Controlling for a confounding variable in regression analysis

Question

This question has come around due to a comment from a reviewer on a journal submission, but it has me interested and I want to see the general discussion on the subject.

I have a study where I'm looking to analyse and compare the pathways that would influence differences of mental wellbeing between elite athletes and the general population. As elite athletes are associated with higher volumes of exercise participation, and that exercise participation is associated with improved mental wellbeing, I have decided to include it as a covariate in the study. This is because I fear that not doing so will likely influence/potentially bias the results of my study. My rationale is that doing so will allow me to account for any variance in mental wellbeing between populations that can be explained by exercise participation.

However, the reviewer is concerned that because athlete status and exercise participation are likely to be confounding, exercise participation should not be included as a covariate, as doing so may likely influence/bias the results of the study.

This has me curious and confused! As both of us agree that exercise participation and athlete status will be confounding, but disagree on how to act on this.

So what is the consensus here? (and can I be cheeky and ask for some good reading recommendations for either side of the argument?)

Answer 1

While the referee may not be using the correct technical language, it sounds like his real concern is that exercise participation may be a collider variable in this analysis. Exercise participation is causally related to one's status as an elite athlete and it is also plausibly causally related to mental wellbeing. Consequently, if you were to condition on exercise participation, this could "block" a valid causal pathway relating status as an elite athlete to mental wellbeing.

In order to deal with this problem, you will need to think more deeply about what causal pathways you are interested in isolating in your analysis. It would be useful to read some literature on causal analysis and collider variables to aid with this (see e.g., Pearl 1988, Hernan and Robins 2006, Pearl 2009, Pearl 2010, Imbens and Rubin 2015, Pearl et al 2016). I recommend that when you re-write your paper you expicitly discuss the issue of the potential collider variable and your approach to this variable, referencing relevant literature.