Collider bias occurs when two variables (X and Y) independently cause a third variable (Z). In this situation Z is a collider, and statistical adjustment for Z will bias the estimated causal association of X (exposure) on Y (outcome) (see Figure 2). Statistical adjustment of the XY association for a variable Z is equivalent to observing this association in a sub-population where all individuals share the same value of Z.1,13 Hence if both X and Y cause participation in a study (Z), then investigating associations in the selected sample (i.e. with Z = 1, indicating participation in the study) is equivalent to conditioning on Z, which in turn may induce collider bias.
