My assertion is that a model of the form P(R|G,T) is always going to be more accurate than a model of the form P(R|T) alone—you can’t gain anything by throwing away the G variable.
That’s all true (modulo the objection about overfitting). However, there is the case where T affects G which in turn affects R. (Presumably this doesn’t apply when T = treatment and G = gender). If what we’re interested in is the effect of T on R (irrespective of which other variables ‘transmit’ the causal influence) then conditioning on G may obscure the pattern we’re trying to detect.
(Apologies for not writing the above paragraph using rigorous language, but hopefully the point is obvious enough.)
That’s all true (modulo the objection about overfitting). However, there is the case where T affects G which in turn affects R. (Presumably this doesn’t apply when T = treatment and G = gender). If what we’re interested in is the effect of T on R (irrespective of which other variables ‘transmit’ the causal influence) then conditioning on G may obscure the pattern we’re trying to detect.
(Apologies for not writing the above paragraph using rigorous language, but hopefully the point is obvious enough.)