  Causal inference with observational longitudinal data and time-varying
exposures is often complicated by time-dependent confounding and attrition. The
G-computation formula is one approach for estimating a causal effect in this
setting. The parametric modeling approach typically used in practice relies on
strong modeling assumptions for valid inference, and moreover depends on an
assumption of missing at random, which is not appropriate when the missingness
is missing not at random (MNAR) or due to death. In this work we develop a
flexible Bayesian semi-parametric G-computation approach for assessing the
causal effect on the subpopulation that would survive irrespective of exposure,
in a setting with MNAR dropout. The approach is to specify models for the
observed data using Bayesian additive regression trees, and then use
assumptions with embedded sensitivity parameters to identify and estimate the
causal effect. The proposed approach is motivated by a longitudinal cohort
study on cognition, health, and aging, and we apply our approach to study the
effect of becoming a widow on memory. We also compare our approach to several
standard methods.
