Thursday, 27 March 2014
Correlation and causation
A fundamental logical principle is that correlation does not equate causation or, as Julius Caesar would have said on the ides of March if the subject of the day had been sophistry and not tyrannicide, "Cum hoc ergo propter hoc". (Instead, he either said "et tu Brute", "tu quoque me fili" or "well, damn!" depending on your sources).
In French, this is called the stork effect because of the observed correlation of the number of stork nests and the birth of babies. The correlation is not causal (if you do know where babies come from, of course. If not, please do not let me rob you of your innocence and read no further). Let's give an example of non-causal correlation that gives the impression that it is meaningful: the case of the horoscope that is right. For today, people born under the sign Leo can expect to have "uncommon energy to undertake new projects". Let's set aside trifles such as how this is a pretty vague prediction and how it might apply to just about anyone, and let's take it at face value. First, we should establish how many people are concerned by the prediction; we must determine our sample size. Very roughly speaking, let's divide the current world population (something around 7 222 378 000 souls) by 12 and say there are 602 000 000 Leos around. Out of all these people, there will certainly be a few who will get out of bed this morning and feel like a million bucks, ready to take on the entire world. Reading their morning paper, they would certainly be entitled to think that the astrologer who wrote their horoscope is a genius, since there is a perfect correlation between the prediction and what they observe. Astrology works, baby!
But see, the point we're making is that it's not enough to see a correlation; even before we try to determine if it is causal, we must demonstrate that it is meaningful and not an illusion. In this case, out of our 600 million Leos, there will be far many more who will feel either quite normal or even a little tired than bursting with energy. (How do I know? Because that's the case with everybody). Should a very patient statistician go around and ask every Leo how they felt this morning, it would probably be revealed that there is a far more convincing negative correlation between the horoscope's prediction and the way a typical Leo feels. In other words, one anecdote, ten testimonies, a thousand stories buttressing a case don't mean anything if they do not show that the association we're trying to demonstrate occurs more often than what would be predicted by chance alone.
A sad and much-publicized story based on a lousy correlation vs causation problem gave rise to the autism and MMR vaccine scare, a societal aberration that started with a medical paper now retracted and that branched into all sorts of nonsense regarding the safety or even efficacy of vaccines in general.
The story starts in the 1990s, with a group of parents of autistic kids who started a class action against the pharmaceutical companies Aventis Pasteur, SmithKlineBeecham and Merck, the makers of three MMR vaccines. The basis for the lawsuit, I'd hazard to guess, is that autism is usually diagnosed in the first few years of a baby's life (when they're around two and saying "no" all the time), an age that also sees kids receiving a lot of shots. The correlation will be there, of course. The lawyer handling the case, wanting some hard data to shore up the case, contacted a researcher who had already published a few papers trying to link certain vaccine strains with bowel disease. A british government outfit called (at the time) the Legal Aid Board started funding the research, which it stopped in 2003 because it judged the evidence was inconclusive.
In 1998, the researcher published a now-infamous paper reporting a link between MMR vaccines, autism and bowel disease in the very serious journal The Lancet. Naturally, as the paper ran against the grain of pretty much all the scientific literature, it was doubted, decried, criticized and heavily scrutinized. Said scrutiny revealed serious flaws in the work, and ten of its co-authors published a partial retraction in 2004, stating plainly that they saw no link between autism and the MMR vaccine. The paper was finally fully retracted by The Lancet in 2010. Adding to the brouhaha was the revelation that the main author of the paper, several co-workers and even one reviewer had received substantial sums from the plaintiffs' legal team and/or their backers. At the very least, this is a conflict of interests. No wonder that desired effects may have been reported.
Unfortunately, even if the retraction of the paper should have brought down the whole anti-vaccine edifice, the harm was already done. Many people, fearing for their children's health, had started refusing to give them their shots; accordingly, as vaccination rates dropped (from 92% in 1996 to a low point of 79% in 2003 in the UK), mumps cases started increasing (4 204 cases in 2003; 16 436 cases in 2004, and 56 390 in 2005). Thank heaven, polio and smallpox are no longer at our door; but even so, many children caught perfectly preventable diseases and some of them died the most futile death imaginable: death by negligence.
It's disheartening to see how a large minority can keep an urban legend alive, despite all the evidence of the remarkable efficiency and safety of most vaccines. Smallpox is gone, for crying out loud, thanks to a global vaccination campaign! "Lord, what fools these mortals be" would exclaim Puck were he around today.
The numbers in Bob's graphic are pretty much accurate, as far as my sources are concerned. The numbers regarding chicken consumption come from here and those concerning GM's market share were calculated from the data given in this article. Other curves showing similar trends (but unrelated to autism, as far as I can tell!) include the number of left-handed people in Australia, average hamburger size since the 1950s, the number of houses having access to a phone and (with a shocking negative correlation value), the number of times a Canadian team won the Stanley cup since the 70s.