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Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models

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  • Ziyue Liu
  • Anne R. Cappola
  • Leslie J. Crofford
  • Wensheng Guo

Abstract

The hypothalamic-pituitary-adrenal (HPA) axis is crucial in coping with stress and maintaining homeostasis. Hormones produced by the HPA axis exhibit both complex univariate longitudinal profiles and complex relationships among different hormones. Consequently, modeling these multivariate longitudinal hormone profiles is a challenging task. In this article, we propose a bivariate hierarchical state space model, in which each hormone profile is modeled by a hierarchical state space model, with both population-average and subject-specific components. The bivariate model is constructed by concatenating the univariate models based on the hypothesized relationship. Because of the flexible framework of state space form, the resultant models not only can handle complex individual profiles, but also can incorporate complex relationships between two hormones, including both concurrent and feedback relationship. Estimation and inference are based on marginal likelihood and posterior means and variances. Computationally efficient Kalman filtering and smoothing algorithms are used for implementation. Application of the proposed method to a study of chronic fatigue syndrome and fibromyalgia reveals that the relationships between adrenocorticotropic hormone and cortisol in the patient group are weaker than in healthy controls. Supplementary materials for this article are available online.

Suggested Citation

  • Ziyue Liu & Anne R. Cappola & Leslie J. Crofford & Wensheng Guo, 2014. "Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 108-118, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:108-118
    DOI: 10.1080/01621459.2013.830071
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    References listed on IDEAS

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    1. Wensheng Guo, 2002. "Functional Mixed Effects Models," Biometrics, The International Biometric Society, vol. 58(1), pages 121-128, March.
    2. Honghu Liu & Yan Zheng & Jie Shen, 2008. "Goodness-of-fit measures of R2 for repeated measures mixed effect models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1081-1092.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    4. Dunson, David B., 2003. "Dynamic Latent Trait Models for Multidimensional Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 555-563, January.
    5. S. J. Koopman & J. Durbin, 2003. "Filtering and smoothing of state vector for diffuse state‐space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 85-98, January.
    6. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    7. Jason Roy & Xihong Lin, 2000. "Latent Variable Models for Longitudinal Data with Multiple Continuous Outcomes," Biometrics, The International Biometric Society, vol. 56(4), pages 1047-1054, December.
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