Modeling diurnal hormone profiles by hierarchical state space models

Adrenocorticotropic hormone (ACTH) diurnal patterns contain both smooth circadian rhythms and pulsatile activities. How to evaluate and compare them between different groups is a challenging statistical task. In particular, we are interested in testing (1) whether the smooth ACTH circadian rhythms in chronic fatigue syndrome and fibromyalgia patients differ from those in healthy controls and (2) whether the patterns of pulsatile activities are different. In this paper, a hierarchical state space model is proposed to extract these signals from noisy observations. The smooth circadian rhythms shared by a group of subjects are modeled by periodic smoothing splines. The subject level pulsatile activities are modeled by autoregressive processes. A functional random effect is adopted at the pair level to account for the matched pair design. Parameters are estimated by maximizing the marginal likelihood. Signals are extracted as posterior means. Computationally efficient Kalman filter algorithms are adopted for implementation. Application of the proposed model reveals that the smooth circadian rhythms are similar in the two groups but the pulsatile activities in patients are weaker than those in the healthy controls.

[1]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[2]  David A. Harville,et al.  Best Linear Recursive Estimation for Mixed Linear Models , 1981 .

[3]  Stanley R. Johnson,et al.  Varying Coefficient Models , 1984 .

[4]  G. Wahba.  Bayesian "Confidence Intervals" for the Cross-validated Smoothing Spline , 1983 .

[5]  Siem Jan Koopman,et al.  Structural Time Series Models , 2005 .

[6]  J. Lalonde,et al.  Distribution and metabolism of adrenocorticotropin in the rat. , 1979, Canadian journal of physiology and pharmacology.

[7]  J. Cowan,et al.  Feedback suppression of ACTH secretion by cortisol in dogs: lags after large signals equal those following very small signals. , 1983, Canadian journal of physiology and pharmacology.

[8]  Ellen Frank,et al.  Chronic stress, glucocorticoid receptor resistance, inflammation, and disease risk , 2012, Proceedings of the National Academy of Sciences.

[9]  Tom Heskes,et al.  Learning and approximate inference in dynamic hierarchical models , 2007, Comput. Stat. Data Anal..

[10]  T. Johnson.  Analysis of Pulsatile Hormone Concentration Profiles with Nonconstant Basal Concentration: A Bayesian Approach , 2007, Biometrics.

[11]  A comparison of methods that characterize pulses in a time series. , 1995, Statistics in medicine.

[12]  Siem Jan Koopman,et al.  Filtering and Smoothing of State Vector for Diffuse State-Space Models , 2001 .

[13]  Hulin Wu,et al.  Mixed‐Effects State‐Space Models for Analysis of Longitudinal Dynamic Systems , 2011, Biometrics.

[14]  D. B. Duncan,et al.  Linear Dynamic Recursive Estimation from the Viewpoint of Regression Analysis , 1972 .

[15]  Yuedong Wang.  Smoothing Spline Models with Correlated Random Errors , 1998 .

[16]  Andrew Harvey,et al.  10 Structural time series models , 1993 .

[17]  M L Johnson,et al.  Amplitude modulation of a burstlike mode of cortisol secretion subserves the circadian glucocorticoid rhythm. , 1989, The American journal of physiology.

[18]  Nichole E Carlson,et al.  Twenty-Four-Hour ACTH and Cortisol Pulsatility in Depressed Women , 2001, Neuropsychopharmacology.

[19]  D. Buskila,et al.  Neuroendocrine mechanisms in fibromyalgia-chronic fatigue. , 2001, Best practice & research. Clinical rheumatology.

[20]  Jeffrey S. Morris,et al.  Wavelet‐based functional mixed models , 2006, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[21]  M. B. Brown,et al.  A flexible model for human circadian rhythms. , 1996, Biometrics.

[22]  L. Arnold.  The pathophysiology, diagnosis and treatment of fibromyalgia. , 2010, The Psychiatric clinics of North America.

[23]  Yuedong Wang,et al.  A Signal Extraction Approach to Modeling Hormone Time Series with Pulses and a Changing Baseline , 1999 .

[24]  C. Ansley,et al.  The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing , 1983 .

[25]  Michael A. West,et al.  Time Series: Modeling, Computation, and Inference , 2010 .

[26]  D. Harville.  Bayesian inference for variance components using only error contrasts , 1974 .

[27]  Yuedong Wang,et al.  Shape‐Invariant Modeling of Circadian Rhythms with Random Effects and Smoothing Spline ANOVA Decompositions , 2003, Biometrics.

[28]  John R. Terry,et al.  Encoding and Decoding Mechanisms of Pulsatile Hormone Secretion , 2010, Journal of neuroendocrinology.

[29]  A. Cleare.  The HPA axis and the genesis of chronic fatigue syndrome , 2004, Trends in Endocrinology & Metabolism.

[30]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

[31]  Jessika Weiss.  Longitudinal Data With Serial Correlation A State Space Approach , 2016 .

[32]  James F. Jones,et al.  Prevalence of chronic fatigue syndrome in metropolitan, urban, and rural Georgia , 2007, Population health metrics.

[33]  Wensheng Guo,et al.  Functional mixed effects models , 2012, Biometrics.

[34]  Wensheng Guo,et al.  Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models , 2014, Journal of the American Statistical Association.

[35]  Yuedong Wang,et al.  Detecting Pulsatile Hormone Secretions Using Nonlinear Mixed Effects Partial Spline Models , 2006, Biometrics.

[36]  Anthony J. Cleare,et al.  Hypothalamic–pituitary–adrenal axis dysfunction in chronic fatigue syndrome , 2012, Nature Reviews Endocrinology.

[37]  Sumeetpal S. Singh,et al.  Particle approximations of the score and observed information matrix in state space models with application to parameter estimation , 2011 .

[38]  M. Payet,et al.  Mechanism of action of ACTH: Beyond cAMP , 2003, Microscopy research and technique.

[39]  N. Shephard,et al.  Exact score for time series models in state space form , 1992 .

[40]  L. Qin,et al.  Functional mixed-effects model for periodic data. , 2005, Biostatistics.

[41]  R. Kohn,et al.  Nonparametric spline regression with prior information , 1993 .

[42]  Siem Jan Koopman,et al.  Time Series Analysis by State Space Methods , 2001 .

[43]  Wensheng Guo.  Functional Mixed Effects Models , 2002 .

[44]  S. Wessely,et al.  The neuroendocrinology of chronic fatigue syndrome and fibromyalgia , 2001, Psychological Medicine.

[45]  B. Goodman,et al.  Coincident plasma ACTH and corticosterone time series: Comparisons between young and old rats , 1994, Experimental Gerontology.

[46]  D. Gamerman,et al.  Dynamic Hierarchical Models , 1993 .

[47]  Leslie A. McClure,et al.  Basal circadian and pulsatile ACTH and cortisol secretion in patients with fibromyalgia and/or chronic fatigue syndrome , 2004, Brain, Behavior, and Immunity.

[48]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[49]  A. Hanukoglu,et al.  Mechanism of corticotropin and cAMP induction of mitochondrial cytochrome P450 system enzymes in adrenal cortex cells. , 1990, The Journal of biological chemistry.

[50]  R. Kohn,et al.  Estimation, Filtering, and Smoothing in State Space Models with Incompletely Specified Initial Conditions , 1985 .