Télécharger le texte intégral - ISPED-Enseignement à distance

Modèle nonlinéaire à processus latent 66Biometrics 62, 1014–1024December 2006DOI: 10.1111/j.1541-0420.2006.00573.xA Nonlinear Model with Latent Process for Cognitive EvolutionUsing Multivariate Longitudinal DataCécile Proust, 1,∗ Hélène Jacqmin-Gadda, 1 Jeremy M. G. Taylor, 2 Julien Ganiayre, 1 and DanielCommenges 11 INSERM E0338, Université de Bordeaux 2, 146 rue Léo Saignat, 33076 Bordeaux Cedex, France2 Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, Michigan 48109,U.S.A. ∗ email: Cecile.Proust@isped.u-bordeaux2.frSummary. Cognition is not directly measurable. It is assessed using psychometric tests, which can beviewed as quantitative measures of cognition with error. The aim of this article is to propose a model todescribe the evolution in continuous time of unobserved cognition in the elderly and assess the impactof covariates directly on it. The latent cognitive process is defined using a linear mixed model includinga Brownian motion and time-dependent covariates. The observed psychometric tests are considered asthe results of parameterized nonlinear transformations of the latent cognitive process at discrete occasions.Estimation of the parameters contained both in the transformations and in the linear mixed model is achievedby maximizing the observed likelihood and graphical methods are performed to assess the goodness of fit ofthe model. The method is applied to data from PAQUID, a French prospective cohort study of ageing.Key words: Cognitive ageing; Mixed model; Multiple outcomes; Random effects.1. IntroductionIn cognitive ageing studies, cognition is generally evaluatedthrough a battery of psychometric tests, which are quantitativemeasures of various dimensions of cognition. Describingcognitive evolution and assessing the impact of covariates onthis evolution is an interesting approach to help us understandthe process of cognitive ageing. As the various psychometrictests are highly correlated, multivariate longitudinal analysesof several psychometric tests are often performed usingmultivariate linear mixed models (Hall et al., 2001; Harvey,Beckett, and Mungas, 2003; Sliwinski, Hofer, and Hall, 2003).These models highlight both the differences in the shapes ofevolution for each dimension and the strong correlation betweenthe dimensions.The idea of a latent cognitive process explaining the cognitivedecline in the elderly is hypothesized in neuropsychology.This latent cognitive process can be viewed as a common cognitivefactor across all the psychometric tests (Salthouse et al.,1996; Fabrigoule et al., 1998) and is supposed to be a betterpredictor of dementia and cognitive decline. As a consequence,it would be of substantial interest to focus the analysis on thislatent process by describing its evolution and evaluating theimpact of covariates directly on it.In a cross-sectional framework, Sammel and Ryan (1996)proposed a latent variable model in which covariates couldaffect directly the latent variable, and the multiple outcomeswere assumed to be measures of the underlying latentvariable with error. In a longitudinal framework, Gray andBrookmeyer (1998) proposed a marginal regression model,with estimation via generalized estimating equations, toassess an overall treatment effect on several continuous and repeatedoutcomes. Roy and Lin (2000) also extended the linearlatent variable model of Sammel and Ryan (1996) to repeatedmultivariate data. In practice, the assumption of a linear relationshipbetween the outcomes and a Gaussian latent variableis frequently too strong, because the psychometric tests oftenhave non-Gaussian distributions due to different metrologicalproperties and different behaviors with ageing (Hall et al.,2001; Amieva et al., 2005). For instance, some tests may bemore sensitive to changes at high levels of cognition than atlow levels of cognition, while others may have the same sensitivityat high and low levels of cognition. Thus, we proposeto introduce parameterized flexible nonlinear transformationsto link the quantitative tests with the latent process. The latentprocess is defined in continuous time by a linear mixedmodel including a Brownian motion, and nonlinear transformationsof the psychometric tests are noisy measures of thelatent process at discrete occasions, the shapes of the estimatednonlinear transformations giving information on themetrological properties of each test.This extension of mixed models to latent variable modelsis related to structural equation models (SEM), mainlydeveloped in psychometrics, because in both approaches thequantity of interest cannot be measured directly and is evaluatedinstead by a set of outcomes or items (Muthén, 2002;Dunson, 2003; Rabe-Hesketh, Skrondal, and Pickles, 2004).Thus the formulation of the model has two components, ameasurement model which links the latent variables with theobservations and a structural model which explains the latentvariable structure. In the last decade, there have been1014 C○ 2006, The International Biometric Society