# Interacting treatment variables with independent variables in matched samples

Can we interact the treatment variables with independent control variables that have been used for matching?

I have a binary treatment variable called 'medicine'. It indicates whether a person received a medicine.

I also have 5 control variables and 1 dependent variable 'days' - counting the days survived.

Using the MatchIt package in R, I match observations in the treatment group (medicine = 1) to similar observations in the control group (medicine=0) using CEM.

After matching I run a Poisson regression to estimate the effect of the medicine on days survived, while controlling for 5 variables.

Question 1: Can I interact the treatment variable (medicine) with the control variables in this matched sample?

Question 2: Assuming the treatment and control group have similar distributions across the control variables (well balanced), what does an interaction between a control variable and treatment tell me?