A hidden Markov model addressing measurement errors in the response and replicated covariates for continuous nondecreasing processes

Abstract

Motivated by a study tracking the progression of Parkinson's disease (PD) based on features extracted from voice recordings, an inhomogeneous hidden Markov model with continuous state-space is proposed. The approach addresses the measurement error in the response, the within-subject variability of the replicated covariates and presumed nondecreasing response. A Bayesian framework is described and an efficient Markov chain Monte Carlo method is developed. The model performance is evaluated through a simulation-based example and the analysis of a PD tracking progression dataset is presented. Although the approach was motivated by a PD tracking progression problem, it can be applied to any monotonic nondecreasing process whose continuous response variable is subject to measurement errors and where replicated covariates play a key role.

Keywords: Bayesian methods; Measurement error; Nondecreasing process; Parkinson’s disease; Replicated measurements; Voice features.