Fig. 1: Directed acyclic graph (DAG) of potential influences linking nonresponse to the association between genetics (G) and target phenotypes (Y₁ and Y₂).

Potential elements of nonresponse include overall item non-response behaviour (I), item-specific nonresponse (I₁ and I₂) and survey or study-level nonparticipation or ascertainment (S). Boxes indicate sets of traits, with paths to/from a box indicating potential paths to one or more traits in the box. GWAS aims to discover direct (α) or indirect (δ×η) associations with genetics G on phenotypes Y conditional on covariates. Analyses of observed data implicitly condition on nonresponse (I,S) and thus may be biased if that conditioning affects the expected joint distribution of genetic data, covariates and phenotypes (for example, β ≠ 0, θ ≠ 0 or γ×δ or γ×η ≠ 0). Modelling the missingness mechanism, including use of mediators as auxiliary variables, can reduce bias from nonresponse that does not depend directly on the missing value (that is, paths other than θ). The current study demonstrates association of genetics with nonresponse (that is, β and δ×γ) and considers the prospect of modelling missingness in GWAS.