a strong association between treatment and confounder, treatment and survival status, and an interaction between treatment, confounder, and survival status. We expect all three methods to perform well in the first scenario because there is little to no confounding. For the second scenario, we expect MSM and our proposed method to perform well because there is no difference in the treatment effect between the principal strata, and other stratification groups. The naïve method should not perform well due to the strong association between treatment and confounder as well as treatment and survival status. Finally, for scenario three, we expect only our proposed method to perform well because an association between the treatment effect and principal strata, $S_{Z_1,\ldots,Z_{t-1}}=S_{Z'_1,\ldots,Z'_{t-1}}=1$, is induced by the stronger interaction effect between treatment, confounder, and survival status. We fit standard linear and logistic regression models rather than BART and PENCOMP with BART since our focus is not on model misspecification but rather, the effect of confounding by indication and censoring by death.

Setup
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To set up our simulation study, we set the size of our target population as 1 million. We then generate a single baseline variable $V$ from a normal distribution. We set $T=3$ and 