A standard way to do this is to regress the outcome on other predictors that do not vary with time, as well as whether the person took the treatment or not. An example is a regression of wages not only on years-of-education but also on test scores meant to measure abilities or motivation. Both years-of-education and test scores are positively correlated with subsequent wages, and when interpreting the findings the coefficient found on years of education has been partly cleansed of the factors predicting which people would have chosen to have more education.
A more advanced method is the Heckman two-step.
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