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Criteria for surrogate end points based on causal distributions

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  • Chuan Ju
  • Zhi Geng

Abstract

Summary. When a treatment has a positive average causal effect (ACE) on an intermediate variable or surrogate end point which in turn has a positive ACE on a true end point, the treatment may have a negative ACE on the true end point due to the presence of unobserved confounders, which is called the surrogate paradox. A criterion for surrogate end points based on ACEs has recently been proposed to avoid the surrogate paradox. For a continuous or ordinal discrete end point, the distributional causal effect (DCE) may be a more appropriate measure for a causal effect than the ACE. We discuss criteria for surrogate end points based on DCEs. We show that commonly used models, such as generalized linear models and Cox's proportional hazard models, can make the sign of the DCE of the treatment on the true end point determinable by the sign of the DCE of the treatment on the surrogate even if the models include unobserved confounders. Furthermore, for a general distribution without any assumption of parametric models, we give a sufficient condition for a distributionally consistent surrogate and prove that it is almost necessary.

Suggested Citation

  • Chuan Ju & Zhi Geng, 2010. "Criteria for surrogate end points based on causal distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 129-142, January.
  • Handle: RePEc:bla:jorssb:v:72:y:2010:i:1:p:129-142
    DOI: 10.1111/j.1467-9868.2009.00729.x
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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. Hua Chen & Zhi Geng & Jinzhu Jia, 2007. "Criteria for surrogate end points," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 919-932, November.
    3. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    4. Steffen L. Lauritzen, 2004. "Discussion on Causality," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 189-193, June.
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    Cited by:

    1. Ying Huang & Shibasish Dasgupta, 2019. "Likelihood-Based Methods for Assessing Principal Surrogate Endpoints in Vaccine Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 504-523, December.
    2. Lu, Jiannan & Ding, Peng & Dasgupta, Tirthankar, 2015. "Construction of alternative hypotheses for randomization tests with ordinal outcomes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 348-355.
    3. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    4. Zhichao Jiang & Peng Ding & Zhi Geng, 2016. "Principal causal effect identification and surrogate end point evaluation by multiple trials," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 829-848, September.
    5. VanderWeele Tyler J, 2011. "Principal Stratification -- Uses and Limitations," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-14, July.
    6. Marshall M. Joffe, 2013. "Discussion on “Surrogate Measures and Consistent Surrogates”," Biometrics, The International Biometric Society, vol. 69(3), pages 569-573, September.
    7. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy," Papers 2005.09130, arXiv.org, revised Jun 2020.
    8. Peng Ding & Jiannan Lu, 2017. "Principal stratification analysis using principal scores," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 757-777, June.
    9. Lu, Jiannan, 2018. "On the partial identification of a new causal measure for ordinal outcomes," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 1-7.
    10. Tyler J. VanderWeele, 2013. "Surrogate Measures and Consistent Surrogates," Biometrics, The International Biometric Society, vol. 69(3), pages 561-565, September.
    11. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1615-1635, October.

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