Hidden Markov Models for Longitudinal Comparisons

• Published in: Journal of the American Statistical Association Vol. 100; no. 470; pp. 359 - 369
• Main Authors: Scott, Steven L, James, Gareth M, Sugar, Catherine A
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2005; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Applications and Case Studies; Biology, psychology, social sciences; Comparative studies; Effectiveness studies; Exact sciences and technology; Health state model; Hierarchical model; Inhomogeneous hidden Markov Model; k-means clustering; Markov analysis; Markov chain Monte Carlo; Markov chains; Markov models; Mathematics; Medical sciences; Medications; Metropolitan areas; Multivariate analysis; Parameter estimation; Parametric models; Polytopes; Probability and statistics; Probability theory and stochastic processes; Psychotropic drugs; Schizophrenia; Sciences and techniques of general use; Side effects; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistical variance; Statistics; Tardive dyskinesia; Tranquilizers; Transition probabilities; Homogeneous model; Parameter estimation; Uncertainty; Conditional distribution; Methodology; Cluster analysis (statistics); Shrinkage estimator; Schizophrenia; Probability distribution; Multivariate analysis; k-means clustering; MCMC algorithm; Markov chain Monte Carlo; Transition probability; Health state model; Bayes estimation; Inhomogeneous hidden Markov model; State space method; Statistical method; Health state; Hidden Markov models; Transition state; Homogeneity; Hidden Markov model; Hierarchical model
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214504000001592

Medical researchers interested in temporal, multivariate measurements of complex diseases have recently begun developing health state models, which divide the space of patient characteristics into medically distinct clusters. The current state of the art in health services research uses k-means clustering to form the health states and a first-order Markov chain to describe transitions between the states. This fitting procedure ignores information from temporally adjacent observations and prevents uncertainty from parameter estimation and cluster assignments from being incorporated into the analysis. A natural way to address these issues is to combine clustering and longitudinal analyses using a hidden Markov model. We fit hidden Markov models to longitudinal data using Bayesian methods that account for all of the uncertainty in the parameters, conditional only on the underlying correctness of the model. Potential lack of time homogeneity in the Markov chain is accounted for by embedding transition probabilities into a hierarchical model that provides Bayesian shrinkage across time. We illustrate this approach by developing a hidden Markov health state model for comparing the effectiveness of clozapine and haloperidol, two antipsychotic medications for schizophrenia. We find that clozapine outperforms haloperidol and identify the types of patients in whom clozapine's advantage is greatest and weakest. Finally, we discuss the advantages and disadvantages of hidden Markov models in comparison with the current methodology.