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Causal Mediation Analysis of Survival Outcome with Multiple Mediators

Huang, Yen-Tsung; Yang, Hwai-I

doi: 10.1097/EDE.0000000000000651

Background: Mediation analyses have been a popular approach to investigate the effect of an exposure on an outcome through a mediator. Mediation models with multiple mediators have been proposed for continuous and dichotomous outcomes. However, development of multimediator models for survival outcomes is still limited.

Methods: We present methods for multimediator analyses using three survival models: Aalen additive hazard models, Cox proportional hazard models, and semiparametric probit models. Effects through mediators can be characterized by path-specific effects, for which definitions and identifiability assumptions are provided. We derive closed-form expressions for path-specific effects for the three models, which are intuitively interpreted using a causal diagram.

Results: Mediation analyses using Cox models under the rare-outcome assumption and Aalen additive hazard models consider effects on log hazard ratio and hazard difference, respectively; analyses using semiparametric probit models consider effects on difference in transformed survival time and survival probability. The three models were applied to a hepatitis study where we investigated effects of hepatitis C on liver cancer incidence mediated through baseline and/or follow-up hepatitis B viral load. The three methods show consistent results on respective effect scales, which suggest an adverse estimated effect of hepatitis C on liver cancer not mediated through hepatitis B, and a protective estimated effect mediated through the baseline (and possibly follow-up) of hepatitis B viral load.

Conclusions: Causal mediation analyses of survival outcome with multiple mediators are developed for additive hazard and proportional hazard and probit models with utility demonstrated in a hepatitis study.

From the aInstitute of Statistical Science, Academia Sinica, Taipei, Taiwan; bDepartments of Epidemiology and Biostatistics, Brown University, Providence, RI; and cGenomics Research Center, Academia Sinica, Taipei, Taiwan.

Submitted May 4 2016; accepted March 13 2017.

Financially supported by NIH/NCI 5R03CA 182937-02 and NIH/NIA 1R01AG048825-01 and Taiwan MOST 105-2118-M-001-014-MY3.

The authors report no conflicts of interest.

Computation code and data are available at and

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Correspondence: Yen-Tsung Huang, Institute of Statistical Science, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei 11529, Taiwan. E-mail:

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