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

Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death