# Statistics Misunderstood: Correlations Tell Us Cancer Causes Us to Smoke

Zachary Walston

Many people commonly state “correlation does not equal causation.” First and foremost, this is true. Unfortunately, this is often treated as the “no offense but…” approach of acknowledging the issue but plowing through anyway. Similar to how someone will proceed to say something really offensive under the assumption that it is now okay following the disclaimer, correlations are still treated as causation and lead to flawed decision-making.

A correlation is simply an association between two variables. This relationship can be positive or negative. For example, studying is positively correlated with better test scores. The more I study, the higher I score. While this correlation makes sense, many correlations can be completed unrelated, but the association remains.

The number of golfers using wooden clubs is inversely correlated with the number of licensed physical therapists over the past century. As the therapist workforce increases, fewer golfers use wooden clubs. I can safely assume therapists are not stealing all the wooden golf clubs for themselves. These have nothing to do with one another, but strictly looking at the data, a relationship exists.

You can find many other entertaining and clearly unrelated examples. Looking at two data sets in a correlation – A and B – the relationship could be A causes B, B causes A, or an unknown C causes A and B.

R.A. Fisher, a successful statistician who has made lasting impacts on assessments of effect sizes, does a great job of outlining the limitations of correlation. To illustrate how misleading correlations can be, let’s look at how he combated the growing public concerns of the negative health implications associated with cigarette smoking. He was a proponent of smoking and took issue with the rise of correlation studies in the 1940s and 1950s linking smoking to cancer. Here is what he had to say regarding the matter:

“Is it possible then, that lung cancer – that is to say, the pre-cancerous condition which must exist and is known to exist for years in those who are going to show overt lung cancer – is one of the causes of smoking cigarettes? I don’t think it can be excluded. I don’t think we know enough to say that it is such a cause. But the pre-cancerous condition is one involving a certain amount of slight chronic inflammation. The causes of smoking cigarettes may be studied among your friends, to some extent, and I think you will agree that a slight cause of irritation – a slight disappointment, an unexpected delay, some sort of mild rebuff, a frustration – are commonly accompanied by pulling out a cigarette and getting a little compensation for life’s minor ills in that way. And so, anyone suffering from a chronic inflammation in part of the body (something that does not give rise to conscious pain) is not unlikely to be associated with smoking more frequently or smoking rather than not smoking. It is the kind of comfort that might be a real solace to anyone in the fifteen years of approaching lung cancer. And to take the poor chap’s cigarettes away from him would be rather like taking away his white stick from a blind man. It would make an already unhappy person a little more unhappy than he needs be.”

As Ellenberg puts it in his book How Not to Be Wrong: The Power of Mathematical Thinking, “one sees here both a brilliant and rigorous statistician’s demand that all possibilities receive fair consideration.” Fisher was correct in his assessment of correlation statistics. The epidemiologist Jan Vanderbroucke stated the arguments “might have become textbook classics for their impeccable logic and clear exposition of data and argument if only the authors had been on the right side.” As we all know, decades of more rigorous studies of varying types have allowed us to conclude that smoking does in fact contribute to the development of cancer. Now the type of assessment Fisher displayed is the opposite of what we typically see when individuals interpret correlation results. It can be very tempting to see a correlation and chonclude that causation must be present. And it might! But we cannot draw a cause and effect conclusion without more evidence.

Some research questions will never pass a review board and thus cannot be tested with a randomized control trial. Regarding smoking, we cannot randomly allocate a few hundred people to smoking one pack of cigarettes a day and allocate another few hundred to a control group then see which group has a higher death rate in 20 years. Additionally, the longer a study progresses, the more potential for external biases and influencers – such as diet and exercise habits – to alter the study. But when we look at all the data, the picture is clear.

While still observational in nature, we have many studies with large subject pools that consistently show increased smoking increases the risk for lung cancer. If you stop smoking, the risk is reversed. If you smoke unfiltered compared to filtered, the risk increases. If you smoke two packs a day compared to one, the risk increases. Any way you look at the problem, smoking increases cancer risk. As compiling a large volume of studies requires substantial time and resources, improving the quality of individual studies can expedite our ability to draw conclusions.

The more bias and variables we eliminate (well-controlled randomized control trials), the larger the trial size, and the more frequently it is reproduced with similar results, the more confident we can be in drawing a conclusion. If we see a large volume of correlation studies pointing to the same conclusions – as has occurred with smoking – we can start feeling more confident with a potential cause and effect relationship. Correlations have a place in research as they point to relationships that may be relevant, but they are an incomplete analysis.

This does not mean all information short of randomized control trials should be ignored. In treatment, for example, the three legs of evidence-based practice are research evidence, clinical expertise, and patient values and perspective. The legs are not equally weighted, but all should be considered.

The foundation is the research, starting with randomized control trials, and the application to patients is then modified by the clinician’s expertise and the patient’s value and perspective. A lumbar manipulation may be indicated based on patient presentation, but if I as a clinician have no experience with or confidence in delivering the technique, or if the patient hates the sound of knuckles cracking and is scared of being manipulated, applying the technique will be a disaster. This issue lies in the inappropriate use of the data. We can, however, compile similar findings across multiple patient populations and with slightly different research questions, to increase our confidence in our assessment.

Reading research is fantastic, but if you do not understand statistics, you may draw incorrect conclusions.