Can you include interactions with the treatment variable as a covariate in linear regression? I'm quite new to regression modelling. I'm trying to predict the average treatment effect of a weight loss intervention by comparing outcomes in control and treated groups. The model currently includes gender, age, age-squared, and treatment as covariates. But being male predicts better outcomes in the treated group and worse outcomes in controls. Adding an interaction term between gender and treatment improves model fit (about 20 AIC points) and the term is significant. But I'm not sure if it makes sense to do that, if the goal is to assess the effect of the treatment. I can't immediately think why it would be a problem, but I haven't seen it done before either.

If it makes a better prediction, then of course it makes sense to include the interaction in the model. In assessing the treatment effect, one has to recognize that by including the interaction with gender, you are saying that the treatment effect depends on gender. So what I suggest doing is estimating the means and comparisons separately at each gender. Something like this, if using R:
library(emmeans)
EMM <- emmeans(model, ~ treat | gender)
EMM ## display the estimated marginal means
contrast(EMM, "pairwise")  ## pairwise comparisons

The marginal means are computed at the average age. Since you have age squared in the model, it is a little tricky because if age^2 is a separate variable, it will also by default use the average of (age^2), which makes no sense because that's not the same as (average age)^2. Your best bet is to fit the model with those variables computed, e.g., poly(age, degree = 2).
Stata help?
Can a Stata expert please show us how to do this in Stata?
