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

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. Copyright © 2016 John Wiley & Sons, Ltd.