Modeling bivariate longitudinal hormone profiles by hierarchical state space models

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)108-118
Number of pages11
JournalJournal of the American Statistical Association
Volume109
Issue number505
DOIs
StatePublished - 2014

Fingerprint

State-space Model
Hierarchical Model
Hormones
Modeling
Univariate
Posterior Mean
Smoothing Algorithm
Marginal Likelihood
Homeostasis
Kalman Filtering
Space Form
Fatigue
Profile
State-space model
Concurrent
State Space
Relationships
Model-based
Model

Keywords

  • Circadian rhythm
  • Feedback relationship
  • HPA axis
  • Kalman filter
  • Periodic splines

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Modeling bivariate longitudinal hormone profiles by hierarchical state space models. / Liu, Ziyue; Cappola, Anne R.; Crofford, Leslie J.; Guo, Wensheng.

In: Journal of the American Statistical Association, Vol. 109, No. 505, 2014, p. 108-118.

Research output: Contribution to journalArticle

Liu, Ziyue ; Cappola, Anne R. ; Crofford, Leslie J. ; Guo, Wensheng. / Modeling bivariate longitudinal hormone profiles by hierarchical state space models. In: Journal of the American Statistical Association. 2014 ; Vol. 109, No. 505. pp. 108-118.
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