Causal mediation analysis with multiple mediators

Abstract

In diverse fields of empirical research-including many in the biological sciences-attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways. For example, we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure (SBP) into effects via body mass index (BMI), via gamma-glutamyl transpeptidase (GGT), and via other pathways. Much progress has been made, mainly due to contributions from the field of causal inference, in understanding the precise nature of statistical estimands that capture such intuitive effects, the assumptions under which they can be identified, and statistical methods for doing so. These contributions have focused almost entirely on settings with a single mediator, or a set of mediators considered en bloc; in many applications, however, researchers attempt a much more ambitious decomposition into numerous path-specific effects through many mediators. In this article, we give counterfactual definitions of such path-specific estimands in settings with multiple mediators, when earlier mediators may affect later ones, showing that there are many ways in which decomposition can be done. We discuss the strong assumptions under which the effects are identified, suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified. These ideas are illustrated using data on alcohol consumption, SBP, BMI, and GGT from the Izhevsk Family Study. We aim to bridge the gap from "single mediator theory" to "multiple mediator practice," highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed.

Keywords: Causal pathways; Decomposition; Multiple mediation; Natural path-specific effects.

Figure 1

Top line: representations of mediation with (A) one, (B) two, and (C) n mediators, causally ordered. Second line: a depiction of mediation through two causally ordered mediators, with each of the four paths from X to Y highlighted; (D) shows the direct path (through neither nor ), (E) the indirect path through alone, (F) the indirect path through alone, and (G) the indirect path through both and . Lines 3 and 4: an illustration of the two possible ways of defining mediator-specific natural effects through three mediators. (H)–(L) show the first way and (M)–(Q) the second.

Figure 2

With (perfect correlation between and given ), all 24 possible decompositions of the total causal effect of heavy drinking on SBP into four path-specific components: a direct effect unmediated by BMI or GGT, an indirect effect via BMI alone, an indirect effect via GGT alone, and an indirect effect via both BMI and GGT. The numbers superimposed on the bars represent the code for that effect type (as defined in the caption of Table 2). The numbers along the x-axis represent the decomposition number, also defined in Table 2.