similar to that of continuous outcomes but with the use of data augmentation methods, i.e. draw a continuous latent variable based on whether $Y=1$ or $Y=0$ and then run the BART algorithm on the drawn latent variables.

[@kapelner_miss] suggested a procedure to allow the BART algorithm to include covariates that might contain missing values. In brief, the missingness in the covariates are not imputed but instead, viewed as a ‘value level’ in the MCMC algorithm. The MCMC algorithm then ‘sends’ missing data to terminal nodes in the regression trees that would maximize the likelihood. This is termed as “Missing Incorporated in Attributes” [MIA, @twala Section 2]. [@kapelner_miss] showed using simulation examples that incorporating MIA within BART allows the appropriate handling of different types of missing mechanism, MCAR, MAR, and NMAR, for each covariate. We utilize this approach to accommodate the missingness in our covariates for the data analysis.

Dealing with Censoring by Death {#chap3:method}
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Determining the principal strata
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To determine the principal strata definition, we first investigated what the data for our problem could potentially look like. We constructed Table \[chap3:eg2\_1\] for $t=3$, $p=1$, and no time-varying covariates without loss of generality. In this table, ‘x’ indicates an 