Bayesian methods for nonignorable dropout in joint models in smoking cessation studies

Inference on data with missingness can be challenging, particularly if the knowledge that a measurement was unobserved provides information about its distribution. Our work is motivated by the Commit to Quit II study, a smoking cessation trial that measured smoking status and weight change as weekly outcomes. It is expected that dropout in this study was informative and that patients with missed measurements are more likely to be smoking, even after conditioning on their observed smoking and weight history. We jointly model the categorical smoking status and continuous weight change outcomes by assuming normal latent variables for cessation and by extending the usual pattern mixture model to the bivariate case. The model includes a novel approach to sharing information across patterns through a Bayesian shrinkage framework to improve estimation stability for sparsely observed patterns. To accommodate the presumed informativeness of the missing data in a parsimonious manner, we model the unidentified components of the model under a non-future dependence assumption and specify departures from missing at random through sensitivity parameters, whose distributions are elicited from a subject-matter expert.