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Dealing with death when studying disease or physiological marker: the stochastic system approach to causality

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  • Daniel Commenges

    (INSERM, U 1219, Bordeaux University)

Abstract

The stochastic system approach to causality is applied to situations where the risk of death is not negligible. This approach grounds causality on physical laws, distinguishes system and observation and represents the system by multivariate stochastic processes. The particular role of death is highlighted, and it is shown that local influences must be defined on the random horizon of time of death. We particularly study the problem of estimating the effect of a factor V on a process of interest Y, taking death into account. We unify the cases where Y is a counting process (describing an event) and the case where Y is quantitative; we examine the case of observations in continuous and discrete time and we study the issue of whether the mechanism leading to incomplete data can be ignored. Finally, we give an example of a situation where we are interested in estimating the effect of a factor (blood pressure) on cognitive ability in elderly.

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  • 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.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:3:d:10.1007_s10985-018-9454-3
    DOI: 10.1007/s10985-018-9454-3
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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. Chenguang Wang & Daniel O. Scharfstein & Elizabeth Colantuoni & Timothy D. Girard & Ying Yan, 2017. "Inference in randomized trials with death and missingness," Biometrics, The International Biometric Society, vol. 73(2), pages 431-440, June.
    3. Fan Yang & Peng Ding, 2018. "Using survival information in truncation by death problems without the monotonicity assumption," Biometrics, The International Biometric Society, vol. 74(4), pages 1232-1239, December.
    4. Anaïs Rouanet & Pierre Joly & Jean‐François Dartigues & Cécile Proust‐Lima & Hélène Jacqmin‐Gadda, 2016. "Joint latent class model for longitudinal data and interval‐censored semi‐competing events: Application to dementia," Biometrics, The International Biometric Society, vol. 72(4), pages 1123-1135, December.
    5. Joffe Marshall, 2011. "Principal Stratification and Attribution Prohibition: Good Ideas Taken Too Far," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-22, September.
    6. D. M. Farewell & C. Huang & V. Didelez, 2017. "Ignorability for general longitudinal data," Biometrika, Biometrika Trust, vol. 104(2), pages 317-326.
    7. VanderWeele Tyler J, 2011. "Principal Stratification -- Uses and Limitations," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-14, July.
    8. Elja Arjas & Jan Parner, 2004. "Causal Reasoning from Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 171-187, June.
    9. Rizopoulos, Dimitris, 2010. "JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i09).
    10. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    11. Mélanie Prague & Daniel Commenges & Julia Drylewicz & Rodolphe Thiébaut, 2012. "Treatment Monitoring of HIV-Infected Patients based on Mechanistic Models," Biometrics, The International Biometric Society, vol. 68(3), pages 902-911, September.
    12. Daniel Commenges & Pierre Joly & Anne Gégout‐Petit & Benoit Liquet, 2007. "Choice between Semi‐parametric Estimators of Markov and Non‐Markov Multi‐state Models from Coarsened Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 33-52, March.
    13. Cécile Proust & Hélène Jacqmin-Gadda & Jeremy M. G. Taylor & Julien Ganiayre & Daniel Commenges, 2006. "A Nonlinear Model with Latent Process for Cognitive Evolution Using Multivariate Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1014-1024, December.
    14. Pearl Judea, 2011. "Principal Stratification -- a Goal or a Tool?," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-13, March.
    15. 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, June.
    16. 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.
    17. 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.
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    1. Richard J. Cook & Jerald F. Lawless, 2020. "Failure time studies with intermittent observation and losses to follow‐up," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1035-1063, December.

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