Mk. Cowles et al., BAYESIAN TOBIT MODELING OF LONGITUDINAL ORDINAL CLINICAL-TRIAL COMPLIANCE DATA WITH NONIGNORABLE MISSINGNESS, Journal of the American Statistical Association, 91(433), 1996, pp. 86-98
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.