Re. E-values for Mendelian Randomization

Swanson and VanderWeele1 argued that E-values can be useful in Mendelian randomization (MR) studies to address confounding of the instrumental variable (IV) and the outcome. We agree but wish to clarify that there are two possible E-values in this context, with different merits.

Swanson and VanderWeele considered the E-value for the IV-outcome association, say
, which measures the degree of IV-outcome confounding required to explain away the association. If
is sufficiently large, then the IV-outcome association cannot plausibly be explained away by confounding, and one can thus infer that the IV has a causal effect on the outcome. Provided that one has faith in the exclusion restriction (the IV only affects the outcome through the exposure), one can then also infer that the exposure has a causal effect on the outcome.

However, if one doubts the validity of the IV, then one could also consider the standard E-value for the exposure–outcome association, say
. This E-value ignores the IV altogether and is thus not part of a “regular” MR analysis. If
is sufficiently large, then the exposure–outcome association cannot plausibly be explained away by confounding, and one can again infer that the exposure has a causal effect on the outcome.