Causal inference with longitudinal outcomes and non-ignorable dropout: estimating the effect of living alone on cognitive decline

type="main" xml:id="rssc12110-abs-0001"> We develop a model to estimate the causal effect of living arrangement (living alone versus living with someone) on cognitive decline based on a 15-year prospective cohort study, where episodic memory function is measured every 5 years. One key feature of the model is the combination of propensity score matching to balance confounding variables between the two living arrangement groups—to reduce bias due to unbalanced covariates at baseline, with a pattern–mixture model for longitudinal data—to deal with non-ignorable dropout. A fully Bayesian approach allows us to convey the uncertainty in the estimation of the propensity score and subsequent matching in the inference of the causal effect of interest. The analysis conducted adds to previous studies in the literature concerning the protective effect of living with someone, by proposing a modelling approach treating living arrangement as an exposure.