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. 2006 Dec;62(4):1014-24.
doi: 10.1111/j.1541-0420.2006.00573.x.

A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data

Cécile Proust  1 , Hélène Jacqmin-Gadda, Jeremy M G Taylor, Julien Ganiayre, Daniel Commenges
Affiliations

A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data

Cécile Proust et al. Biometrics. 2006 Dec.

Abstract

Cognition is not directly measurable. It is assessed using psychometric tests, which can be viewed as quantitative measures of cognition with error. The aim of this article is to propose a model to describe the evolution in continuous time of unobserved cognition in the elderly and assess the impact of covariates directly on it. The latent cognitive process is defined using a linear mixed model including a Brownian motion and time-dependent covariates. The observed psychometric tests are considered as the 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 achieved by maximizing the observed likelihood and graphical methods are performed to assess the goodness of fit of the model. The method is applied to data from PAQUID, a French prospective cohort study of ageing.

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Figures

Figure 1
Figure 1
Examples of Beta transformations for various pairs of parameter values
Figure 2
Figure 2
Estimated Beta transformation for each test (solid line) and the 95% pointwise confidence interval (dashed line, obtained by bootstrap)
Figure 3
Figure 3
Normal-Quantile plot of the standardized marginal residuals for each test (solid lines = ’y=x’ reference line and 95% confidence interval)
Figure 4
Figure 4
(a) Predicted mean evolution for the latent process for ε4 carriers and for ε4 non-carriers and (b) estimated and observed mean evolutions for each test with the number of subjects used for the computation of each observed mean (solid line with crosses = observed mean evolution; solid line with dots = estimated marginal mean evolution; dashed line with dots = estimated subject-specific mean evolution; dashed line = 95% confidence interval of the observed mean)
See this image and copyright information in PMC

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