Fig. 1. Illustrative example of collider bias.

a A directed acyclic graph (DAG) illustrating a scenario in which collider bias would distort the estimate of the causal effect of the risk factor on the outcome. Directed arrows indicate causal effects and dotted lines indicate induced associations. Note that the risk factor and the outcome can be associated with sample selection indirectly (e.g. through unmeasured confounding variables), as shown in b. The type of collider bias induced in graph (b) is sometimes referred to as M-bias. To illustrate the example in a, consider academic ability and sporting ability to each influence selection into a prestigious school. As shown in c, these traits are negligibly correlated in the general population (blue dotted line), but because they are selected for enrolment they become strongly correlated when analysing only the selected individuals (red dotted line).