By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social

Last month’s post discussed the subtle (and not so subtle) difficulties that can arise when using statistics to identify causes of phenomena. The example I used that time was the probability that use of the popular pain-reliever Tylenol by a pregnant woman led to an increased risk of her child being born autistic.

Such arguments generally have two parts. First, see if there is a significant correlation between use of the drug and the phenomenon. If so, determine whether use of the drug caused the phenomenon. That second step is by far the most challenging.

Just after I had submitted that post to the MAA, I came across another example: whether drinking a small glass of wine with lunch or dinner can protect the heart, reduce diabetes risk, or even help you live longer. Studies have found evidence for all of those. But are they valid?

I wrote a Devlin’s Angle post about alcohol risks way back in January 2020, having posted a somewhat more detailed article (December 2019) on my SUMOP educational site. (You need to scroll down to that date.) My focus then was how to interpret the scary statement “Just one drink daily was linked to a 13% increased risk of breast cancer,” which I had come across. As I showed, in that case the increased risk was still extremely low. (See the SUMOP post for that.)

Against that, there were studies showing a somewhat unexpected association between how much alcohol someone drank and their risk of death. People who said they drank heavily had an increased risk, as you might expect. But those who drank nothing at all also had an increased risk compared with those who drank one or two servings of alcohol per day.

It seemed, therefore, that people with moderate alcohol consumption tended to live longer than those who drank no alcohol. Many articles were written about that study. One explanation suggested at the time that seemed reasonable to me (there were several) was that moderate wine drinking produced a feeling of relaxation that helped heal the body after a stressful day at work. Another theory was that people in Mediterranean countries, where wine with a meal is common, had a longer lifespan than those in the USA. (I felt that one was at best a correlation, not causation.)

Then, on August 19 this year, a news release from Stanford University caught my eye. Researchers had looked more carefully at those studies showing that moderate alcohol consumption is better than none. And they found them faulty.

To uncover the error, you have to find out how the data was collected. In that case, the classification of drinking habits was based on current consumption. (The data had not been collected to look at comparative health risks. The study was made on a dataset that happened to be lying around somewhere.) That means that the “non-drinkers” included not just the “never drank” group, but also those who had been heavy drinkers but had stopped, generally on medical advice. That group increased the average for “non-drinkers”), making it higher than the “never drank” group. It was not that avoiding alcohol altogether led to increased risk. Rather it was the other way round; increased risk and/or ill health made people become non-drinkers.

This is hardly mathematics. You could call it basic number sense, but in the general run of things, it’s a simple category confusion. Yet that one mistake led to a belief that many wine drinkers internalized and repeated, myself included. Articles that say doing A leads to an increased risk of B should always be questioned. Establishing such causality is generally very hard; but it is often fairly easy to determine why it must be false.

As for me, I long ago reduced my wine consumption by using 2-ounce tasting glasses. Wine with a meal was too important a part (for me) to drop it completely. So I treat it the same way I do road cycling. I accept the (reduced) risk because wine with a meal gives me so much pleasure. I still follow my own version of the Mediterranean Diet. Everything in life involves risk. The wise decision is to weigh each one and adapt accordingly. Math is good for that!