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 (alpha) or indirect (delta x eta) 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, beta not equal to 0, theta not equal to 0 or gamma x delta or gamma x eta not equal to 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 theta). The current study demonstrates association of genetics with nonresponse (that is, beta and delta x gamma) and considers the prospect of modelling missingness in GWAS.
