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Dynamic modeling of multivariate dimensions and their temporal relationships using latent processes: Application to Alzheimer's disease

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  • Bachirou O. Taddé
  • Hélène Jacqmin‐Gadda
  • Jean‐François Dartigues
  • Daniel Commenges
  • Cécile Proust‐Lima

Abstract

Alzheimer's disease gradually affects several components including the cerebral dimension with brain atrophies, the cognitive dimension with a decline in various functions, and the functional dimension with impairment in the daily living activities. Understanding how such dimensions interconnect is crucial for Alzheimer's disease research. However, it requires to simultaneously capture the dynamic and multidimensional aspects and to explore temporal relationships between dimensions. We propose an original dynamic structural model that accounts for all these features. The model defines dimensions as latent processes and combines a multivariate linear mixed model and a system of difference equations to model trajectories and temporal relationships between latent processes in finely discrete time. Dimensions are simultaneously related to their observed (possibly multivariate) markers through nonlinear equations of observation. Parameters are estimated in the maximum likelihood framework enjoying a closed form for the likelihood. We demonstrate in a simulation study that this dynamic model in discrete time benefits the same causal interpretation of temporal relationships as models defined in continuous time as long as the discretization step remains small. The model is then applied to the data of the Alzheimer's Disease Neuroimaging Initiative. Three longitudinal dimensions (cerebral anatomy, cognitive ability, and functional autonomy) measured by six markers are analyzed, and their temporal structure is contrasted between different clinical stages of Alzheimer's disease.

Suggested Citation

  • Bachirou O. Taddé & Hélène Jacqmin‐Gadda & Jean‐François Dartigues & Daniel Commenges & Cécile Proust‐Lima, 2020. "Dynamic modeling of multivariate dimensions and their temporal relationships using latent processes: Application to Alzheimer's disease," Biometrics, The International Biometric Society, vol. 76(3), pages 886-899, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:886-899
    DOI: 10.1111/biom.13168
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    References listed on IDEAS

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    1. Daniel Commenges & Anne Gégout‐Petit, 2009. "A general dynamical statistical model with causal interpretation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 719-736, June.
    2. Mélanie Prague & Daniel Commenges & Jon Michael Gran & Bruno Ledergerber & Jim Young & Hansjakob Furrer & Rodolphe Thiébaut, 2017. "Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study," Biometrics, The International Biometric Society, vol. 73(1), pages 294-304, March.
    3. Vanessa Didelez, 2008. "Graphical models for marked point processes based on local independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 245-264, February.
    4. Odd O. Aalen & Arnoldo Frigessi, 2007. "What can Statistics Contribute to a Causal Understanding?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 155-168, March.
    5. Soetaert, Karline & Petzoldt, Thomas & Setzer, R. Woodrow, 2010. "Solving Differential Equations in R: Package deSolve," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i09).
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