Direct, Indirect, and Total Genetic Effects

Introduction

In genetic mediation, a genetic variant may influence an exposure, which may then influence an outcome both directly and through an intermediate phenotype. The same overall genetic association with the outcome can therefore represent several different pathways. Separating those pathways is essential for stating what an effect estimate means.

This tutorial defines direct, indirect, and total effects for a linear exposure–mediator–outcome pathway, with a genetic variant as a possible source of variation in the exposure. The central distinction is between effects per unit change in the exposure and effects per allele of the variant. These are related, but they are not the same estimand.

A Linear Pathway Model

Consider the following additive structural equations. They specify the relationships represented by the pathway diagram and the scale on which the path coefficients are defined.

Here, \(\pi\) is the change in the mean of \(X\) per additional allele of \(G\); \(a\) is the change in the mean of \(M\) per unit increase in \(X\); \(b\) is the change in the mean of \(Y\) per unit increase in \(M\), holding \(X\) fixed; and \(c'\) is the change in the mean of \(Y\) per unit increase in \(X\), holding \(M\) fixed. The intercepts are \(\alpha_X,\alpha_M,\alpha_Y\), and the \(\varepsilon\) terms represent structural disturbances.

The equations describe a linear, additive model with no exposure–mediator interaction: the coefficient \(b\) does not depend on the value of \(X\). For the path decomposition below, assume the equations represent the stated pathways, their coefficients apply to the same target population, and there are no additional directed paths from \(X\) to \(Y\). To interpret the coefficients causally, the structural relationships must also have a valid causal interpretation; an algebraic decomposition alone does not establish that observational data identify causal effects.

The product \(ab\) follows the two links in the mediated path. A one-unit increase in \(X\) changes \(M\) by \(a\) units; each unit change in \(M\) changes \(Y\) by \(b\) units. Their product is therefore the change in \(Y\) transmitted along \(X \to M \to Y\), per unit increase in \(X\).

Why the Total Effect Is the Sum of the Paths

The decomposition can be justified directly by substituting the mediator equation into the outcome equation. Doing so expresses the outcome using \(X\) and the structural disturbances, rather than \(M\).

The coefficient multiplying \(X\) is \(c'+ab\). Thus, under this model, the total change in \(Y\) per unit change in \(X\) is the direct contribution \(c'\) plus the mediated contribution \(ab\). For this coefficient to also be the slope in a regression of \(Y\) on \(X\), the composite disturbance \(b\varepsilon_M+\varepsilon_Y\) must not be associated with \(X\) in the relevant model. For a causal interpretation, the structural equations and their assumptions must be appropriate for the causal question as well.

Effects Can Reinforce or Oppose Each Other

Direct and indirect effects need not have the same sign. If both are positive, they reinforce one another. If one is positive and the other negative, they oppose one another, and the total can be smaller than either path contribution. The total effect may even have a different sign from one of its component paths.

For this reason, the direct, indirect, and total effects should be reported with their signs and units. A proportion mediated, sometimes formed by dividing the indirect effect by the total effect, can be difficult to interpret when the effects oppose each other or the total is near zero. It is not needed to define the pathway-specific effects.

Moving From the Exposure Scale to the Allele Scale

The coefficients \(c'\), \(ab\), and \(c'+ab\) are effects per unit increase in \(X\). If the variant changes \(X\) by \(\pi\) units per allele, the corresponding effects along the specified pathways per allele are obtained by multiplying by \(\pi\). This follows because each additional allele changes \(X\) by \(\pi\), and the exposure-scale pathway effects apply to each unit change in \(X\).

These are effects of the variant transmitted through the stated exposure pathways. They are not the same estimands as the exposure effects themselves: \(\pi c'\) is measured per allele, while \(c'\) is measured per unit of \(X\). The equations also presume that the variant’s effect on \(Y\) operates through \(X\) in this pathway model. A direct route from \(G\) to \(Y\) outside \(X\) would contribute an additional term to the total genetic effect.

What the Path Decomposition Does—and Does Not—Say

A path diagram and its structural equations make the estimands explicit: which variable changes, which route carries the effect, and what units the coefficient uses. But writing a path model does not, by itself, show that its effects can be estimated causally from observed genetic associations. That requires suitable identification assumptions about the pathway and data. It is useful to keep the definition of an effect separate from the question of whether a particular analysis identifies it.

The simple product \(ab\) also depends on the additive model used here. If the effect of \(M\) on \(Y\) varies with \(X\), then a single constant \(b\) does not describe that relationship, and the decomposition cannot be used in this form without modification. The direct, indirect, and total effects must always be tied to their model and scale.

Common Mistake

• Wrong reasoning: “The indirect effect is \(a+b\), because \(a\) and \(b\) are the two coefficients on the mediated path.”
• Correction: The path coefficients multiply. A unit increase in \(X\) changes \(M\) by \(a\), and that change in \(M\) changes \(Y\) by \(b\) per mediator unit. Therefore the indirect effect per unit of \(X\) is \(ab\), not \(a+b\).
• Another scale error: “The effect per allele is the same as the effect per unit of \(X\).” The per-allele effect through the pathway is multiplied by the variant–exposure association \(\pi\); it has units per allele.