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Comparison of Effect Size Measures for Mediation Analysis of Survival Outcomes with Application to the Framingham Heart Study

There is an increasing trend of research in mediation analysis for survival outcomes. Such analyses help researchers to better understand how exposure affects disease outcomes through mediators. However, due to censored observations in survival outcomes, it is not straightforward to extend mediation analysis from linear models to survival outcomes. In this article, we extend a mediation effect size measure based on $R^2$ in linear regression to survival outcomes. Due to multiple definitions of $R^2$ for survival models, we compare and evaluate five $R^2$ measures for mediation analysis. Based on extensive simulations, we recommend two $R^2$ measures with good operating characteristics. We illustrate the utility of the $R^2$-based mediation measures by analyzing the mediation effects of multiple lifestyle risk factors on the relationship between environmental exposures and time to coronary heart disease and all-cause mortality in the Framingham Heart Study.