Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models

REFERENCES

• Ansley, C.F., and Kohn, R. (1985), “Estimation, Filtering and Smoothing in State Space Models With Incomplete Specified Initial Conditions,” The Annals of Statistics, 13, 1286–1316.
   Web of Science ®Google Scholar
• Ansley, C.F., Kohn, R., and Wong, C.M. (1993), “Nonparametric Spline Regression With Prior Information,” Biometrika, 80, 75–88.
   Web of Science ®Google Scholar
• Arnold, L.M. (2010), “The Pathophysiology, Diagnosis and Treatment of Fibromyalgia,” Psychiatric Clinics of North America, 33, 375–408.
   PubMed Web of Science ®Google Scholar
• Aschbacher, K., Adam, E.K., Crofford, L.J., Kemeny, M.E., Demitrack, M.A., and Ben-Zvi, A. (2012), “Linking Disease Symptoms and Subtypes With Personalized Systems-Based Phenotypes: A Proof of Concept Study,” Brain, Behavior, and Immunity, 26, 1047–1056.
   PubMed Web of Science ®Google Scholar
• Box, G. E.P., Jenkins, G.M., and Reinsel, G.C. (2008), Time Series Analysis: Forecasting and Control (4th ed.), Hoboken, NJ: Wiley.
   Google Scholar
• Carlson, N.E., Johnson, T.D., and Brown, M.B. (2009), “A Bayesian Approach to Modeling Associations Between Pulsatile Hormones,” Biometrics, 65, 650–659.
   PubMed Web of Science ®Google Scholar
• Crofford, L.J., Young, E.A., Engleberg, N.C., Korszun, A., Brucksch, C.B., McClure, L.A., Brown, M.B., and Demitrack, M.A. (2004), “Basal Circadian and Pulsatile ACTH and Cortisol Secretion in Patients With Fibromyalgia and/or Chronic Fatigue Syndrome,” Brain, Behavior, and Immunity, 18, 314–325.
   PubMed Web of Science ®Google Scholar
• Dunson, D.B. (2003), “Dynamic Latent Trait Models for Multidimensional Longitudinal Data,” Journal of the American Statistical Association, 98, 555–563.
   Web of Science ®Google Scholar
• Durbin, J., and Koopman, S.J. (2012), Time Series Analysis by State Space Methods (2nd ed.), Oxford, UK: Oxford University Press.
   Google Scholar
• Fieuws, S., and Verbeke, G. (2004), “Joint Modelling of Multivariate Longitudinal Profiles: Pitfalls of the Random-Effects Approach,” Statistics in Medicine, 23, 3093–3104.
   PubMed Web of Science ®Google Scholar
• Fink, G., Pfaff, D.W., and Levine, J. E. (eds.) (2012), Handbook of Neuroendocrinology (1st ed.), London: Academic Press.
   Google Scholar
• Funatogawa, I., Funatogawa, T., and Ohashi, Y. (2008), “A Bivariate Autoregressive Linear Mixed Effects Model for the Analysis of Longitudinal Data,” Statistics in Medicine, 27, 6367–6378.
   PubMed Web of Science ®Google Scholar
• Gordon, N., Salmond, D.J., and Smith, A. F.M. (1993), “A Novel Approach to Nonlinear and Non-Gaussian Bayesian State Estimation,” IEEE Proceedings Part F: Radar and Sonar Navigation, 140, 107–113.
   Google Scholar
• Gudmundsson, A., and Carnes, M. (1997), “Pulsatile Adrenocorticotropic Hormone: An Overview,” Biological Psychiatry, 41, 342–365.
   PubMed Web of Science ®Google Scholar
• Guo, W. (2002), “Functional Mixed Effects Models,” Biometrics, 58, 121–128.
   PubMed Web of Science ®Google Scholar
• Guo, W., and Brown, M.B. (2001), “Cross-Related Structural Time Series Models,” Statistica Sinica, 11, 961–979.
   Web of Science ®Google Scholar
• Guo, W., Wang, Y., and Brown, M.B. (1999), “A Signal Extraction Approach to Modeling Hormone Time Series With Pulses and a Changing Baseline,” Journal of the American Statistical Association, 94, 746–756.
   Web of Science ®Google Scholar
• Harville, D.A. (1974), “Bayesian Inference for Variance Components Using Only Error Contrasts,” Biometrika, 61, 383–385.
   Web of Science ®Google Scholar
• Koopman, S.J., and Durbin, J. (2003), “Filtering and Smoothing of State Vector for Diffuse State-Space Models,” Journal of Time Series Analysis, 24, 85–98.
   Web of Science ®Google Scholar
• Laird, N.M., and Ware, J.H. (1982), “Random-Effects Models for Longitudinal Data,” Biometrics, 38, 963–974.
   PubMed Web of Science ®Google Scholar
• Liu, H., Zheng, Y., and Shen, J. (2008), “Goodness-of-Fit Measures of R2 for Repeated Measures Mixed Effects Models,” Journal of Applied Statistics, 35, 1081–1082.
   Web of Science ®Google Scholar
• Papadopoulos, A.S., and Cleare, A.J. (2012), “Hypothalamic-Pituitary-Adrenal Axis Dysfunction in Chronic Fatigue Syndrome,” Nature Reviews Endocrinology, 8, 22–32.
   Web of Science ®Google Scholar
• Parker, A. J.R., Wessely, S., and Cleare, A.J. (2001), “The Neuroendocrinology of Chronic Fatigue Syndrome and Fibromyalgia,” Psychological Medicine, 31, 1331–1345.
   PubMed Web of Science ®Google Scholar
• Qin, L., and Guo, W. (2006), “Functional Mixed-Effects Model for Periodic Data,” Biostatistics, 7, 225–234.
   PubMed Web of Science ®Google Scholar
• Reeves, W.C., Jones, J.F., Maloney, E., Heim, C., Hoaglin, D.C., Boneva, R.S., Morrissey, M., and Devlin, R. (2007), “Prevalence of Chronic Fatigue Syndrome in Metropolitan, Urban and Rural Georgia,” Population Health Metrics, 5, 5.
   PubMedGoogle Scholar
• Reinsel, G. (1982), “Multivariate Repeated-Measurement or Growth Curve Models With Multivariate Random-Effects Covariance Structure,” Journal of the American Statistical Association, 77, 190–195.
   Web of Science ®Google Scholar
• Riva, R., Mork, P.J., Westgaard, R.H., Rø, M., and Lundberg, U. (2010), “Fibromyalgia Syndrome is Associated With Hypocortisolism,” International Journal of Behavioral Medicine, 17, 223–233.
   PubMed Web of Science ®Google Scholar
• Rosen, O., and Thompson, W.K. (2009), “A Bayesian Regression Model for Multivariate Functional Data,” Computational Statistics & Data Analysis, 53, 3773–3786.
   PubMed Web of Science ®Google Scholar
• Roy, J., and Lin, X. (2000), “Latent Variable Models for Longitudinal Data With Multiple Continuous Outcomes,” Biometrics, 56, 1047–1054.
   PubMed Web of Science ®Google Scholar
• Sallas, W.M., and Harville, D.A. (1981), “Best Linear Recursive Estimation for Mixed Linear Models,” Journal of the American Statistical Association, 76, 860–869.
   Web of Science ®Google Scholar
• Shah, A., Laird, N., and Schoenfeld, D. (1997), “Random-Effects Model for Multiple Characteristics With Possibly Missing Data,” Journal of the American Statistical Association, 92, 775–779.
   Web of Science ®Google Scholar
• Spiga, F., Liu, Y., Aguilera, G., and Lightman, S.L. (2011), “Temporal Effect of Adrenocorticotrophic Hormone on Adrenal Glucocorticoid Steriodogenesis: Involvement of the Transducer of Regulated Cyclic AMP-Response Element-Binding Protein Activity,” Journal of Neuroendocrinology, 23, 136–142.
   PubMed Web of Science ®Google Scholar
• Sy, J.P., Taylor, J. M.G., and Cumberland, W.G. (1997), “A Stochastic Model for the Analysis of Bivariate Longitudinal AIDS Data,” Biometrics, 53, 542–555.
   PubMed Web of Science ®Google Scholar
• Thiébaut, R., Jacqmin-Gadda, H., Chene, G., Leport, C., and Commenges, D. (2002), “Bivariate Linear Mixed Models Using SAS Proc MIXED,” Computer Methods and Programs in Biomedicine, 69, 249–256.
   PubMed Web of Science ®Google Scholar
• Wahba, G. (1978), “Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression,” Journal of the Royal Statistical Society, Series B, 40, 364–372.
   Google Scholar
• Wang, Y. (1998), “Smoothing Spline Models With Corrrelated Random Errors,” Journal of the American Statistical Association, 93, 341–348.
   Web of Science ®Google Scholar
• Wecker, W.E., and Ansley, C.F. (1983), “The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing,” Journal of the American Statistical Association, 78, 81–89.
   Web of Science ®Google Scholar
• Wu, L., Liu, W., and Hu, X.J. (2010), “Joint Inference on HIV Viral Dynamics and Immune Suppression in Presence of Measurement Errors,” Biometrics, 66, 327–335.
   PubMed Web of Science ®Google Scholar
• Zeger, S.L., and Liang, K.Y. (1991), “Feedback Models for Discrete and Continuous Time Series,” Statistica Sinica, 1, 51–64.
   Web of Science ®Google Scholar
• Zhou, L., Huang, J.Z., and Carroll, R.J. (2008), “Joint Modelling of Paired Sparse Functional Data Using Principal Components,” Biometrika, 95, 601–619.
   PubMed Web of Science ®Google Scholar