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Stat Med. 2016 Apr 30;35(9):1549-57. doi: 10.1002/sim.6861. Epub 2016 Jan 18.

A hidden Markov model approach to analyze longitudinal ternary outcomes when some observed states are possibly misclassified.

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Texas Institute for Measurement, Evaluation, and Statistics and Department of Basic Vision Sciences, College of Optometry, The University of Houston, Houston, TX, 77204, U.S.A.
Department of Biostatistics, The University of Texas Health Science Center at Houston, Houston, TX, 77030, U.S.A.
Department of Biostatistics, The University of Kansas Medical Center, Kansas City, KS, 66160, U.S.A.
Alzheimer's Disease and Memory Disorders Center, Department of Neurology, Baylor College of Medicine, Houston, TX, 77030, U.S.A.


Understanding the dynamic disease process is vital in early detection, diagnosis, and measuring progression. Continuous-time Markov chain (CTMC) methods have been used to estimate state-change intensities but challenges arise when stages are potentially misclassified. We present an analytical likelihood approach where the hidden state is modeled as a three-state CTMC model allowing for some observed states to be possibly misclassified. Covariate effects of the hidden process and misclassification probabilities of the hidden state are estimated without information from a 'gold standard' as comparison. Parameter estimates are obtained using a modified expectation-maximization (EM) algorithm, and identifiability of CTMC estimation is addressed. Simulation studies and an application studying Alzheimer's disease caregiver stress-levels are presented. The method was highly sensitive to detecting true misclassification and did not falsely identify error in the absence of misclassification. In conclusion, we have developed a robust longitudinal method for analyzing categorical outcome data when classification of disease severity stage is uncertain and the purpose is to study the process' transition behavior without a gold standard.


disease progression; hidden Markov model; longitudinal data analysis; misclassification

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