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On the identification of individual level pleiotropic, pure direct, and principal stratum direct effects without cross world assumptions

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  • Jaffer M. Zaidi
  • Tyler J. VanderWeele

Abstract

The analysis of natural direct and principal stratum direct effects has a controversial history in statistics and causal inference as these effects are commonly identified with either untestable cross world independence or graphical assumptions. This article demonstrates that the presence of individual level natural direct and principal stratum direct effects can be identified without cross world independence assumptions. We also define a new type of causal effect, called pleiotropy, that is of interest in genomics, and provide empirical conditions to detect such an effect as well. Our results are applicable for all types of distributions concerning the mediator and outcome.

Suggested Citation

  • Jaffer M. Zaidi & Tyler J. VanderWeele, 2021. "On the identification of individual level pleiotropic, pure direct, and principal stratum direct effects without cross world assumptions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 881-907, September.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:3:p:881-907
    DOI: 10.1111/sjos.12464
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    References listed on IDEAS

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    1. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    2. Zhihong Cai & Manabu Kuroki & Judea Pearl & Jin Tian, 2008. "Bounds on Direct Effects in the Presence of Confounded Intermediate Variables," Biometrics, The International Biometric Society, vol. 64(3), pages 695-701, September.
    3. Sonja A. Swanson & Miguel A. Hernán & Matthew Miller & James M. Robins & Thomas S. Richardson, 2018. "Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 933-947, April.
    4. Kosuke Imai & Dustin Tingley & Teppei Yamamoto, 2013. "Experimental designs for identifying causal mechanisms," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(1), pages 5-51, January.
    5. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    6. Tyler J. Vanderweele & James M. Robins, 2008. "Empirical and counterfactual conditions for sufficient cause interactions," Biometrika, Biometrika Trust, vol. 95(1), pages 49-61.
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