# Which covariates need to be adjusted for in a model

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

• Have you just added a new DAG at the top ? This one has just one sufficient set, parent and x2 but please don't change the question like that, especially when someone has already posted answer ! Jun 6, 2021 at 11:39
• Hi @Robert, I am sorry, I was trying to write it as a comment but I could not add the new image in a comment.
– Milo
Jun 6, 2021 at 14:19

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.

• Thank you very much, Robert. I made a mistake in a graph as the arrow from x4 should go to x1, not x3, but I do not think it affects the adjustment set. I have uploaded the correct graph. There seems to exist a set of variables that are typicaly adjusted for in studies where the
– Milo
Jun 6, 2021 at 13:05
• You're welcome, but if you are referring the new DAG at the top the question, there are other differences apart from the arc betwen x4 and x1 (or x3). Anyway, the (only) minimally sufficient set for the DAG at the top of the question is parent and x2 Jun 6, 2021 at 13:35
• You have tried to edit my question to make a comment !!! The site does not work like that. If you want to make a comment, the click on "Add a comment" ! As for the DAG, if you think there are other causal paths then you must include them. As for "There seems to exist a set of variables that are as a rule adjusted for (for example in epidemiological studies): age, ethnicicty, sex. X3 and x4 are these variables." those are commonly adjusted for because they are potential confounders, but it doesn't mean they always should be adjusted for. Jun 6, 2021 at 14:22
• Thank you again @Robert.
– Milo
Jun 6, 2021 at 15:15