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I have some troubles finding a strategy to identify the causal effect I am looking for from my observed data. I am assuming the following DAG:

dag

where $Z$ is the result of a coin toss (randomization), $A$ is the exposure of interest and $Y$ is the outcome of interest. I am assuming that $A$ is binary (0 or 1) and $Y$ is continuous. The estimand of interest is:

$$E\left(Y_6^{\bar{A} = \bar{1}} - Y_6^{\bar{A} = \bar{0}}\right)$$

where $Y_6^{\bar{A}=\bar{1}}$ denotes the value of $Y$ that would be observed at $t = 6$ if $A$ was set to $1$ at every considered point in time. $Y_6^{\bar{A}=\bar{0}}$ follows the same definition, but with $A$ being set to $0$ for all points in time. All variables are observed completely without any missing values or measurement error.

I do think it should be possible to estimate this effect in an unbiased manner given the data, but I am not sure how to do it. I have thought about using a mixed model, but that would not really give me the marginal estimate i am interested in.

Would a structural marginal model work? If yes, how would I apply one to this data? If anyone could point me in the right direction, that would be great.

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    $\begingroup$ Yes, a marginal structural model would work for the causal structure provided. More generally, any of the g-methods would work for estimation of the parameter of interest. For a general introduction to g-methods see ncbi.nlm.nih.gov/pmc/articles/PMC6074945 $\endgroup$
    – pzivich
    Commented Nov 10, 2023 at 14:15
  • $\begingroup$ Thanks, I will definitly look into it. $\endgroup$
    – Denzo
    Commented Nov 10, 2023 at 14:20

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