Bayesian Sensitivity Analysis for Non-ignorable Missing Data in Longitudinal Studies

The use of Bayesian statistical methods to handle missing data in biomedical studies has become popular in recent years. In this paper, we propose a novel Bayesian sensitivity analysis (BSA) technique that accounts for the influences of missing outcome data on the estimation of treatment effects in longitudinal studies with non-ignorable missing data. The approach uses a pattern-mixture model for the complete data, which is indexed by non-identifiable sensitivity parameters that accounts for the effect of missingness on the observations. We implement the method using the probabilistic programming language Stan, and apply it to data from the Vancouver At Home Study, which is a randomized control trial that provided housing to homeless people with mental illness. We compare the results of BSA to those from an existing Bayesian longitudinal model that ignores the missing data mechanism in the outcome. Furthermore, we demonstrate in a simulation study that when we use a diffuse conservative prior that describes a range of assumptions about the non-ignorable missingness, then BSA credible intervals have greater length and higher coverage rate of the target parameters than existing methods.