Fig. 1

Graphical representation of a moderator which influences the confounder-exposure and confounder-outcome relationships. The moderator, \({\varvec{M}}\), by definition influences the relationship between the exposure, \({\varvec{T}}\), and outcome, \({\varvec{Y}}\), but also may influence the relationship between a confounder, \({\varvec{X}}\), and the exposure and/or the relationship between a confounder and the outcome. The moderator may also be a confounder between the exposure and outcome (shown via a dotted line), but not necessarily