I am interested in estimating a Poisson regression for mortality rates, with number of deaths as the dependent variable and log(population size) as the offset. I have 50 observations (states).

I am aware of rules of thumbs in various regression models to figure out the maximum number of predictors. For example: Cox model: at least 5 events per predictor, logistic regression: at least 5 observations where Y=1 per predictor etc...

Is there a similar rule of thumb for Poisson models?