I have run a poisson regression with two categorical predictors (treatment and disease severity) and their interaction, controlling for a number of relevant covariates. Treatment has two levels (control = 0, intervention = 1) and disease severity has three levels (none = 0, mild = 1, moderate = 2). My output shows a significant interaction between treatment and moderate disease severity in predicting my outcome (exp(-0.63) = IRR 0.53.
My question is: Can I interpret the 0.53 directly? Is this meaningful? In other words, is it the case that those with moderate disease severity who received the intervention had 0.53 the incident rate of those with moderate disease severity in the control group? Or do I need to look at the difference between the IRR of the main effect of disease severity and the interaction term in order to draw this conclusion?