estimates. For MSM and our proposed method, the models were specified using Equations \[chap3:ztime1\] to \[chap3:ytime3\] respectively. For our proposed method, because our focus is not on model misspecification but rather, confounding by indication and censoring by death, we chose to implement a simpler version of our method by skipping Steps 3 and 7 of our algorithm and using $Y_{z_1^{(b)}}^{(b)}|Z_1^{(b)}=z_1^{(b)},X_{z_1^{(b)}}^{(b)},W_1^{(b)},V^{(b)}$ and $Y_{z_1^{(b)},z_2^{(b)}}^{(b)}|Z_1^{(b)}=z_1^{(b)},Z_2^{(b)}=z_2^{(b)},Y_{z_1^{(b)}}^{(b)},X_{z_1^{(b)}}^{(b)},X_{z_1^{(b)},z_2^{(b)}}^{(b)},W_1^{(b)},W_2^{(b)},V^{(b)}$ for Steps 4 and 8 respectively. We also simplified the prediction of the potential outcomes and survival status by using linear and logistic regression instead of BART.

Results
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Table \[chap3:sim\_res1\] shows the simulation results for sample size of 4,000. As expected, under Scenario 1, all three methods were relatively unbiased with all three methods achieving similar RMSE. MSM and our proposed method reported slightly greater than nominal coverage due to the wider AIL. Under Scenario 2, the absolute bias of the naïve method was always larger than MSM and our proposed method. RMSE was larger as well in comparison and coverage was often far below the nominal 95% value. For this scenario MSM produced the less conservative coverage while our proposed method suggested better bias performance and reduced RMSE. Finally, under Scenario 3, the naïve method was 