Marginal Bayesian Semiparametric Modeling of Mismeasured Multivariate Interval-Censored Data

Motivated by data gathered in an oral health study, we propose a Bayesian nonparametric approach for population-averaged modeling of correlated time-to-event data, when the responses can only be determined to lie in an interval obtained from a sequence of examination times and the determination of the occurrence of the event is subject to misclassification. The joint model for the true, unobserved time-to-event data is defined semiparametrically; proportional hazards, proportional odds, and accelerated failure time (proportional quantiles) are all fit and compared. The baseline distribution is modeled as a flexible tailfree prior. The joint model is completed by considering a parametric copula function. A general misclassification model is discussed in detail, considering the possibility that different examiners were involved in the assessment of the occurrence of the events for a given subject across time. We provide empirical evidence that the model can be used to estimate the underlying time-to-event distribution and the misclassification parameters without any external information about the latter parameters. We also illustrate the effect on the statistical inferences of neglecting the presence of misclassification. Supplementary materials for this article are available online.