Correction to: Is population structure in the genetic biobank era irrelevant, a challenge, or an opportunity?

Correction to: Human Genetics https://doi.org/10.1007/s00439-019-02014-8

In the original article publication, there is an incorrect impression that Fig. 1 formed a formal Directed Acyclic Graph (DAG) by describing it as a causal model. However, it was not correct if interpreted in this way. The correct Fig. 1 is with a model that is correct when interpreted as a DAG, by making the differences between the model representation of ancestry and the true ancestry, which is always unobserved, explicit. We stress that there are other ways to introduce these biases, and it need not act through the separation between observed and true ancestry.

Fig. 1

Causal models including ancestry for the effect of a SNP (G) on a trait (T). The true ancestry (A) is never observed, but is measured through A₀. a Correction for stratification will be accurate when observed ancestry (A₀) is confounding T. b Correction for structure may give biased inference when observed ancestry A₀ is associated with the causal pathway by which the SNP acts, leading to a correlation in the effect of the SNP on ancestry and the trait. For example, the same SNPs are predictive of height and ancestry. Alternatively, ancestry may be associated with a trait T_A (e.g. skin tone) that causes a trait (e.g. skin cancer). c Correction for structure will be incomplete when ancestry is associated with the environment (E) due to shared history and geography (H), for example T = BMI with E = diet choice. d Correction for structure when using causal inference is robust to complexity, provided the assumptions of Mendelian randomization (see text) are met; particularly all remaining effects of ancestry go through the trait (T) so there is no direct effect of ancestry (A) on the outcome (O)