Recent advances in causal mediation analysis have formalized conditions for estimating direct and indirect effects in various contexts. These approaches have been extended to a number of models for survival outcomes including accelerated failure time models, which are widely used in a broad range of health applications given their intuitive interpretation. In this setting, it has been suggested that under standard assumptions, the “difference” and “product” methods produce equivalent estimates of the indirect effect of exposure on the survival outcome. We formally show that these two methods may produce substantially different estimates in the presence of censoring or truncation, due to a form of model misspecification. Specifically, we establish that while the product method remains valid under standard assumptions in the presence of independent censoring, the difference method can be biased in the presence of such censoring whenever the error distribution of the accelerated failure time model fails to be collapsible upon marginalizing over the mediator. This will invariably be the case for most choices of mediator and outcome error distributions. A notable exception arises in case of normal mediator–normal outcome where we show consistency of both difference and product estimators in the presence of independent censoring. These results are confirmed in simulation studies and two data applications.
From the Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA.
Research reported in this publication was supported by the National Institute of Allergy and Infectious Diseases of the National Institute of Health under Award Number T32AI007358 (for I.R.F.) and Grant Number AI104459 (for E.T.T.). P.L.W. received funding from the Pediatric HIV/AIDS Cohort Study (PHACS), which is supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development with co-funding from other NIH institutes through cooperative agreements with the Harvard T.H. Chan School of Public Health (HD052102) and the Tulane University School of Medicine (HD052104).
The authors report no conflicts of interest.
Availability of Data/Code for Replication: Data are not available for replication because special permission is necessary to access them. Sample code for mediation analysis is provided in eAppendix (http://links.lww.com/EDE/B212).
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Correspondence: Isabel R. Fulcher, 655 Huntington Avenue, Building 2, 4th Floor, Boston, MA 02115. E-mail: email@example.com.