For analysis of the first event, I am wondering if Poisson model has any advantage over Cox model, besides some people find rate ratio easier to interpret than hazard ratio?
I notice some people use Poisson model to analyze treatment effect in different strata of time. For example, for COVID studies, they can analyze the effect during a certain variant period. Or they can analyze whether the effect remains the same from 3-6 month compared to the first 3 month. Are these achievable by the Cox model too?