BAYESIAN TOBIT MODELING OF LONGITUDINAL ORDINAL CLINICAL-TRIAL COMPLIANCE DATA WITH NONIGNORABLE MISSINGNESS

In the Lung Health Study (LHS), compliance with the use of inhaled med ication was assessed at each follow-up visit both by self-report and b y weighing the used medication canisters. One or both of these assessm ents were missing if the participant failed to attend the visit or to return all canisters. Approximately 30% of canister-weight data and 5% to 15% of self-report data were missing at different visits. We use G ibbs sampling with data augmentation and a multivariate Hastings updat e step to implement a Bayesian hierarchical model for LHS inhaler comp liance. Incorporating individual-level random effects to account for c orrelations among repeated measures on the same participant, our model is a longitudinal extension of the Tobit models used in econometrics to deal with partially unobservable data. It enables (a) assessment of the relationships among visit attendance, canister return, self-repor ted compliance level, and canister weight compliance, and (b) determin ation of demographic, physiological, and behavioral predictors of comp liance. In addition to addressing the estimation and prediction questi ons of substantive interest, we use sampling-based methods for covaria te screening and model selection and investigate a range of informativ e priors on missing data.