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I'm looking for specific, real cases in which a causal relationship was inappropriately inferred from evidence of a correlation.

Specifically, I'm interested in examples that meet the following criteria:

  • Existence of the causal relationship was accepted as fact widely enough to have notable effects (on public policy, discourse, individual decisions, etc.).
  • The link was inferred solely on the basis of correlative evidence (perhaps along with the existence of a coherent but unproven causal mechanism).
  • Causality has been objectively falsified or at least called into serious doubt.

The two examples that came to mind for me aren't quite ideal:

  1. Sodium intake and blood pressure: As I understand it, it has since been determined that salt intake only increases blood pressure in sodium-sensitive individuals. The existence of a valid causal relationship (although not quite the one that was originally accepted) make this example less compelling.
  2. Vaccines and autism: I may have the background wrong, but I believe this link was surmised on the basis of both correlations and (fraudulent) experimental evidence. This example is weakened by the fact that (fake) direct evidence existed.

Note: I've seen this similar question:

Examples for teaching: Correlation does not mean causation

My question differs primarily in that it focuses on notable, real-world examples and not on examples in which a causal link is clearly absent (e.g., weight and musical skill).

Community
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Aaron Novstrup
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    In a big city at summer, murder rate positively correlates with rate of ice-cream consumption. – ttnphns Jul 24 '14 at 07:03
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    One of your criteria is "Causality has been objectively falsified or at least called into serious doubt." IMO that's too strong. An estimated correlation is a biased estimator of a causal effect, assuming some confounding. Generally people are interested in magnitudes of effects, not just their existence. – generic_user Jul 24 '14 at 08:31
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    Also, I bet that with a big enough sample size, a RCT that randomly allocated ice cream in hot cities would find a negative effect of ice cream consumption on likelihood of committing murder. – generic_user Jul 24 '14 at 08:33
  • @ACD Chiming in in agreement to make explicit that of course RCTs still have threats to causal inference. – Alexis Jul 24 '14 at 15:20
  • @ACD How would you suggest modifying that criterion while keeping with the character of the question (specifically, I intended it to make reasonable sense to a layperson)? My objective with that criterion was to clarify the meaning of "inappropriately inferred" -- are you suggesting that the criterion should admit examples where the true causal relationship was much weaker than implied by correlative evidence? – Aaron Novstrup Jul 24 '14 at 17:07
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    @ttnphns That's a good example of the type that I intended to *exclude* with my criteria, unless you're suggesting that a misguided belief that ice cream consumption causes murder has had notable effects on human behavior. ;-) – Aaron Novstrup Jul 24 '14 at 17:10
  • Why only `belief that ice cream consumption causes murder`? Think of the opposite, how cool is the ice-cream after a man killing party? ;-) – ttnphns Jul 24 '14 at 17:17
  • It's fine with me if this question is made CW, by the way, if that would be more appropriate for this community. A question like this would almost certainly be CW on StackOverflow, but I'm not familiar with the norms on CV. – Aaron Novstrup Jul 24 '14 at 17:18
  • In fact, temperature predisposes for both violence and ice-cream. When you wash out the effect of heat, correlation disappears. – ttnphns Jul 24 '14 at 17:23
  • Mathmetician Ionica Smeets has a great TEDx Talk with several examples that range from the obvious to the not-so-obvious. https://www.youtube.com/watch?v=8B271L3NtAw – ShaneMW May 17 '17 at 13:32
  • Respectfully, the sodium intake summary is incorrect because a) that's not a universally held view, b) it is a bit oversimplified, and c) evidence does not singularly point to this result. – AdamO Jan 26 '18 at 22:30

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For many years large observational epidemiological studies interpreted by researchers using Bradford Hill-style heuristic criteria for inferring causation asserted evidence that hormone replacement therapy (HRT) in females decreased risk of coronary heart disease, and it was only after two large scale randomized trials demonstrated the opposite, that clinical understanding and clinical recommendations regarding HRT changed. This a classic cautionary tale in contemporary epidemiology that you can read about in textbooks (e.g., Leon Gordis' Epidemiology), and on the Wikipedia article on David Hume's classic maxim.

That said, The Bradford Hill criteria have not been understood as the state of the art for a good while now, with counterfactual causal inference (a la Judea Pearl, Jamie Robbins, Sander Greenland, and others) being the really heavy lifter. It is possible to make reasonably strong causal inferences without conducting randomized experiments, using, for example, instrumental variables, Mendelian randomization, etc. (which is good for science, since we cannot conduct randomized experiments on much, if not most, of the universe).

Alexis
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    This is a great answer and exactly the kind I was hoping for. However, I want to point out for other potential answerers that a good example need not concern an inference that was made by researchers/statisticians (and, in particular, not only those using the best available methods). Rather, an equally good example might describe a case in which the media, the public, or some other group drew an invalid causal inference from correlative evidence (as long as this incorrect inference had notable effects). – Aaron Novstrup Jul 24 '14 at 20:37
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Not the most glamorous topic, but Nora T. Gedgaudas (Ch. 18) summarizes very nicely the turnaround in findings about fiber's role in preventing colon cancer. Fiber, widely thought for 25 years to be an important preventative factor (based on correlation), was shown through the 16-year, 88,000-subject Nurses' Study to be merely a correlate of other factors that mattered. These included the consumption of fruits and vegetables high in certain nutrients (which decrease risk) and of red meat and especially processed red meat (which increase risk). The author notes that the myth "seems to doggedly persist, nonetheless," even among doctors. As so often happens, once word of a pattern gets out, it's very difficult to eradicate the idea.

rolando2
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    Caveat: the Nurses Studies were observational designs also. While there *are* strategies to strengthen causal inference, the data from these studies are also based on correlation. – Alexis Jul 25 '14 at 23:33
  • Although your answer gave a good example in which experimental controls trumped statistical ones, that doesn't necessarily call into question purely statistical controls as used in other cases. I think here the statistical controls fit the bill very well. – rolando2 Jul 26 '14 at 00:12
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    Statistics cannot "control" for causal bias: that's a function of study design. Any potential confounder one adds to a model may *itself* be confounding the causal relationship you are trying to estimate. Causal inference through study design comes in through causal identifiability (which is guaranteed by random assignment); no method of estimation or inference can provide that. – Alexis Jul 26 '14 at 01:04
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Pellagra

According to this book chapter, pellagra, a disease characterized by dizziness, lethargy, running sores, vomiting, and severe diarrhea that had reached epidemic proportions in the US South by the early 1900s, was widely attributed to an unknown pathogen on the basis of a correlation with unsanitary living conditions. Dr. Joseph Goldberger was instrumental in showing experimentally that the disease was, in fact, caused by a poor diet, which (along with unsanitary living conditions) stemmed from widespread poverty in the postbellum South. His work was largely ignored until the late 1930s, when researchers finally proved that the disease was caused by a lack of niacin.

Ocular Literacy Training

From the same source - a correlation between reading (in)ability and erratic eye movements during reading was taken as evidence of a causal relationship in the wrong direction, and "eye movement training programs" were implemented to improve literacy. These were ineffective, and later work showed that causality runs in the opposite direction; reading difficulties lead to the regressions and fixations observed in poor readers.

Aaron Novstrup
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  • What kind of later work? – rolando2 Jul 26 '14 at 00:15
  • @rolando2 I don't know, unfortunately. That book chapter cites "Olsen & Forsberg, 1993" for that claim, which I can guess is [this chapter from Visual Processes in Reading and Reading Disabilities](http://books.google.com/books?id=o4TjKN1fZ3MC&lpg=PA377&ots=_VHl9Csgyl&lr&pg=PA377#v=onepage&q&f=false). [This paper](http://psycnet.apa.org/journals/xlm/21/6/1430/) also backs up the claim. – Aaron Novstrup Jul 26 '14 at 14:47
  • If anyone recognizes [this book](http://psych.unl.edu/psycrs/450/e3/chapt/stanovich_c5.pdf), by the way, I'd like to replace the link with a proper citation. The link appears to be from a psych course page and its likely to disappear someday. – Aaron Novstrup Jul 26 '14 at 14:50
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    On similar lines one might mention malaria which as the name suggests was believed to be caused by bad air on the basis of a correlation with low-lying regions and swamps (see the Wikipedia article https://en.wikipedia.org/wiki/Malaria) – mdewey May 17 '17 at 13:54