Correlation Is Not Causation. Except When It Is.

Anyone with even a passing familiarity with data and statistics has heard the old maxim “correlation is not causation.” If that's true, though, why use statistics at all?
Headshot of author Edward Hearn
Edward Hearn
Expert Columnist
March 30, 2021
Updated: July 13, 2021
Headshot of author Edward Hearn
Edward Hearn
Expert Columnist
March 30, 2021
Updated: July 13, 2021

The expression “correlation is not causation” has a distinct place in the statistical canon as a sort of trump card against deterministic interpretations about statistical associations between variables. If statistics can’t at least address questions about causal inference, however, what’s the point of drawing any conclusions at all?

Although statistical evidence can never prove direct causes, there’s a strong case to be made that data can give us probabilistic reasons to suspect that a causal mechanism might be at play. Through the extended example of how researchers proved the causative link between cigarette smoking and lung cancer, among other adverse health outcomes, I want to illustrate how, when and where data can give insight into potential root causes.

Bradford Hill Criteria

  1. The size of the effect is massive enough that there is no other confounder that could explain it.
  2. The effect occurs after the cause, and, if there is an expectation of a delay between them, the effect occurs at the end of this delay.
  3. Assuming a non-singular causal incidence, the size of the effect should increase if the causal variable increases.
  4. There is a theoretical reason why a given cause results in the observed effect.
  5. The effect fits into what has already been observed.
  6. Replication of studies with new data result in the same or similar effects as the initial study.
  7. The effect shows up in different lines of observational evidence.

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Bradford Hill Criteria

In the 1950s and 60s, the tobacco industry had taken to employing reputable scientists to cast doubt on the statistical association between cigarettes and lung cancer and other health problems. At the time, a growing body of observational evidence suggested that cigarettes were killing people. The arguments these scientists made to counter that claim questioned the veracity of non-clinical medical evidence by injecting so-called reasonable doubt about the cause of cancer being cigarette smoke.

The scientists pointed to other potential causes that could and did, in fact, lead to cancer. This raised a fundamental question: How can anyone deduce the cause of something simply from examining non-clinically collected information? More broadly, how can researchers get at the reasons behind observed effects when these effects are difficult, unethical or impossible to control for in either a lab setting or via a random-controlled trial?

In order to make a strong “balance of probabilities” case for getting at a root cause, researchers should look for a certain set of attributes. These were dubbed the Bradford Hill” criteria, after the English epidemiologist Austin Bradford Hill. Hill and his colleague, physician-turned-epidemiologist Richard Doll, used this checklist of factors to provide evidence of a causative link between smoking and lung cancer.

With these criteria, Bradford Hill and Doll sought to counter the reasonable doubt arguments of the tobacco industry scientists and others who primarily employed a “correlation is not causation” argument to undermine the link between smoking and lung cancer. The criteria, in order of the strength of their evidence, are: 

  1. The size of the effect is massive enough that there is no other confounder that could explain it.
     
  2. The effect occurs after the cause, and, if there is an expectation of a delay between them, the effect occurs at the end of this delay.
     
  3. Assuming a non-singular causal incidence, the size of the effect should increase if the causal variable increases.
     
  4. There is a theoretical reason why a given cause results in the observed effect.
     
  5. The effect fits into what has already been observed.
     
  6. Replication of studies with new data result in the same or similar effects as the initial study.
     
  7. The effect shows up in different lines of observational evidence.

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Applying the Criteria

With respect to the first and second criteria, the 1964 Surgeon General’s Report established a direct link between smoking and a 10- to 20-fold increase in the risk of contracting lung cancer. The report also showed that smokers faced a 70 percent increase in age-corrected mortality relative to non-smokers. These massive increases in the probabilities of adverse outcomes for smokers clearly fit the description of massive effects that were not explainable by other confounding factors.

What’s more, both the American Cancer Society in the U.S. and Bradford Hill and Doll in the U.K. had carried out large-scale, longitudinal studies in the mid-1950s and the early 60s, respectively. These types of studies followed the same groups of smokers and non-smokers over an extended period of time. Because the two groups were selected on the basis of their not having lung cancer or other adverse health consequences when first observed, longitudinal studies effectively put cause before effect.

These same groups of smokers and non-smokers were subsequently studied in different cities, states and countries over an extended period of time to see if adverse health effects occurred in one group relative to the other. A large difference in outcomes between the smoking and non-smoking groups, such as an elevated proportion of smokers contracting lung cancer or other types of disease relative to the non-smoking group, would suggest that smoking was the likeliest cause of the adverse health effect.

Richard Doll conducted a follow-up study of U.K. doctors over 40 to 50 years that fulfilled the third Bradford Hill criterion. He found that U.K. doctors who were born before the turn of the 20th century had a far lower propensity to contract and die from lung cancer than doctors born in the 1910s and 1920s, after the advent of mass production of cigarettes for public consumption.

Prior to the 20th century, lung cancer was particularly rare. As a result, individuals reaching adulthood in the first third of the century would not have been susceptible to the increased proliferation of smoking throughout their lives. The doctors coming of age in the middle part of the century, however, faced a much higher exposure to cigarette availability, particularly during the World Wars. Doll and his colleagues found that British doctors who smoked lost 10 years of life versus their non-smoking peers. Furthermore, for those born in the 1870s, the probability of surviving from age 70 to 90 was 10 percent for smokers and 12 percent for non-smokers. This same statistic for those born in the 1910s, however, was 7 percent and 33 percent.

The fourth of the Bradford Hill criteria requires a plausible theoretical reason why smoking leads to lung cancer. The work of two pathologists, Oscar Auerbach and Anderson Hilding, supplied two theoretical mechanisms. In 1956, Auerbach, who had been observing the lungs of deceased smokers for years, posited that cigarette smoke led to ciliastasis, a condition that deadens the hair-like cilia in the lungs, which help people clear particulate matter from their respiratory system.

Auerbach had noted that the lungs of smokers who had died from lung cancer were more likely to show signs of ciliastasis. He suggested that the deadened cilia brought about by smoking effectively impaired the ability of the lungs to expel carcinogenic particulates contained in cigarette smoke.

That very same year, Hilding discovered that cigarettes contained many of the same carcinogenic chemical compounds that had been discovered in coal tar in the 1930s. Ten years earlier, John Fishel of Ohio State University had likewise discovered that cigarette smoke contained the carcinogen benzopyrene. This and the discovery of many other known carcinogens in cigarettes into the early 60s provided chemical and physiological methods by which cigarette smoking could lead to lung cancer.

The last three of the Bradford Hill criteria are fulfilled by examining research into cigarette smoking from the early 20th century. As early as 1912, the German-American physician Isaac Adler had examined a study carried out in 1898 Germany concerning the elevated incidence of lung tumors in tobacco workers.

The medical student who carried out the study had concluded that dust resulting from the cultivation of the tobacco plants was the primary culprit. Adler, reviewing this study and others 15 years later, came to a different conclusion: Smoking the tobacco rather than harvesting it was to blame for the increasing rate of pulmonary tumors in Germans at the turn of the 20th century. Adler noted that most of the workers and many others who contracted lung cancer during this time period reported that they were smokers.

Other German researchers and physicians continued to study smoking’s deleterious effects on health. Much of this research was suppressed or ignored due to the affiliations of many of the scientists with the Nazi party in the 1930s and 40s, however. Thus, the observational findings of American and British researchers that smoking cigarettes was a potential cause of lung cancer fit in with a patchwork of evidence to this effect that spanned the late 19th up through the first half of the 20th century.

Moreover, most of these studies were effectively replications of each other. Bradford Hill and Doll’s longitudinal study served as a replication of the American Cancer Society’s longitudinal study in the U.S. This work was followed up by other cohort analyses such as Doll’s second study of U.K. doctors, Barnhard Hill and Doll’s research colleague Richard Petos’ 1970s longitudinal study confirmed that cessation of smoking resulted in an increased life expectancy, and others all confirmed that cigarette smoking led to a huge increase in the probability of lung cancer, heart disease, emphysema and bronchitis.

Furthermore, the amalgamation of different strands of pathological, chemical, observational and historical data fulfilled the seventh of the b Hill criteria: namely, that an increase in the propensity of contracting and dying from lung cancer, as well as other smoking-related maladies, came about from many different lines of evidence that all converged on these same conclusions.

 

Correlations Compass

The 1964 Surgeon General’s report on smoking and lung cancer represented the culmination of a half-century of research on the deleterious health effects of cigarette smoking. More broadly, the methods by which the evidence for the report was collected presented a methodological breakthrough. In establishing rigorous criteria by which to evaluate whether observational, non-clinical evidence can be brought to bear on questions of inductive inference, Barnhard Hill and his colleagues opened new pathways by which researchers can explore what and how causative associations can be discovered. By appealing to probabilistic causation rather than strict determinism, the criteria allowed for the exploration of causative questions of interest outside of the traditional clinical framework. Thus, many important population-level research questions in the social sciences and public health could never have been addressed empirically without these guidelines.

The Bradford Hill criteria should be viewed today as the means by which observational or indirect evidence can be used to infer a probabilistic cause of some observed effect or outcome. Thus, these criteria present an ideal checklist that researchers can employ to know where a potential root cause might be. And, while it’s true that correlation is not causation, when approached dynamically, rigorously and carefully, observational evidence and the correlations arising from it can heavily imply a causal effect.

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