Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models

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 longitudin...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 109; no. 505; pp. 108 - 118
Main Authors: Liu, Ziyue, Cappola, Anne R., Crofford, Leslie J., Guo, Wensheng
Format: Journal Article
Language:English
Published: United States Taylor & Francis 2014
Taylor & Francis Group, LLC
Taylor & Francis Ltd
Subjects:
Algorithms
Applications and Case Studies
Brain
Chronic fatigue syndrome
Circadian rhythm
Complexity
Coping
corticotropin
Cortisol
Data smoothing
Disease models
Feedback
Feedback relationship
Fibromyalgia
Hierarchies
Homeostasis
Hormones
HPA axis
Hypothalamic-pituitary-adrenal axis
Inference
Kalman filter
Kalman filters
Multilevel models
Nonparametric models
patients
Periodic splines
Profiles
Statistical discrepancies
Statistics
Stress
Time series analysis
Time series models
Feedback Relationship
HPA axis
Periodic splines
Circadian rhythm
Kalman filter
ISSN:1537-274X, 0162-1459, 1537-274X
Online Access:Get full text
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Summary: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.
Bibliography:http://dx.doi.org/10.1080/01621459.2013.830071
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ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2013.830071