Hidden Markov Models for Longitudinal Comparisons

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 which account for all 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 where clozapine’s advantage is greatest and weakest. Finally, we discuss the advantages and disadvantages of hidden Markov models in comparison with the current methodology. Key Words: inhomogeneous hidden Markov model, Markov chain Monte Carlo, health state model, k-means clustering, hierarchical model