Challenges Raised by Mediation Analysis in a High-Dimension Setting

Abstract

Background: Mediation analysis is used in epidemiology to identify pathways through which exposures influence health. The advent of high-throughput (omics) technologies gives opportunities to perform mediation analysis with a high-dimension pool of covariates.

Objective: We aimed to highlight some biostatistical issues of this expanding field of high-dimension mediation.

Discussion: The mediation techniques used for a single mediator cannot be generalized in a straightforward manner to high-dimension mediation. Causal knowledge on the relation between covariates is required for mediation analysis, and it is expected to be more limited as dimension and system complexity increase. The methods developed in high dimension can be distinguished according to whether mediators are considered separately or as a whole. Methods considering each potential mediator separately do not allow efficient identification of the indirect effects when mutual influences exist among the mediators, which is expected for many biological (e.g., epigenetic) parameters. In this context, methods considering all potential mediators simultaneously, based, for example, on data reduction techniques, are more adapted to the causal inference framework. Their cost is a possible lack of ability to single out the causal mediators. Moreover, the ability of the mediators to predict the outcome can be overestimated, in particular because many machine-learning algorithms are optimized to increase predictive ability rather than their aptitude to make causal inference. Given the lack of overarching validated framework and the generally complex causal structure of high-dimension data, analysis of high-dimension mediation currently requires great caution and effort to incorporate a priori biological knowledge. https://doi.org/10.1289/EHP6240.

Figure 1.

Example of the effect of a single exposure E whose effect on outcome Y is mediated by a single mediator M. Exposure–outcome (${\mathit{C}}_1$), exposure–mediator (${\mathit{C}}_2$) and mediator–outcome confounders (${\mathit{C}}_3$) need to be controlled for. Adapted from VanderWeele (2015).

Figure 2.

Example of mediation with two mediators $M_1$ and $M_2$ influencing each other.

Figure 3.

High-dimension mediation. Hypothesized relation between an exposure E; a health outcome Y; an exposure–outcome confounder ${\mathit{C}}_1$; a high-dimension mediator $M={\left(M_i\right)}_{i\le p}$, where p is typically larger than the number of observations in the data set, an exposure–mediator confounder ${\mathit{C}}_2$; and a mediator–outcome confounder ${\mathit{C}}_3$. Causal influences also exist among the candidate mediators (here, $M_j$ influences $M_i$). p is typically much larger than the number of observations n in the data set.

Figure 4.

Raw distribution of the p-values of the Sobel mediation test for 5,000 simulated variables that are putative mediators (in red, not uniform) and corrected distribution (blue) after using the fdrtool package (R version 3.6.1; R Development Core Team). After correction, the distribution is closer to that expected under the simulated causal model, which assumes the presence of mediators, so that one observes a mixture of a uniform distribution and a distribution with an excess of small p-values. The distribution of the raw p-values should be uniform except for an excess of small p-values corresponding to true mediators. The fact that the (red) distribution is not uniform may indicate several deviations from the null model such as confounding factors or poor standardization of the test statistic. The red histogram indicates that the Sobel test is too conservative (MacKinnon et al. 1995). Here we use the R package fdrtool that implements an empirical null distribution approach to transform initial p-values to uniformly distributed p-values and that provides control of the false discovery rate (Strimmer 2008). To perform simulations, we consider the mediation model of Equation 4, where there are 500 random mediators influenced by the environment that affect the simulated outcome according to Equation 4. We considered 4,500 additional putative mediators distributed according to a multivariate distribution that did not depend on environment and outcome (see code on GitHub https://github.com/mblumuga/opinion_mediation/blob/master/Simus_Sobel_FDR.R).