Semi-parametric latent process model for longitudinal ordinal data: Application to cognitive decline
Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi‐parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an...
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| Published in | Statistics in medicine Vol. 29; no. 26; pp. 2723 - 2731 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
20.11.2010
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 1097-0258 |
| DOI | 10.1002/sim.4035 |
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| Abstract | Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi‐parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non‐parametric function of time, f(t), to model the expected change over time. This model includes random‐effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f(t) and all the model parameters are estimated by penalized likelihood using a cubic‐spline approximation for f(t). The smoothing parameter is estimated by an approximate cross‐validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time‐course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects. Copyright © 2010 John Wiley & Sons, Ltd. |
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| AbstractList | Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi‐parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non‐parametric function of time, f ( t ), to model the expected change over time. This model includes random‐effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f( t ) and all the model parameters are estimated by penalized likelihood using a cubic‐spline approximation for f ( t ). The smoothing parameter is estimated by an approximate cross‐validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time‐course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects. Copyright © 2010 John Wiley & Sons, Ltd. Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi-parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non-parametric function of time, f(t), to model the expected change over time. This model includes random-effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f(t) and all the model parameters are estimated by penalized likelihood using a cubic-spline approximation for f(t). The smoothing parameter is estimated by an approximate cross-validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time-course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects. Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi-parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non-parametric function of time, f(t), to model the expected change over time. This model includes random-effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f(t) and all the model parameters are estimated by penalized likelihood using a cubic-spline approximation for f(t). The smoothing parameter is estimated by an approximate cross-validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time-course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects. [PUBLICATION ABSTRACT] Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi-parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non-parametric function of time, f(t), to model the expected change over time. This model includes random-effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f(t) and all the model parameters are estimated by penalized likelihood using a cubic-spline approximation for f(t). The smoothing parameter is estimated by an approximate cross-validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time-course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects.Ordinal and quantitative discrete data are frequent in biomedical and neuropsychological studies. We propose a semi-parametric model for the analysis of the change over time of such data in longitudinal studies. A threshold model is defined where the outcome value depends on the current value of an underlying Gaussian latent process. The latent process model is a Gaussian linear mixed model with a non-parametric function of time, f(t), to model the expected change over time. This model includes random-effects and a stochastic error process to flexibly handle correlation between repeated measures. The function f(t) and all the model parameters are estimated by penalized likelihood using a cubic-spline approximation for f(t). The smoothing parameter is estimated by an approximate cross-validation criterion. Confidence bands may be computed for the estimated curves for the latent process and, using a Monte Carlo approach, for the outcome in its natural scale. The method is applied to the Paquid cohort data to compare the time-course over 14 years of two cognitive scores in a sample of 350 future Alzheimer patients and in a matched sample of healthy subjects. |
| Author | Proust-Lima, Cécile Jacqmin-Gadda, Hélène Amiéva, Hélène |
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| Cites_doi | 10.1137/0111030 10.1002/sim.4780141106 10.1016/0022-3956(75)90026-6 10.2307/2533433 10.1111/j.2517-6161.1983.tb01239.x 10.2307/1390625 10.2307/2986151 10.1080/01621459.1998.10474115 10.1093/biostatistics/kxp009 10.1093/biomet/80.3.527 10.1002/sim.1225 10.1093/oxfordjournals.aje.a009137 10.2307/2532504 10.2307/1390838 10.1093/ije/23.6.1256 10.1080/01621459.1998.10473723 10.1080/01621459.1994.10476806 10.2307/2529876 10.1002/ana.21509 10.1111/j.1467-9469.2006.00536.x 10.2307/2532783 10.1007/s10985-007-9057-x 10.1212/WNL.34.7.939 10.2307/2290687 10.2307/2532087 10.1111/1467-9876.00154 10.1017/CBO9780511755453 10.1111/j.1541-0420.2006.00573.x 10.1002/1097-0258(20001230)19:24<3377::AID-SIM526>3.0.CO;2-E 10.1016/S0398-7620(06)76695-0 |
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| References_xml | – reference: Wahba G. Bayesian 'confidence intervals' for the cross-validated smoothing spline. Journal of the Royal Statistical Society B 1983; 45:133-150. – reference: Shi M, Weiss RE, Taylor JMG. An analysis of paediatric CD4 counts for acquired immune deficiency syndrome using flexible random curves. Applied Statistics 1996; 45:151-164. – reference: Proust-Lima C, Taylor JMG. Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: a joint modeling approach. Biostatistics 2009; 10(3):535-549. – reference: Letenneur L, Commenges D, Dartigues JF, Barberger-Gateau P. Incidence of dementia and Alzheimer's disease in elderly community residents of southwestern France. International Journal of Epidemiology 1994; 23:1256-1261. – reference: Marquardt D. An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics 1963; 11:431-441. – reference: Wang Y. Smoothing spline models with correlated random errors. Journal of the American Statistical Association 1998; 93:341-348. – reference: Joly P, Commenges D, Letenneur L. A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia. Biometrics 1998; 47:161-175. – reference: Jacqmin-Gadda H, Joly P, Commenges D, Binquet C, Chne G. Penalized likelihood approach to estimate smooth mean curve on longitudinal data. Statistics in Medicine 2002; 21:2391-2402. – reference: Ruppert D, Wand MP, Carroll RJ. Semiparametric Regression. Cambridge University Press: Cambridge, 2003. – reference: Genz A. Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics 1992; 1:141-149. – reference: Breslow NE, Clayton DG. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 1993; 88:9-25. – reference: Wang Y, Taylor JMG. Inference for smooth curves in longitudinal data with application to an AIDS clinical trial. Statistics in Medicine 1995; 14:1205-1218. – reference: Pinheiro JC, Bates DM. Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics 1995; 4:12-35. – reference: Amieva H, Le Goff M, Millet X, Prs K, Orgogozo JM, Bargerger-Gateau P, Jacqmin-Gadda H, Dartigues JF. Evidencing the beginning of the predementia phase of Alzheimer's disease: emergence of cognitive deficits, memory complaints, depressive symptoms and functional decline. Annals of Neurology 2008; 64:492-498. – reference: McKhann G, Drachman D, Folstein M, Katzman R, Price D, Stadlan EM. Clinical diagnosis of Alzheimer's disease: report of the NINCDS-ADRDA Work Group under the auspices of Department of Health and Human Services Task Force on Alzheimer's disease. Neurology 1984; 34:939-944. – reference: Jones RH, Boadi-Boateng F. Unequally spaced longitudinal data with AR(1) serial correlation. Biometrics 1991; 47:161-175. – reference: Taylor JMG, Cumberland WG, Sy JP. A stochastic model for analysis of longitudinal AIDS data. Journal of the American Statistical Association 1994; 89:727-736. – reference: Hedeker D, Gibbons RD. A random-effects ordinal regression model for multilevel analysis. Biometrics 1994; 50:9933-9944. – reference: Carrière I, Bouyer J. Random-effect models for ordinal responses: application to self-reported disability among older persons. Revue d'Epidemiologie et Sante Publique 2006; 54(1):61-72. – reference: Molenberghs G, Verbeke G. Models for Discrete Longitudinal Data. Springer: Berlin, 2006. – reference: Commenges D, Joly P, Ggout-Petit A, Liquet B. Choice between semi-parametric estimators of Markov and non-Markov multi-state models from coarsened observations. Scandinavian Journal of Statistics 2007; 34:33-52. – reference: Verbyla AP, Cullis BR, Kenward MG, Welham SJ. 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| SubjectTerms | Aged Aged, 80 and over Alzheimer Disease - physiopathology Alzheimer's disease Approximation Cognition Disorders - physiopathology Cohort Studies cross-validation France Humans Interviews as Topic latent process Likelihood Functions Longitudinal Studies - statistics & numerical data Medical statistics Mental Status Schedule Models, Statistical Monte Carlo simulation Normal Distribution ordinal data penalized likelihood threshold model |
| Title | Semi-parametric latent process model for longitudinal ordinal data: Application to cognitive decline |
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