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Partially Ordered Mixed Hidden Markov Model for the Disablement Process of Older Adults

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  • Edward Ip
  • Qiang Zhang
  • Jack Rejeski
  • Tammy Harris
  • Stephen Kritchevsky

Abstract

At both the individual and societal levels, the health and economic burden of disability in older adults is enormous in developed countries, including the U.S. Recent studies have revealed that the disablement process in older adults often comprises episodic periods of impaired functioning and periods that are relatively free of disability, amid a secular and natural trend of decline in functioning. Rather than an irreversible, progressive event that is analogous to a chronic disease, disability is better conceptualized and mathematically modeled as states that do not necessarily follow a strict linear order of good to bad. Statistical tools, including Markov models, which allow bidirectional transition between states, and random effects models, which allow individual-specific rate of secular decline, are pertinent. In this article, we propose a mixed effects, multivariate, hidden Markov model to handle partially ordered disability states. The model generalizes the continuation ratio model for ordinal data in the generalized linear model literature and provides a formal framework for testing the effects of risk factors and/or an intervention on the transitions between different disability states. Under a generalization of the proportional odds ratio assumption, the proposed model circumvents the problem of a potentially large number of parameters when the number of states and the number of covariates are substantial. We describe a maximum likelihood method for estimating the partially ordered, mixed effects model and show how the model can be applied to a longitudinal dataset that consists of N = 2903 older adults followed for 10 years in the Health Aging and Body Composition Study. We further statistically test the effects of various risk factors upon the probabilities of transition into various severe disability states. The result can be used to inform geriatric and public health science researchers who study the disablement process. Supplementary materials for this article are available online.

Suggested Citation

  • Edward Ip & Qiang Zhang & Jack Rejeski & Tammy Harris & Stephen Kritchevsky, 2013. "Partially Ordered Mixed Hidden Markov Model for the Disablement Process of Older Adults," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 370-384, June.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:370-384
    DOI: 10.1080/01621459.2013.770307
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    References listed on IDEAS

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    7. Edward H. Ip & Alison Snow Jones & D. Alex Heckert & Qiang Zhang & Edward D. Gondolf, 2010. "Latent Markov Model for Analyzing Temporal Configuration for Violence Profiles and Trajectories in a Sample of Batterers," Sociological Methods & Research, , vol. 39(2), pages 222-255, November.
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    Cited by:

    1. Xinyuan Song & Yemao Xia & Hongtu Zhu, 2017. "Hidden Markov latent variable models with multivariate longitudinal data," Biometrics, The International Biometric Society, vol. 73(1), pages 313-323, March.
    2. Francesco Bartolucci & Alessio Farcomeni, 2015. "A discrete time event-history approach to informative drop-out in mixed latent Markov models with covariates," Biometrics, The International Biometric Society, vol. 71(1), pages 80-89, March.
    3. Liu, Hefei & Song, Xinyuan & Zhang, Baoxue, 2022. "Varying-coefficient hidden Markov models with zero-effect regions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    4. Lin, Yiqi & Song, Xinyuan, 2022. "Order selection for regression-based hidden Markov model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    5. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2016. "Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 146-179, April.
    6. Sabina B. Gesell & Kayla de la Haye & Evan C. Sommer & Santiago J. Saldana & Shari L. Barkin & Edward H. Ip, 2020. "Identifying Social Network Conditions that Facilitate Sedentary Behavior Change: The Benefit of Being a “Bridge” in a Group-based Intervention," IJERPH, MDPI, vol. 17(12), pages 1-13, June.
    7. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 457-485, June.
    8. Zhou, Jie & Song, Xinyuan & Sun, Liuquan, 2020. "Continuous time hidden Markov model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).

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