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I made a very simple scenario:

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Let's assume 'total work time' has a positive association with 'income' (more you work, more you earn).

But when I adjust to one of the following DAG's members, what should most likely happen with the association between exposure and outcome?

a) work time job1 (mediator)

b) colleagues visited at job1 (descendant)

c) quality time (collider)

My own understanding is that the effect of the exposure on the outcome most likely decreases in all three cases. Is this correct? Is this the reason why adjusting to them is bad, meaning that we will get biased estimates?

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Adjusting on the mediator will get you biased results, if your goal is to get the total effect. If you just want the direct effect, you should condition on that mediator and on nothing else (well, technically, conditioning on the descendant of the mediator shouldn't hurt anything).

Conditioning only on the descendant shouldn't change anything much.

Conditioning on the collider will open up the collider and allow causal information to flow from the cause to the effect along another path. However, the collider is not a confounder, because the arrow is from the cause to the collider, not the other way around. I would still be hesitant to condition on the collider: I think you might introduce collider bias. It's not confounder bias, but it is collider bias.

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  • $\begingroup$ Thanks but what about the most likely changes in the effect of exposure of outcome while adjusting to these? "Biased" can mean anything. (Please consider in answering that we have this simple, simulated DAG). $\endgroup$
    – st4co4
    Mar 15, 2022 at 6:37
  • $\begingroup$ I'm not sure it's possible to say in advance which direction the biases will go in each case. It should be enough in most cases to know that adjusting for certain things will bias your result, so it's best not to do that. Curious why you would need to know the direction of the bias? $\endgroup$
    – Adrian Keister
    Mar 15, 2022 at 12:26
  • $\begingroup$ Good question. I'm working on simulating data that should show effects according to my made-up DAG, meaning that the whole simulation should look somewhat realistic (e.g. adjusting to mediator changes the effect of exposure on outcome etc). In other words, this data should cover all main cases: collider, descendant, mediator. I hope that such an all-in-one example helps to understand causal modelling. $\endgroup$
    – st4co4
    Mar 15, 2022 at 13:40
  • $\begingroup$ Ah, I see. Well, that's beyond me. Honestly, I would think it would be easier to dream up a real-world example and collect real data that follows that DAG and use that, rather than simulating your own data to show such relationships. Or you could experiment with some packages in R or Python that do causality. There are several. $\endgroup$
    – Adrian Keister
    Mar 15, 2022 at 13:57

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