Semi-parametric latent process model for longitudinal ordinal data: Application to cognitive decline

• Published in: Statistics in medicine Vol. 29; no. 26; pp. 2723 - 2731
• Main Authors: Jacqmin-Gadda, Hélène, Proust-Lima, Cécile, Amiéva, Hélène
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.11.2010; Wiley Subscription Services, Inc
• Subjects: 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; France
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.4035

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.