Modeling of Multivariate Monotone Disease Processes in the Presence of Misclassification

Abstract

Motivated by a longitudinal oral health study, the Signal–Tandmobiel® study, we propose a multivariate binary inhomogeneous Markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior. The multivariate baseline distributions and Markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions. Distinct misclassification models are discussed. In all cases, the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account. A full Bayesian implementation of the model is described and its performance is evaluated using simulated data. We provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters. Finally, the analyses of the motivating study are presented. Appendices 1–7 are available in the online supplementary materials.

KEY WORDS:

• Hidden Markov model
• Incidence estimation
• Misclassification
• Monotone binary processes
• Multivariate binary data

Acknowledgments

The first author was supported by the FONDECYT (Fondo Nacional de Desarrollo Cientìífíco y Tecnológico) grant 11110033. The second author was supported by FONDECYT 11100144 grant. The first and the third author were supported by the research grant OT/05/60 and they also acknowledge the partial support from the Interuniversity Attraction Poles (IAP) Program P6/03 of the Federal Office for Scientific, Technical and Cultural Affairs, Belgium. The authors thank Sofía Jara and Garritt Page for proofreading. The authors are grateful to the editor, associate editor, and reviewers for many detailed suggestions and helpful comments, which led to considerable improvement of the article. Data collection was supported by Unilever, Belgium. The Signal–Tandmobiel® study comprises the following partners: D. Declerck (Dental School, Katholieke Universiteit Leuven), L. Martens (Dental School, University of Ghent), J. Vanobbergen (Dental School, University of Ghent), P. Bottenberg (Dental School, University of Brussels), E. Lesaffre (L-BioStat, Katholieke Universiteit Leuven), and K. Hoppenbrouwers (Youth Health Department, Katholieke Universiteit Leuven, and the Flemish Association for Youth Health Care).