# Correct and clear wording for non-causal correlation

Despite reading multiple statistics and epidemiology texts as well as studies, I have trouble describing the following in plain English for a public of doctors (so, non-statisticians or biomedical epidemiologists). We have a variable A that usually correlates with variable B, so that it has been previously assumed that A causes B (increases the probability of B). We now hypothesize that it is a case of "correlation is not causation", with actually a third variable C causing (increasing the probability) independently both A and B. So, A does not actually play a causal role but just hints at the presence of C. My problem is: how do you describe "A"? "Side-effect"? "Collateral effect"? "Accidental effect"? What would be a correct and clear wording in English? I don't need one single word or expression, I would be happy with even a lengthy sentence, but clear for a public with no background in statistics or epidemiology!

Edit october 2015: My supervisor has finally found the perfect wording she had been looking for: it is "innocent bystander". Indeed, I have found this expression used in several papers. Does anybody recognise the expression as common or clear?

• You may find resonance using terms such as "parent...child...sibling" or "upstream...downstream...side channel." Often multiple metaphors or visuals are needed. Jul 26, 2015 at 11:25

I think there might be no need for any particular terminology:

"Previous authors assumed that A caused B (references). In this paper, we suggest that C causes both A and B with no causal link between A and B."

If this is a key point of your paper that might be hard to understand, I would suggest maybe adding a diagram with arrows between the different variables.

If you want to get technical, A is independent of B given C. Additional terminology for this might be found in Judea Pearl's book on Causality, but it might be a bit difficult for medical readers.

• +1 good answer and great reference, but note that there may not be a cause C. Jul 25, 2015 at 22:16

If A is correlated with B, then there are more than the three possibilities: A causes B, B causes A, and A and B have a common cause. There are other causal structures that could lead to A and B being correlated! Therefore, you may not even be able to find a common cause C.

I think you just say that you don't have enough evidence to conclude that A causes B despite their correlation. Rather than claiming there is a common cause, you can suggest that there may be confounders.

Here's Pearl's description:

Whenever we undertake to evaluate the effect of one factor (X) on another (Y), the question arises as to whether we should adjust our measurements for possible variations in some other factors (Z), otherwise known as "covariates," "concomitants," or "confounders" (Cox 1958, p. 48). Adjustment amounts to partitioning the population into groups that are homogeneous relative to Z, assessing the effect of X on Y in each homogeneous group, and then averaging the results (as in (3.13)). The illusive nature of such adjustment was recognized as early as 1899, when Karl Pearson discovered what is now called Simpson's paradox (see Section 6.1): Any statistical relationship between two variables may be reversed by including additional factors in the analysis. For example, we may find that students who smoke obtain higher grades than those who do not smoke but, adjusting for age, smokers obtain lower grades in every age group and, further adjusting for family income, smokers again obtain higher grades than nonsmokers in every income-age group, and so on.

In plain English, I would start with Pearl's smoking example as an introduction to how critical it is to know which variables to adjust for. Then just say that you think you're missing at least one variable C, which could eliminate the apparent causal relationship between A and B.

• you are absolutely right: wonderful topic. However, Pearl's excursus could well be in the introduction of all existing biomedical papers: we must assume the reader knows what correlation implies and does not imply. I have to state a specific hypothesis among the infinite possible scenarios, and the hypothesis I need to convey is that 1) A confounds the causal relationship between C and B; 2) the confounding does not originate - for instance - from sampling problems in previous studies, but from a real causal relationship between C and A. Thank you for the perspective though! Jul 27, 2015 at 12:05
• @torwart Pearl is not just saying that correlation does not imply causation. He is explaining how an adjustment can reverse an apparent causal relationship — over and over again. This is often counterintuitive. The confounding does originate in either sampling problems from previous studies or modelling problems now, because if you had known what the confounders were and had recorded their values, you could adjust for them and your problem would be solved. Jul 27, 2015 at 15:56