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A general dynamical statistical model with causal interpretation

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  • Daniel Commenges
  • Anne Gégout-Petit

Abstract

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. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:719-736
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    References listed on IDEAS

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    1. Sara Geneletti, 2007. "Identifying direct and indirect effects in a non-counterfactual framework," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 199-215.
    2. 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.
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    4. Karl Jöreskog, 1978. "Structural analysis of covariance and correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 443-477, December.
    5. J. Guedj & R. Thiébaut & D. Commenges, 2007. "Maximum Likelihood Estimation in Dynamical Models of HIV," Biometrics, The International Biometric Society, vol. 63(4), pages 1198-1206, December.
    6. Judith Lok & Richard Gill & Aad van der Vaart & James Robins, 2004. "Estimating the causal effect of a time-varying treatment on time-to-event using structural nested failure time models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 271-295.
    7. James M. Robins, 2003. "Uniform consistency in causal inference," Biometrika, Biometrika Trust, vol. 90(3), pages 491-515, September.
    8. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
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    10. 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.
    11. Daniel Commenges & Anne Gégout-Petit, 2007. "Likelihood for Generally Coarsened Observations from Multistate or Counting Process Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 432-450.
    12. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
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    Cited by:

    1. Douglas J. Miller & George Judge, 2015. "Information Recovery in a Dynamic Statistical Markov Model," Econometrics, MDPI, Open Access Journal, vol. 3(2), pages 1-12, March.
    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. 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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