Tackling non-ignorable dropout in the presence of time varying confounding

We explore the sensitivity of time varying confounding adjusted estimates to different dropout mechanisms. We extend the Heckman correction to two time points and explore selection models to investigate situations where the dropout process is driven by unobserved variables and the outcome respectively. The analysis is embedded in a Bayesian framework which provides several advantages. These include fitting a hierarchical structure to processes that repeat over time and avoiding exclusion restrictions in the case of the Heckman correction. We adopt the decision theoretic approach to causal inference which makes explicit the no-regime-dropout dependence assumption. We apply our methods to data from the 'Counterweight programme' pilot: a UK protocol to address obesity in primary care. A simulation study is also implemented.