Statistical Modelling 22 (5) (2022), 385–408

A mixed hidden Markov model for multivariate monotone disease processes in the presence of measurement errors

Lizbeth Naranjo,
Departamento de Matemáticas,
Facultad de Ciencias,
Universidad Nacional Autónoma de México,
Ciudad de México,
Mexico.
e-mail: lizbethna@ciencias.unam.mx

Emmanuel Lesaffre,
L-BioStat,
School of Public Health,
KU Leuven,
Leuven,
Belgium.

Carlos J. Pérez,
Departamento de Matemáticas,
Universidad de Extremadura,
Cáceres,
Spain.

Abstract:

Motivated by a longitudinal oral health study, the Signal-Tandmobiel® study, an inhomogeneous mixed hidden Markov model with continuous state-space is proposed to explain the caries disease process in children between 6 and 12 years of age. The binary caries experience outcomes are subject to misclassification. We modelled this misclassification process via a longitudinal latent continuous response subject to a measurement error process and showing a monotone behaviour. The baseline distributions of the unobservable continuous processes are defined as a function of the covariates through the specification of conditional distributions making use of the Markov property. In addition, random effects are considered to model the relationships among the multivariate responses. Our approach is in contrast with a previous approach working on the binary outcome scale. This method requires conditional independence of the possibly corrupted binary outcomes on the true binary outcomes. We assumed conditional independence on the latent scale, which is a weaker assumption than conditional independence on the binary scale. The aim of this article is therefore to show the properties of a model for a progressive longitudinal response with misclassification on the manifest scale but modelled on the latent scale. The model parameters are estimated in a Bayesian way using an efficient Markov chain Monte Carlo method. The model performance is shown through a simulation-based example, and the analysis of the motivating dataset is presented.

Keywords:

Bayesian analysis, conditional independence, measurement error, misclassification, mixed hidden Markov model, monotone continuous process

Downloads:

R Code in zipped archive and Supplementary material.

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