Correcting for misclassification for a monotone disease process with an application in dental research

Motivated by a longitudinal oral health study, we evaluate the performance of binary Markov models in which the response variable is subject to an unconstrained misclassification process and follows a monotone or progressive behavior. Theoretical and empirical arguments show that the simple version of the model can be used to estimate the prevalence, incidences, and misclassification parameters without the need of external information and that the incidence estimators associated with the model outperformed approaches previously proposed in the literature. We propose an extension of the simple version of the binary Markov model to describe the relationship between the covariates and the prevalence and incidence allowing for different classifiers. We implemented a Bayesian version of the extended model and show that, under the settings of our motivating example, the parameters can be estimated without any external information. Finally, the analyses of the motivating problem are presented.