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Causal mediation analysis for the Cox proportional hazards model with a smooth baseline hazard estimator
Author(s) -
Wang Wei,
Albert Jeffrey M.
Publication year - 2017
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12188
Subject(s) - mediation , proportional hazards model , causal inference , estimator , statistics , hazard ratio , econometrics , hazard , confounding , confidence interval , mathematics , inference , computer science , artificial intelligence , chemistry , organic chemistry , law , political science
Summary An important problem within the social, behavioural and health sciences is how to partition an exposure effect (e.g. treatment or risk factor) among specific pathway effects and to quantify the importance of each pathway. Mediation analysis based on the potential outcomes framework is an important tool to address this problem and we consider the estimation of mediation effects for the proportional hazards model. We give precise definitions of the total effect, natural indirect effect and natural direct effect in terms of the survival probability, hazard function and restricted mean survival time within the standard two‐stage mediation framework. To estimate the mediation effects on different scales, we propose a mediation formula approach in which simple parametric models (fractional polynomials or restricted cubic splines) are utilized to approximate the baseline log‐cumulative‐hazard function. Simulation study results demonstrate low bias of the mediation effect estimators and close‐to‐nominal coverage probability of the confidence intervals for a wide range of complex hazard shapes. We apply this method to the Jackson heart study data and conduct a sensitivity analysis to assess the effect on the mediation effects inference when the no unmeasured mediator–outcome confounding assumption is violated.