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I am looking for a direct effect and I have a total of 12 variables (exposure, outcome, 8 observed, 2 possibly important unobserved variables).

Dagitty packages gives 5 adjustment sets possible for adjusting. The goal of regression is to prove the difference between exposure variable levels in outcome variable.

What approaches can be used or should be considered for choosing the best adjustment set for matching? More the better?

Also, am I correct that by temporarily turning unobserved variables as observed ones, I can check their role/importance in terms of adjusting? E.g. if unobserved variables are recommended for adjusting, then they would be important in our work (I must admit a limitation). However, if dagitty package gives such options for analysing a direct effect.

  1. observedA, observedB, observedC
  2. observedA, observedD, unobservedU

As both sets are recommended, can I just use the first and say that I can bypass the need for unobserved variables for analysis? Or in other words, My adjusting would be good enough without unobserved variables? Of course, we must assume that the DAG is correct.

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  • $\begingroup$ Can you expand your post please ? What do you mean by "Dagitty packages gives 5 adjustment sets" - are you saying that from your DAG, it produces 5 different sets ? What do you mean by "matching" ? What are you modelling ? You mention unobserved variables - but these cannot be included in a model, by definition. $\endgroup$
    – Robert Long
    Sep 25, 2020 at 7:28
  • $\begingroup$ Thank you! I am looking for a direct effect, thus adjusting for mediators is necessary. I edited the initial post. I somewhat wanted to say that if I play with unobserved variables, by marking them as observed ones before checking adjustment sets, I can assess their possible importance in my work (is it a limitation or not in terms of adjustment). $\endgroup$
    – st4co4
    Sep 25, 2020 at 11:54
  • $\begingroup$ Thanks for the further details. I still don't know what you mean by matching ? $\endgroup$
    – Robert Long
    Sep 25, 2020 at 11:57

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It is good that you say:

Of course, we must assume that the DAG is correct.

However please note:

The goal of regression is to prove the difference between exposure variable levels in outcome variable.

...is not correct. We can never prove things with statistics. In the frequentist approach to regression we can compute probabilities that the data or data more extreme would be observed if the null hypothesis is true. We can also estimate effect sizes which tell us the association of a change in a variable on an outcome while contolling for the effect of other variables. We can use regression models as a tool to assess whether a particular causal model is plausible.

Also, am I correct that by temporarily turning unobserved variables as observed ones, I can check their role/importance in terms of adjusting

Yes I think this is a reasonable approach.

As for choosing from competing adjustment sets, if one or more of the adjustment sets contains unobserved variables (that you temporarily made observed in order to understand their impact), and one of the other sets contains only observed variables then yes, you are completely justified in choosing that set. If you have 2 sets that include only observed variables then some care is needed. Remember that DAGs are non-parametric, so you want to look for issues such as highly correlated covariates. Ultimately you will probably want to fit both models and hope that they provide similar inferences and perhaps choose the one that gives you the most precise measure of the effect you want to estimate.

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  • $\begingroup$ Thank you! By matching, I used it as a synonym of adjusting. We matched group A and B for analysis, we matched group A and B for analysis. Is it wrong? $\endgroup$
    – st4co4
    Sep 27, 2020 at 9:24
  • $\begingroup$ I still don't know what you mean. What does "We matched group A and B mean" ? "matching" can mean a lot of things, such as choosing only those observations where some variables are equal.between groups Or it can mean other things. What did you actually do ? $\endgroup$
    – Robert Long
    Sep 27, 2020 at 10:38
  • $\begingroup$ Thus, it seems that I am using these terms wrongly. I thought that adjusting and matching is the same thing - adding variables into to the model to reduce confounding. E.g. group B's mean age is 70, and group A'c mean age is 100. For meaningful comparison of mortality, the age of these groups needs to be adjusted/matched. Or how do these terms differ? $\endgroup$
    – st4co4
    Sep 28, 2020 at 6:08

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