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 thesis, we propose a novel Bayesian sensitivity analysis (BSA) model that accounts for the influences of missing outcome data on the estimation of treatment effects in randomized control trials with non-ignorable missing data. We implement the method using the probabilistic programming language Stan, and apply it to data from the Vancouver At Home (VAH) 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 missingness in the outcome. Furthermore, we demonstrate in a simulation study that, when a diffuse conservative prior that describes a range of assumptions about the bias effect is used, BSA credible intervals have greater length and higher coverage rate of the target parameters than existing methods, and that sensitivity increases as the percentage of missingness increases.