  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.
