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.

[1]  L. Baum,et al.  A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains , 1970 .

[2]  R. Rosychuk,et al.  Comparison of variance estimation approaches in a two‐state Markov model for longitudinal data with misclassification , 2006, Statistics in medicine.

[3]  Ardo van den Hout,et al.  Multi‐state analysis of cognitive ability data: A piecewise‐constant model and a Weibull model , 2008, Statistics in medicine.

[4]  D. Pfeffermann,et al.  The estimation of gross flows in the presence of measurement error using auxiliary variables , 1998 .

[5]  S. Folstein,et al.  "Mini-mental state". A practical method for grading the cognitive state of patients for the clinician. , 1975, Journal of psychiatric research.

[6]  Wenyaw Chan,et al.  A CONTINUOUS-TIME MARKOV CHAIN APPROACH ANALYZING THE STAGES OF CHANGE CONSTRUCT FROM A HEALTH PROMOTION INTERVENTION. , 2010, JP journal of biostatistics.

[7]  Jing Zhang,et al.  ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS , 2005 .

[8]  W. Chan,et al.  Changing Patient Characteristics and Survival Experience in an Alzheimer’s Center Patient Cohort , 2005, Dementia and Geriatric Cognitive Disorders.

[9]  A. Petkau,et al.  Application of hidden Markov models to multiple sclerosis lesion count data , 2005, Statistics in medicine.

[10]  A semi‐Markov model for binary longitudinal responses subject to misclassification , 2001 .

[11]  F. Carrat,et al.  Monitoring epidemiologic surveillance data using hidden Markov models. , 1999, Statistics in medicine.

[12]  Simon G. Thompson,et al.  Multistate Markov models for disease progression with classification error , 2003 .

[13]  W. Chan,et al.  Analysis of Longitudinal Multinomial Outcome Data , 2006, Biometrical journal. Biometrische Zeitschrift.

[14]  Penelope Vounatsou,et al.  Estimation of infection and recovery rates for highly polymorphic parasites when detectability is imperfect, using hidden Markov models , 2003, Statistics in medicine.

[15]  M. Folstein,et al.  Clinical diagnosis of Alzheimer's disease , 1984, Neurology.

[16]  M. Kataki,et al.  A Method for Estimating Duration of Illness in Alzheimer’s Disease , 2003, Dementia and Geriatric Cognitive Disorders.

[17]  Alexandre Bureau,et al.  Applications of continuous time hidden Markov models to the study of misclassified disease outcomes , 2003, Statistics in medicine.

[18]  Hung-Wen Yeh,et al.  Intermittent Missing Observations in Discrete-Time Hidden Markov Models , 2012, Commun. Stat. Simul. Comput..

[19]  Baojiang Chen,et al.  Analysis of interval‐censored disease progression data via multi‐state models under a nonignorable inspection process , 2010, Statistics in medicine.

[20]  Momiao Xiong,et al.  Analysis of transtheoretical model of health behavioral changes in a nutrition intervention study—a continuous time Markov chain model with Bayesian approach , 2015, Statistics in medicine.