Non-linear random effects models with continuous time autoregressive errors: A Bayesian approach

Statistics in Medicine

Volumn 25, Issue 9, 2006, Pages 1471-1484

  De la Cruz Mesía, Rolando ^a   Marshall, Guillermo ^a,b  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

Author keywords

Continuous time autoregressive process; Gibbs sampler; Longitudinal data; Non linear random effects model

Indexed keywords

ANALYTICAL ERROR; ARTICLE; BAYES THEOREM; CHILE; CLINICAL STUDY; CONTROLLED STUDY; CORRELATION ANALYSIS; DATA ANALYSIS; FEMALE; GESTATIONAL AGE; HUMAN; INFORMATION PROCESSING; LONGITUDINAL STUDY; MATHEMATICAL COMPUTING; NONLINEAR REGRESSION ANALYSIS; NONLINEAR SYSTEM; OBSERVATIONAL METHOD; OUTCOME ASSESSMENT; PLASMA VOLUME; PREGNANCY; RANDOMIZATION; REGRESSION ANALYSIS; RESEARCH SUBJECT; SAMPLING; TIME;

BAYES THEOREM; FEMALE; FETAL GROWTH RETARDATION; GESTATIONAL AGE; HUMANS; LONGITUDINAL STUDIES; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PLASMA VOLUME; PREGNANCY;

EID: 33646238025     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.2290     Document Type: Article

References (42)

1. Wakefield J. The Bayesian analysis of population pharmacokinetic models. Journal of the American Statistical Association 1996; 92:62-75.
2. Beal SL, Sheiner LB. Estimating population kinetics. CRC Critical Reviews in Biomedical Engineering 1982; 8:195-222.
3. Lindstrom MJ, Bates DM. Nonlinear mixed effects models for repeated measures data. Biometrics 1990; 46: 673-687.
4. Potthoff RF, Roy SN. A generalized multivariate analysis of variance model useful specially for growth curve problems. Biometrika 1964; 51:313-326.
5. Jones RH. Repeated measures, interventions and time series analysis. Psychoneuroendocrinology 1985; 10: 5-14.
6. Pantula SG, Pollock KH. Nested analysis of variance with autocorrelated errors. Biometrics 1985; 41:909-920.
7. Ware JH. Linear models for the analysis of longitudinal studies. The American Statistician 1985; 39:95-101.
8. Jennrich RI, Schluchter MD. Unbalanced repeated-measures models with structured covariance matrices. Biometrics 1986; 42:805-820.
9. Lee JC. Prediction and estimation of growth curves with special covariance structures. Journal of the American Statistical Association 1988; 83:432-440.
10. Chi EM, Reinsel GC. Models for longitudinal data with random effects and AR(1) errors. Journal of the American Statistical Association 1989; 84:452-459.
11. Liski EP, Nummi T. Prediction in repeated-measures models with engineering applications. Technometrics 1996; 38:25-36.
12. Jones RH, Boadi-Boateng F. Unequally spaced longitudinal data with AR(1) serial correlation. Biometrics 1991; 47:161-175.
13. Zimmerman DL, Núñez-Antón V. Parametric modelling of growth curve data: an overview (with discussion). Test 2001; 10:1-73.
14. Broemeling LD, Cook P. A Bayesian analysis of regression models with continuous errors with application to longitudinal studies. Statistics in Medicine 1997; 16:321-332.
15. Menzefricke U. Bayesian predictions in growth-curve models with correlated errors. Test 1998; 8:75-93.
16. Glasbey CA. Correlated residuals in nonlinear regression applied to growth data. Applied Statistics 1979; 28:252-259.
17. Palmer MJ, Phillips BF, Smith GT. Application of nonlinear models with random coefficients to growth data. Biometrics 1991; 47:623-635.
18. De la Cruz-Mesía R, Marshall G. A Bayesian approach for nonlinear regression models with continuous errors. Communications in Statistics: Theory and Methods 2003; 32(8):1631-1646.
19. Davidian M, Gallant AR. The nonlinear mixed effects model with a smooth random effects density. Biometrika 1993; 80:475-488.
20. Walker S. An EM algorithm for nonlinear random effects models. Biometrics 1996; 52:934-944.
21. Davidian M, Giltinan DM. Nonlinear Models for Repeated Measurement Data. Chapman & Hall: London, 1995.
22. Vonesh EF, Chinchilli VM. Linear and Nonlinear Models for the Analysis of Repeated Measurements. Marcel Dekker: New York, 1997.
23. Pinheiro JC, Bates DM. Mixed-effects Models in S and S-PLUS. Springer: New York, 2000.
24. Racine-Poon A. A Bayesian approach to nonlinear random effects models. Biometrics 1985; 41:1015-1024.
25. Wakefield JC, Smith AFM, Racine-Poon A, Gelfand AE. Bayesian analysis of linear and non-linear population models by using the Gibbs Sampler. Applied Statistics 1994; 43:201-221.
26. Bennett JE, Racine-Poon A, Wakefield JC. MCMC for nonlinear hierarchical models. In Markov Chain Monte Carlo in Practice, Gilks WR, Richardson S, Spiegelhalter DJ (eds). Oxford University Press: Oxford, 1995.
27. Wakefield J, Bennet J. Bayesian modeling of covariates for population pharmacokinetic models. Journal of the American Statistical Association 1996; 91:917-927.
28. Arnorld L. Stochastics Differential Equations: Theory and Applications. Wiley: New York, 1971.
29. Brockwell PJ, Hyndman RJ, Grunwald GK. Continuous time threshold autoregressive models. Statistica Sinica 1991; 1:401-410.
30. Diggle PJ, Heagerty P, Kung-Yee L, Zeger SL. Analysis of Longitudinal Data (2nd edn). Oxford University Press: Oxford, 2002.
31. Jones RH. Longitudinal Data With Serial Correlations: A State Space Approach. Chapman & Hall: London, 1993.
32. Hobert JP, Casella G. The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. Journal of the American Statistical Association 1996; 91:1461-1473.
33. Pineda RA. A nonlinear mixed effects model for maternal plasma volume expansion. M.Sc. Thesis, Department of Statistics, Pontificial Catholic University of Chile (in Spanish), 1997.
34. Best NG, Cowles MK, Vines SK. CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output, Version 0.3. MRC Biostatistics Unit: Cambridge, 1995.
35. Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian Statistics 4, Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds). Oxford University Press: Oxford, 1995.
36. Heidelberger P, Welch P. Simulation run length control in the presence of an initial transient. Operations Research 1983; 31:1109-1144.
37. Gelfand AE, Dey DK, Chang H. Model determination using predictive distributions with implementation via sampling-based methods (with discussion). In Bayesian Statistics 4, Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds). Oxford University Press: Oxford, 1995.
38. Chen MH, Shao QM, Ibrahim JG. Monte Carlo Methods in Bayesian Computation. Springer: New York, 2000.
39. Jones RH. Fitting continuous time autoregressions to discrete data. In Applied Time Series Analysis II, Findley DF (ed.). Academic Press: New York, 1981; 651-682.
40. Jones RH, Ackerson LM. Serial correlation in unequally spaced longitudinal data. Biometrika 1990; 77:721-731.
41. Zimmerman DL, Núñez-Antón V, El-Barmi H. Computational aspects of likelihood based estimation of first-order antedependence models. Journal of Statistical Computation and Simulation 1998; 60:67-84.
42. Müller P, Rosner GL. A Bayesian population model with hierarchical mixture priors applied to blood count data. Journal of the American Statistical Association 1997; 92:1279-1292.