Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 6, November 2017, Pages: 290-296
Received: Oct. 4, 2017; Accepted: Oct. 28, 2017; Published: Dec. 7, 2017
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Yosuke Inaba, Department of Data Science, National Center for Global Health and Medicine, Tokyo, Japan; Department of Mathematical Science for Information Science, Tokyo University of Science, Tokyo, Japan
Asanao Shimokawa, Department of Mathematics, Tokyo University of Science, Tokyo, Japan
Etsuo Miyaoka, Department of Mathematics, Tokyo University of Science, Tokyo, Japan
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A hidden Markov model (HMM) is a method for analyzing a sequence of transitions for a set of data by considering the outcomes Y to be output from latent state X, which has the Markov property. The HMM has been widely applied, with applications that include speech recognition, genomic analysis, and finance forecasting. The HMM was originally a method for dealing with single-process data. Thus, it is a natural extension to apply it to data with a repeated measure structure by incorporating random effects in it. This is called the mixed hidden Markov model (MHMM). With this extension, the MHMM was recently applied to clinical research data with repeated measurements, e.g. multiple sclerosis, alcohol consumption, and primary biliary cirrhosis. In relation to parameter inference, because regular HMM methods can be used in an MHMM framework, some legacy knowledge is applicable. The likelihood can be obtained by simply adding a random effect parameter to a single process HMM, and the conventional maximum-likelihood method can be used for parameter estimation. On the other hand, much work must still be performed. For instance, the mathematical property of the maximum likelihood estimator has not yet been thoroughly examined. In this study, the asymptotic normality and consistency of the maximum likelihood estimator of the MHMM concerned with time points are examined via simulation, and found that these properties were almost fine. These methods are applied to actual study data, and future perspectives are provided in the conclusion.
Hidden Markov Models, Random Effects, Gaussian Quadrature, Newton–Raphson Method, Epilepsy Data, Poisson Distribution, Count Data
To cite this article
Yosuke Inaba, Asanao Shimokawa, Etsuo Miyaoka, Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 6, 2017, pp. 290-296. doi: 10.11648/j.ajtas.20170606.15
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