MR Dictionary

Collider

A collider is a variable that is a common consequence of two variables. For example, in an epidemiological setting, a collider can be a variable that is caused by both the exposure and the outcome of interest. The term "collider" refers to the fact that, in a directed acyclic graph (DAG), arrow heads showing directional associations from the exposure and outcome variables collide into a third variable (i.e., the collider). 

Adjusting for a collider in any epidemiological setting can induce an association between the two variables that cause its variation (e.g., the exposure and outcome in the above example). In an MR context, collider bias can be induced if adjusting for a collider (e.g., the exposure would be a collider of the genetic instrumental variable (IV) and any confounding factors of the exposure and outcome).  See Collider bias.

Collider bias. This figure illustrates collider bias in an MR study exploring the effect of maternal pregnancy body mass index (X: Mat. BMI) on offspring body mass index in later adult life (Y: Off. BMI). There is a clear violation of the assumption that the genetic instrumental variable (Z: Mat. BMI genetic IVs) is not related to the outcome (Y) other than via the exposure (X). It is clear that maternal BMI genetic IVs will influence offspring BMI genes (Off. BMI genes), which in turn will influence offspring BMI. This path can be blocked by adjusting for offspring genetic variants (this is illustrated by the box around offspring BMI genes). However, both maternal and paternal BMI genes (Z: Pat. BMI genes) ‘collide’ on offspring BMI genes and this generates a spurious association between maternal and paternal BMI genes. As only maternal and paternal BMI genes determine offspring BMI genes once we condition maternal genes on offspring genes, we know to some extent what paternal genotype is (e.g., if mother is a homozygote for a BMI increasing allele at a gene and offspring is heterozygous at the same gene, then dad must be heterozygous or homozygous for the alternative (not BMI increasing) allele). If it is not possible to condition on paternal genotype (which is often the case) and paternal BMI genes directly influence offspring BMI, this collider bias will bias the MR analysis of maternal pregnancy BMI on subsequent offspring BMI (26).
Figure 4.1 - Collider bias. This figure illustrates collider bias in an MR study exploring the effect of maternal pregnancy body mass index (X: Mat. BMI) on offspring body mass index in later adult life (Y: Off. BMI). There is a clear violation of the assumption that the genetic instrumental variable (Z: Mat. BMI genetic IVs) is not related to the outcome (Y) other than via the exposure (X). It is clear that maternal BMI genetic IVs will influence offspring BMI genes (Off. BMI genes), which in turn will influence offspring BMI. This path can be blocked by adjusting for offspring genetic variants (this is illustrated by the box around offspring BMI genes). However, both maternal and paternal BMI genes (Z: Pat. BMI genes) ‘collide’ on offspring BMI genes and this generates a spurious association between maternal and paternal BMI genes. As only maternal and paternal BMI genes determine offspring BMI genes once we condition maternal genes on offspring genes, we know to some extent what paternal genotype is (e.g., if mother is a homozygote for a BMI increasing allele at a gene and offspring is heterozygous at the same gene, then dad must be heterozygous or homozygous for the alternative (not BMI increasing) allele). If it is not possible to condition on paternal genotype (which is often the case) and paternal BMI genes directly influence offspring BMI, this collider bias will bias the MR analysis of maternal pregnancy BMI on subsequent offspring BMI (26).

References

Other terms in 'Sources of bias and limitations in MR':