Random example, but let's say I'm examining the effect of a health program on influenza cases in India. They just randomly start the program in 7 of the 29 states. I have data on the number of flu cases in every state for a few years before and after the program was initiated. So I can run a diff-in-diff:
F = B0 + B1(Post*Treat),
where F is the # of flu cases, and B1 is the treatment effect, and I find B1 to be neg and significant. But what if the underlying population changed during these years? If untreated states' population grew relative to treated states, that might explain the difference rather than an effective program. So how do I control for population? I've read that using the rate instead of total number of cases is problematic (denominator of the outcome would be pop, which causes issues in the regression as I understand), but I don't think I can just do:
F = B0 + B1(Post*Treat) + B3(logPop),
where logPop is log population (obviously), right? Assume I have the data of population for each state for every year.
Thank you for all help!
P.S. I use R, so any answers that put it in terms of R would be a plus