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In many observational studies, researchers assume that the treatment decision is based on observable covariates (that is, the ignorability assumption).

In this case, there are diverse methods that can be used to account for the selection bias (e.g. matching, inverse probability weighting, and so on).

But, what if the treatment decision is based on treatment effects? Does any problem occur if individuals choose to get a treatment considering the expected treatment effects?

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No, this is not a problem. The treatment assignment rule is still a function of the baseline covariates (although it depends on the data-generating distribution).

Specifically, the treatment rule is $d(W) := 1(E[Y\mid A=1,\,W] - E[Y \mid A=0,\, W] > 0 )$ where $W$ are the covariates, $A$ is a binary treatment and $Y$ is the outcome. You can estimate $d(W)$ by estimating $E[Y\mid A,\, W]$.

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