Is it better to stratify or adjust confounders in the model with small sample size? My questions is for Poisson models and Cox models. The context is rare/small number of events. We want to adjust for a few categorical confounders: sex, age group, baseline risk, but are not interested in their effects. There will be some empty cells, but there will likely be events in each marginal category.
It seems adjusting confounders in the model is more common. I wonder if the stratifying approach has any disadvantage in this context.
Uncertain which approach to use.

A stratified Cox model can be used when you believe that the instantaneous hazard function varies markedly by a confounder or by time (ie, violates the proportional hazards assumption), but I don’t see it as a method that should be routinely used to ameliorate the limitations of small sample size.
