American Journal of Theoretical and Applied Statistics

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Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements

Received: 04 October 2017    Accepted: 28 October 2017    Published: 07 December 2017
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Abstract

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.

DOI 10.11648/j.ajtas.20170606.15
Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6, November 2017)
Page(s) 290-296
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hidden Markov Models, Random Effects, Gaussian Quadrature, Newton–Raphson Method, Epilepsy Data, Poisson Distribution, Count Data

References
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Author Information
  • 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

  • Department of Mathematics, Tokyo University of Science, Tokyo, Japan

  • Department of Mathematics, Tokyo University of Science, Tokyo, Japan

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    Yosuke Inaba, Asanao Shimokawa, Etsuo Miyaoka. (2017). Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements. American Journal of Theoretical and Applied Statistics, 6(6), 290-296. https://doi.org/10.11648/j.ajtas.20170606.15

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    ACS Style

    Yosuke Inaba; Asanao Shimokawa; Etsuo Miyaoka. Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements. Am. J. Theor. Appl. Stat. 2017, 6(6), 290-296. doi: 10.11648/j.ajtas.20170606.15

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    AMA Style

    Yosuke Inaba, Asanao Shimokawa, Etsuo Miyaoka. Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements. Am J Theor Appl Stat. 2017;6(6):290-296. doi: 10.11648/j.ajtas.20170606.15

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  • @article{10.11648/j.ajtas.20170606.15,
      author = {Yosuke Inaba and Asanao Shimokawa and Etsuo Miyaoka},
      title = {Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {6},
      pages = {290-296},
      doi = {10.11648/j.ajtas.20170606.15},
      url = {https://doi.org/10.11648/j.ajtas.20170606.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20170606.15},
      abstract = {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.},
     year = {2017}
    }
    

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    T1  - Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements
    AU  - Yosuke Inaba
    AU  - Asanao Shimokawa
    AU  - Etsuo Miyaoka
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    DO  - 10.11648/j.ajtas.20170606.15
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    EP  - 296
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajtas.20170606.15
    AB  - 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.
    VL  - 6
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    ER  - 

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