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 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 (C) 2010 John Wiley & Sons, Ltd