at random assumption, worked well in situations where the non-linear main and interaction effects are complex for the mean and propensity model. For situations with simpler non-linear effects like a quadratic relationship, using BART to estimate the propensity score and imputing the missing values using penalized splines of propensity prediction [@zhang_little PENCOMP version for missing data] worked better. Using PENCOMP with a BART estimated propensity score for Steps 4 and 8 would be an interesting alternative. However, our aim of Steps 4 and 8 was to ease the implementation burden on the researcher. Hence, we suggest the use of PENCOMP with a BART estimated propensity score for Steps 4 and 8 only if the researcher is certain that the non-linear effect has a simple form for example, a quadratic or cubic relationship.

Simulation
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We conducted a simulation study to determine how well our proposed method would perform compared to the naïve method and MSM in three scenarios: 1) where there is low association between treatment allocation and confounder as well as treatment and survival status; 2) where there is a strong association between treatment and confounder as well as treatment and survival status; and finally 3) where there is 