My recent post, What do the anti-vaxers want, generated a lot of commentary from the anti-vax crowd, much more that I had expected to be honest. I do not intend to go over that commentary here. What I intend to do is to analyse a study that was linked to by one of the anti-vax enthusiasts. This study has been making the rounds lately in the anti-vax crowd (hello Mike “The Health Danger” Adams) because it purports to show a relationship between vaccine doses received and Infant Mortality Rates (IMR). The study in question has been published here, and David Gorski has done a thorough review of it over at Science-Based Medicine blog. I will not repeat what he wrote.
What I intend to do here is to show how easily numbers can be manipulated to show a trend which can then be touted as proof of a relationship. We always say that correlation does not equal causation, yet that is hard for some people to grasp without an example. This study provided the perfect example to illustrate the concept. So without further ado, let us show why this study does not really show anything in connection with vaccines.
What does the study say?
You can read the full thing yourself, but in a nutshell the authors looked at IMR in the U.S. and noticed that for the year 2009 it ranked 34th. They then took the IMRs for the other 33 countries that did better than the U.S. Then they counted the vaccine doses recommended for each country (they used a funny way of counting DTaP as 3 doses each time, but we’ll let that slide for the sake of our exercise). Then they plotted, in a graph, the number of vaccine doses vs. the IMR rate for each country. The results were SHOCKING:
Clearly the line is inching upwards as more and more doses are added to the vaccine schedule. The equation of the best fit line is : Y =0.148x + 1.566
To explain that quickly it is saying that at x=0 (unvaccinated person) we’d expect 1.566 deaths per 1,000 live births within the first year of live. For every additional x (every additional dose added to the vaccine schedule) we can expect an additional 0.148 deaths/1,000 live births. Or, that would be the case if there was actual causation.
Clearly, the anti-vaxers have been saying for the past few days, an expanded vaccine schedule leads to more infant deaths. They maintain this graph shows causation. Too many, too soon might have been right after all. Or has it?
We will follow the authors’ footsteps and do what they did, in a quicker, dirtier way of course (this is a blog after all), but we will replace automobile deaths for Infant Mortality Rates. Starting with the original list of countries, I searched for auto death rates, by country for 2009 and I stumbled accross this site. I have not verified that the numbers they provide represent faithfully the WHO numbers. Again this is a blog, and this exercise is for illustration purposes only.
I took the rates (listed as #of auto deaths/100,000 population) for the same 34 countries the authors used in their study for the same year (2009). Data was not available for five countries out of the 34, so they were excluded. Two had higher death rates than the US, so in line with what the study authors did, I excluded those, and looked only at the other countries that had better/lower death rates than the US, a total of 26 countries. I then plotted vaccine doses vs. auto deaths. The results may shock you.
This line is inching upwards too; not only that but it is doing so at a faster rate (slope=0.227 vs. 0.148 for IMRs). In other words if the study’s graph implied that adding 7 doses of vaccines leads to one extra death, this graph implies that it take only about 4.5 doses of vaccines to lead to an extra auto death, presumably a good number of years after the fact, since the assumption is that in most countries infants don’t drive. Apparently vaccines lead to more auto deaths, than infant deaths. That is if there was causation of course.
No one in their right track of mind, would say that the correlation thus showed between vaccine doses and auto deaths implies causation. This is a perfect example that correlation does not imply causation.
So why would someone deduce, from a weaker correlation (slope=0.227 vs. 0.148 for IMRs), that vaccines affect Infant Mortality Rates? Would it not make more sense that if we cannot trust the stronger correlation, the weaker one is even less worthy of our trust?