I am building a time to event model. I have many variables, but I would prefer a simple, but correct model, so I have drawn a DAG with daggity, to decide what variables to adjust for. My exposure is a derived variable - income per person, it is derived by dividing total income by number people in a house. I also have a variable presence of children in a house. It is strongly correlarted to the exposure, with childless families having a higher income per person. I know that one of the strategies in covariates adjustment is to adjust for parents of exposure, outcome or both,which would mean I should adjust. On the other hand , using backdoor criterion I could just adjust for x1-x4. could I ask for a piece of advice on which adjsutment startegy is correct for the parent variable? Adjusting by this covariate completely changes the effect of exposure. Than you
There is no reason why there should be only 1 minimally sufficient set for estimating the total casual effect of an exposure on an outcome.
In this case, from the DAG given:
it would be sufficient to condition on:
- x4 and parent, or
- x1, x3 and x4
Note by conditioning on parent, this blocks the backdoor paths from x1, x2 and x3, so only x4 needs to also be conditioned on.
Also you wouldn't condition on x2 if you are also conditioning on x1. That would be over adjustment.