

The only real figures I have is that according to this article at least 15 out of 20 people infected were not vaccinated.

So, lacking anything close to what might resemble actual figures, let's assume that the vaccination rate at the park during exposure could have been anywhere between 80-99%. I'm giving it a wider range than is probably accurate to demonstrate that the fallacy still stands even with figures more in favor of anti-vax proponents.

Assuming that 10,000 people had been exposed (for ease of computation), that 20 contracted it, and that 15 were unvaccinated, here are some figures:

If 80% of the exposed population were vaccinated, the chances of contracting the disease for the vaccinated was 1 in 1,600 while for the non-vaccinated it was 1 in 133. That leaves the unvaccinated at 12x more likely to contract the disease.

If 85% of the exposed population were vaccinated, the chances of contracting the disease for the vaccinated was 1 in 1,700 while for the non-vaccinated it was 1 in 100. That leaves the unvaccinated at 17x more likely to contract the disease.

If 90% of the exposed population were vaccinated, the chances of contracting the disease for the vaccinated was 1 in 1,800 while for the non-vaccinated it was 1 in 66.667. That leaves the unvaccinated at 27x more likely to contract the disease.

If 95% of the exposed population were vaccinated, the chances of contracting the disease for the vaccinated was 1 in 1,900 while for the non-vaccinated it was 1 in 33. That leaves the unvaccinated at 57x more likely to contract the disease.

If 99% of the exposed population were vaccinated, the chances of contracting the disease for the vaccinated was 1 in 1,980 while for the non-vaccinated it was 1 in 6.667. That leaves the unvaccinated at 297x more likely to contract the disease.

In fact, in order for the argument to stand that vaccines are not effective because 5 people who contracted the disease were vaccinated, the vaccination rate in the population would have had to have been 25% to make it equal to the chances of the unvaccinated contracting the disease.

The fact that the vaccination rate was much higher shows that the vaccine has a huge protective effect. In fact, even the examples of 80-85% are a very low estimate, and I believe it is highly unlikely that the population at Disneyland during that time was anywhere near that percentage. Even at those rates, however, I would take a 12x protective effect for any risk out there, let alone a 57x protective effect, which is more in range of the probable vaccination rate.

The sad part about this to me is that those individuals who were vaccinated (or too young to get vaccinated, I believe there were 2) and contracted it anyway had a higher chance of doing so since 13 extra (and unnecessary) carriers were running around with the disease.

I highly believe in agency and the right to make choices for your own body. I am thankful that I was not forced into vaccinating my kids when I was not yet ready. (That may have caused those forced into it to move into extreme political views that would have perhaps been more detrimental to society on a large scale than 20 people contracting the Measles.) That being said, I am also thankful that my hesitancy did not cause pain and illness for another person.

I do believe that people should have the right to chose. However, I believe that the right to choice should only come with the willingness to take responsibility for that choice as well. What form that would take, I do not know. For me personally, if I were to continue to chose not to vaccinate, I believe it would have been wrong for me to send my children to a public school, for example.

I do wish there were some way for those who decide not to vaccinate to obtain the necessary "natural immunity" so that they do not increase the risk for those who are willing to vaccinate. Perhaps if this trend continues and the number of anti-vaxxers continues to climb, a clinic where these families can go to get exposed to the disease in a controlled, isolated environment, and at a suitable age, would be a prudent measure. (As prudent as one could be in the situation, at least.) Of course the incurred medical costs should be the responsibility of the family. It seems that if they would not be willing to submit their children to the natural disease in this way, nor to get the vaccines, then they are simply desiring a free ride from society.

That's really not OK in my book.