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Causal mediation of semicompeting risks

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  • Yen‐Tsung Huang

Abstract

The semi‐competing risks problem arises when one is interested in the effect of an exposure or treatment on both intermediate (e.g., having cancer) and primary events (e.g., death) where the intermediate event may be censored by the primary event, but not vice versa. Here we propose a nonparametric approach casting the semi‐competing risks problem in the framework of causal mediation modeling. We set up a mediation model with the intermediate and primary events, respectively as the mediator and the outcome, and define an indirect effect as the effect of the exposure on the primary event mediated by the intermediate event and a direct effect as that not mediated by the intermediate event. A nonparametric estimator with time‐varying weights is proposed for direct and indirect effects where the counting process at time t of the primary event N2n1(t) and its compensator An1(t) are both defined conditional on the status of the intermediate event right before t, N1(t−)=n1. We show that N2n1(t)−An1(t) is a zero‐mean martingale. Based on this, we further establish theoretical properties for the proposed estimators. Simulation studies are presented to illustrate the finite sample performance of the proposed method. Its advantage in causal interpretation over existing methods is also demonstrated in a hepatitis study.

Suggested Citation

  • Yen‐Tsung Huang, 2021. "Causal mediation of semicompeting risks," Biometrics, The International Biometric Society, vol. 77(4), pages 1143-1154, December.
  • Handle: RePEc:bla:biomet:v:77:y:2021:i:4:p:1143-1154
    DOI: 10.1111/biom.13525
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    References listed on IDEAS

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    1. Weijing Wang, 2003. "Estimating the association parameter for copula models under dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 257-273, February.
    2. Tchetgen Tchetgen Eric J, 2011. "On Causal Mediation Analysis with a Survival Outcome," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-38, September.
    3. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
    4. Kyu Ha Lee & Sebastien Haneuse & Deborah Schrag & Francesca Dominici, 2015. "Bayesian semiparametric analysis of semicompeting risks data: investigating hospital readmission after a pancreatic cancer diagnosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(2), pages 253-273, February.
    5. Yen-Tsung Huang & Tianxi Cai, 2016. "Mediation analysis for survival data using semiparametric probit models," Biometrics, The International Biometric Society, vol. 72(2), pages 563-574, June.
    6. Weijing Wang, 2003. "Nonparametric estimation of the sojourn time distributions for a multipath model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 921-935, November.
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    Cited by:

    1. Yen‐Tsung Huang, 2021. "Rejoinder to “Causal mediation of semicompeting risks”," Biometrics, The International Biometric Society, vol. 77(4), pages 1170-1174, December.
    2. Yuhao Deng & Haoyu Wei & Xia Xiao & Yuan Zhang & Yuanmin Huang, 2024. "Sequential Ignorability and Dismissible Treatment Components to Identify Mediation Effects," Mathematics, MDPI, vol. 12(15), pages 1-20, July.

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