Causal inference with longitudinal outcomes and non-ignorable drop-out: Estimating the effect of living alone on cognitive decline.

In this paper 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 five years. One key feature of the model is the combination of propensity score matching to balance confounding variables between the two living arrangement groups -in order to reduce bias due to unbalanced covariates at baseline, with a pattern mixture model for longitudinal data -in order to deal with non-ignorable drop-out. 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 here adds to previous studies in the literature concerning the protective effect of living with someone, by proposing a modeling approach treating living arrangement as an exposure.