IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v76y2020i3p886-899.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13168
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13168?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. 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.
    4. 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).
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel Commenges, 2019. "Dealing with death when studying disease or physiological marker: the stochastic system approach to causality," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 381-405, July.
    2. Petrović, Ljiljana & Dimitrijević, Sladjana, 2012. "Causality with finite horizon of the past in continuous time," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1219-1223.
    3. Eichler, M. & Didelez, V., 2009. "On Granger-causality and the effect of interventions in time series," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. 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.
    5. Fatima-Zahra Jaouimaa & Daniel Dempsey & Suzanne Van Osch & Stephen Kinsella & Kevin Burke & Jason Wyse & James Sweeney, 2021. "An age-structured SEIR model for COVID-19 incidence in Dublin, Ireland with framework for evaluating health intervention cost," PLOS ONE, Public Library of Science, vol. 16(12), pages 1-25, December.
    6. 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.
    7. Belém Barbosa & José Ramón Saura & Dag Bennett, 2024. "How do entrepreneurs perform digital marketing across the customer journey? A review and discussion of the main uses," The Journal of Technology Transfer, Springer, vol. 49(1), pages 69-103, February.
    8. Overstall, Antony M. & Woods, David C. & Martin, Kieran J., 2019. "Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 126-142.
    9. Serrouya, R. & Dickie, M. & DeMars, C. & Wittmann, M.J. & Boutin, S., 2020. "Predicting the effects of restoring linear features on woodland caribou populations," Ecological Modelling, Elsevier, vol. 416(C).
    10. Zadoki Tabo & Chester Kalinda & Lutz Breuer & Christian Albrecht, 2023. "Adapting Strategies for Effective Schistosomiasis Prevention: A Mathematical Modeling Approach," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    11. Moore, Christopher M. & Catella, Samantha A. & Abbott, Karen C., 2018. "Population dynamics of mutualism and intraspecific density dependence: How θ-logistic density dependence affects mutualistic positive feedback," Ecological Modelling, Elsevier, vol. 368(C), pages 191-197.
    12. Emanuele Gramuglia & Geir Storvik & Morten Stakkeland, 2021. "Clustering and automatic labelling within time series of categorical observations—with an application to marine log messages," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 714-732, June.
    13. Jan M. Hoem & Lesia Nedoluzhko, 2008. "Marriage formation as a process intermediary between migration and childbearing," MPIDR Working Papers WP-2008-015, Max Planck Institute for Demographic Research, Rostock, Germany.
    14. Yan, Chuan & Zhang, Zhibin, 2018. "Dome-shaped transition between positive and negative interactions maintains higher persistence and biomass in more complex ecological networks," Ecological Modelling, Elsevier, vol. 370(C), pages 14-21.
    15. Cécile Cathalot & Erwan G. Roussel & Antoine Perhirin & Vanessa Creff & Jean-Pierre Donval & Vivien Guyader & Guillaume Roullet & Jonathan Gula & Christian Tamburini & Marc Garel & Anne Godfroy & Pier, 2021. "Hydrothermal plumes as hotspots for deep-ocean heterotrophic microbial biomass production," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
    16. Lamonica, Dominique & Herbach, Ulysse & Orias, Frédéric & Clément, Bernard & Charles, Sandrine & Lopes, Christelle, 2016. "Mechanistic modelling of daphnid-algae dynamics within a laboratory microcosm," Ecological Modelling, Elsevier, vol. 320(C), pages 213-230.
    17. Karl Friston, 2009. "Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging," PLOS Biology, Public Library of Science, vol. 7(2), pages 1-6, February.
    18. Stahl, Gerhard & Wang, Shaohui & Wendt, Markus, 2011. "Validate Correlation of an ESG: Treasury Yields across," Hannover Economic Papers (HEP) dp-476, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    19. Alex Root, 2019. "Mathematical Modeling of The Challenge to Detect Pancreatic Adenocarcinoma Early with Biomarkers," Challenges, MDPI, vol. 10(1), pages 1-15, April.
    20. Chevallier, Damien & Mourrain, Baptiste & Girondot, Marc, 2020. "Modelling leatherback biphasic indeterminate growth using a modified Gompertz equation," Ecological Modelling, Elsevier, vol. 426(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:886-899. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.