In other words, sample selection can bias associations between variables that influence participation or retention in a study. This can include inducing spurious associations when no such association exists in the intended study population or, if two variables are correlated in the intended study population and both cause selection, biasing the estimated correlation in the selected sample. Moreover, this selection bias will apply to the genetic correlates (or other ancestors) of these variables, unless the phenotypes are also controlled for. Therefore if genes Gx and Gy cause X (exposure) and Y (outcome), respectively, and both X and Y influence participation, then in the selected sample Gx will appear to be associated with Y (unless X is also controlled for). More complex situations can also give rise to collider bias, such as when the outcome (Y) does not directly cause selection into the study (i.e. it is a downstream consequence of something else that is causing selection into the study).
