Causal Mediation Analysis in a Survival

General Information

Short Report

Wei Wang, PhD^*

¹Center of Biostatistics and Bioinformatics, University of Mississippi Medical Center, Jackson, MS, USA

Corresponding author

Wei Wang, PhD, Assistant Professor, Center of Biostatistics and Bioinformatics, University of Mississippi Medical Center, 2500 North State Street, Jackson, Mississippi 39216, Tel: (601) 984-4361; Fax: (601) 984-1939; Email: wwang@umc.edu

Received Date: 19^th May 2015

Accepted Date: 22^nd May 2015

Published Date: 26^th May 2015

Citation

Wang W (2015) Causal Mediation Analysis in a Survival Context. Enliven: Biostat Metr 1(1):003

Copyright

@ 2015 Dr. Wei Wang. This is an Open Access article published and distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

The importance of mediation analysis in health and medical research relies on the need to illuminate the mechanisms by which an exposure exerts a causal effect on an outcome variable. In practice, a mediational model hypothesizes that the exposure variable causes one or more measured intermediate variables (mediators), which in turn affects the outcome variable. Traditionally, causal mediation analysis has been implemented within the framework of linear structural equation modeling (LSEM) [1] involving a series of liner regression models and two approaches have been proposed to quantify mediation as difference in coefficients method [2] and product of coefficients method [3]. For regression models using standard least squares without missing data, the estimators from both approaches are identical [4]. Recently, the methods developed in the LSEM framework were generalized to nonlinear models, e.g. proportional hazards model for survival data. Warner et al. [5] and Lu et al. [6] compared the hazard ratios of the exposure from Cox model both with and without adjusting for the potential mediators and a change in hazard ratios is taken as evidence of mediation through the mediators. Lange and Hansen argued that, such mediation analysis for survival data has severe shortcomings [7]. First of all, the observed changes in hazard ratios cannot be given a causal interpretation, and also it cannot be satisfied that the proportional hazards assumption holds for both models with and without the mediator.

More recently, researchers have addressed causal mediation analysis using the potential outcomes framework, which allows definition of mediation effects in causal terms and clear specification of assumptions required for a causal inference [8-10]. One very general approach for causal mediation analysis based on the potential outcomes framework is what Pearl refers to as the ?mediation formula?. This approach allows the estimation of expected potential outcomes, used in the definition of causal mediation effects, to be estimated as a function of association parameters for the outcome model that are directly estimable from the observed data [11]. The assumptions required by the mediation formula approach is that of ?sequential ignorability? [10], in which the exposure is first assumed to be ignorable given the baseline covariates, and then the mediator variable is assumed to be ignorable given observed values of exposure status and the baseline covariates. Imai et al. provided a general approach based on the mediation formula that can be applied to linear and nonlinear relationship, parametric and nonparametric models, continuous and discrete mediators, and various types of outcome variables [12]. One missing component in Imai et al. [10]?s approach is the mediation analysis for the survival data.Lange and Hansen gave formal counterfactual definitions of the causal direct and indirect effects for the Aalen?s additive hazard model, and proved that the ?product of coefficient? mediation effect estimate is mathematically consistent and allows a causal interpretation [7]. For the survival data mediation analysis, VanderWeele stated that there are multiple ways or scales by which a total effect might be decomposed into direct and indirect effects, for example, mediation effects on survival functions, hazard functions, mean or median survival time [13]. In the same paper, VanderWeele extended Lange and Hansen?s approach to proportional hazards model assuming a rare outcome or accelerated failure time models generally. A SAS macro is compiled and provided to apply VanderWeele?s method for the survival mediation analysis [14]. In addition, TchetgenTchetgen proposed theory to deliver the robust estimators for the natural direct and indirect effects under proportional hazards models and additive hazards models, as well as sensitivity analysis techniques for assessing the impact of the violation of the mediator?s ignorability assumption [15].TchetgenTchetgen also describes a new inverse odds ratio-weighted approach to estimate the natural direct and indirect effects in a number of commonly used models including the Cox proportional hazards regression for a survival outcome. An additional advantage of TchetgenTchetgen?s new method is that it can easily incorporate multiple categorical, discrete or continuous mediators [16].

Although we now have, at least some methods as described above for the causal mediation analysis in a survival context, a number of challenges still exist. First of all, survival data in biomedical research are often modelled with semi-parametric models, as Cox proportional hazards model or accelerated failure time model, which has the advantage of estimating covariate effects without the need to estimate the baseline hazard, and on the other hand, the parametric baseline hazard is necessary for the application of mediation formula-based causal mediation analysis. Secondly, the extensive computation issue due to multiple integration is another challenge for survival mediation analysis in complex causal models with multiple and/or multiple-stage mediators. Finally, corresponding sensitivity analysis approaches must be developed to assess the robustness of the conclusion regarding the survival mediation effects when the untestable no mediator-outcome confounder assumption is violated.