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Bounds on Direct Effects in the Presence of Confounded Intermediate Variables

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  • Zhihong Cai
  • Manabu Kuroki
  • Judea Pearl
  • Jin Tian

Abstract

Summary This article considers the problem of estimating the average controlled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded (hence identifiable). Kaufman et al. (2005, Statistics in Medicine24, 1683–1702) applied a linear programming software to find the minimum and maximum possible values of the ACDE for specific numerical data. In this article, we apply the symbolic Balke–Pearl (1997, Journal of the American Statistical Association92, 1171–1176) linear programming method to derive closed‐form formulas for the upper and lower bounds on the ACDE under various assumptions of monotonicity. These universal bounds enable clinical experimenters to assess the direct effect of treatment from observed data with minimum computational effort, and they further shed light on the sign of the direct effect and the accuracy of the assessments.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:695-701
    DOI: 10.1111/j.1541-0420.2007.00949.x
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    References listed on IDEAS

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    1. Yue Wang & Jeremy M. G. Taylor, 2002. "A Measure of the Proportion of Treatment Effect Explained by a Surrogate Marker," Biometrics, The International Biometric Society, vol. 58(4), pages 803-812, December.
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    1. Lixiong Li & D'esir'e K'edagni & Ismael Mourifi'e, 2020. "Discordant Relaxations of Misspecified Models," Papers 2012.11679, arXiv.org, revised Dec 2022.
    2. 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.
    3. Martin Huber, 2015. "Causal Pitfalls in the Decomposition of Wage Gaps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 179-191, April.
    4. Ting Ye & Luke Keele & Raiden Hasegawa & Dylan S. Small, 2020. "A Negative Correlation Strategy for Bracketing in Difference-in-Differences," Papers 2006.02423, arXiv.org, revised Jun 2022.
    5. Chiba, Yasutaka, 2010. "Estimating the principal stratum direct effect when the total effects are consistent between two standard populations," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 958-961, June.
    6. Bampasidou, Maria & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2011. "Unbundling the Degree Effect in a Job Training Program for Disadvantaged Youth," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania 103619, Agricultural and Applied Economics Association.
    7. Martin Huber & Lukáš Lafférs, 2022. "Bounds on direct and indirect effects under treatment/mediator endogeneity and outcome attrition," Econometric Reviews, Taylor & Francis Journals, vol. 41(10), pages 1141-1163, November.
    8. Sjölander Arvid, 2020. "A note on a sensitivity analysis for unmeasured confounding, and the related E-value," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 229-248, January.
    9. Mealli Fabrizia & Mattei Alessandra, 2012. "A Refreshing Account of Principal Stratification," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-19, April.
    10. Manabu Kuroki & Takahiro Hayashi, 2016. "On the Estimation Accuracy of Causal Effects using Supplementary Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 505-519, June.
    11. Eduardo Fé, 2021. "Pension eligibility rules and the local causal effect of retirement on cognitive functioning," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 812-841, July.
    12. Chiba Yasutaka & Taguri Masataka, 2013. "Alternative Monotonicity Assumptions for Improving Bounds on Natural Direct Effects," The International Journal of Biostatistics, De Gruyter, vol. 9(2), pages 235-249, July.
    13. Sjölander Arvid, 2020. "A note on a sensitivity analysis for unmeasured confounding, and the related E-value," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 229-248, January.

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