Consider the definition of a confounding variable is a variable that causes both treatment and outcome. In addition, we say that A is a effect modifier when the average causal effect of X on Y varies across levels of A (Hernán & Robins, 2020).
So, can a confounding variable be used as a moderating variable? Intuitively, when a variable satisfies the condition of confounding, it seems to satisfy the condition of being a moderating variable as well. But I am confused about some of these issues. As a common cause of X and Y, the confounding variable A has a causal effect on Y; at that point, if the causal effect of X on Y differs at different levels of A, then the moderating effect of A on the causal effect of X on Y becomes an interaction, and then we need to assume (conditional) exchangeability for both X and A. I am not sure if my analysis above is correct.
A variable can be both a confounder and an effect modifier.
It all depends on the person doing the research. Does he/she want to study the effect of A alone, while removing the effect of B as a confounder which distorts the relation between A and the outcome or does he/she want to actually study the effect of B in modifying the effect of A on the outcome.
a good example is asbestos/smoking and lung cancer
@James Leigh Thank you for your comments.
I also found some points from other scholars: "If a factor is both a confounder and an effect modifier, the need for exploring the nature of effect modification would supersede the need for controlling confounding factors."( Zheng, T. , Boffetta, P. , & Boyle, P. . (2012). Epidemiology and Biostatistics.)
In any case, what we can now be sure of is that : "A variable can be both a confounder and an effect modifier.".
Further, can I argue that if I am primarily concerned with the moderating role of A in the effect of X on Y, then no additional assumptions need to be made about A, such as the (conditional) exchangeability of A in the population, even if A is a confounding factor. All I need to do then is to think of A as an ordinary moderating variable.
I think the whole concept of an effect modifier needs to be revisited. Hernan states that the odds ratio is not a parameter of interest in causal inference but perhaps the reality is that it is only the odds ratio that can be used to define effect modification. See this preprint:
Preprint Redefining effect modification
Assuming that X, Y and M are independent, dependent and moderating (and also confounding) variables respectively.
1. when we want to assess the causal effect of X on Y, by conditioning on M and eliminating the non-causal correlations arising from confounding (assuming there are no other confounders);
2. when we want to assess the moderating role played by M in the causal effect of X on Y, in the case of regression, we should include X,M and X*M, respectively, in the regression equation (assuming that our functional form and model specification are correctly specified);
3. since we know that M is a direct cause of Y (because M is a confounder, it is a common cause of both X and Y), when we want to assess the interaction between M and X in the causal effect on Y, we should include in the regression equation not only X, M and X*M, but also the possible existence of a common cause U of M and Y, i.e. assuming the (conditional) exchangeability of both X and M.
The proper thing to do for a variable that is both confounding and effect modifying is to compute the main effect separately by strata of M. If the main effect in each stratum is the same there is no modifying effect. If they differ this is more likely an artifact of the sample than effect modification. The solution then is to find several studies and only if the difference in effect across strata is consistent do you conclude modification. An important point in all this is that ONLY noncollapsible measures of effect are suitable for such analyses as the collapsible ones will form pseudo-modifications just to keep probabilities between 0 and 1 (I am referring to binary outcomes here). Pls read my preprint posted above. I do not agree with the book by Zheng, T. , Boffetta, P. , & Boyle, P. that you quoted as there is no point in looking for modification when confounding is uncontrolled.
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