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A general dynamical statistical model with causal interpretation

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  • Daniel Commenges
  • Anne Gégout‐Petit

Abstract

Summary. We develop a general dynamical model as a framework for causal interpretation. We first state a criterion of local independence in terms of measurability of processes that are involved in the Doob–Meyer decomposition of stochastic processes; then we define direct and indirect influence. We propose a definition of causal influence using the concepts of a ‘physical system’. This framework makes it possible to link descriptive and explicative statistical models, and encompasses quantitative processes and events. One of the features of the paper is the clear distinction between the model for the system and the model for the observation. We give a dynamical representation of a conventional joint model for human immunodeficiency virus load and CD4 cell counts. We show its inadequacy to capture causal influences whereas in contrast known mechanisms of infection by the human immunodeficiency virus can be expressed directly through a system of differential equations.

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  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:719-736
    DOI: 10.1111/j.1467-9868.2009.00703.x
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    Cited by:

    1. 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.
    2. Douglas J. Miller & George Judge, 2015. "Information Recovery in a Dynamic Statistical Markov Model," Econometrics, MDPI, vol. 3(2), pages 1-12, March.
    3. 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.
    4. 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.
    5. Jeremie Guedj & Rodolphe Thiébaut & Daniel Commenges, 2011. "Joint Modeling of the Clinical Progression and of the Biomarkers' Dynamics Using a Mechanistic Model," Biometrics, The International Biometric Society, vol. 67(1), pages 59-66, March.

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