Causal inference with observational longitudinal data is often complicated by time-dependent confounding and attrition. In this project we develop flexible Bayesian semiparametric algorithms for assessing causal effects in a setting with non-ignorable dropout. The approach is to specify models for the observed data using MCMC and Bayesian statistical learning, 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. The properties of the estimators are evaluated in simulation studies that approximate the sampling distribution.