Collider-stratification bias is a type of bias induced in causal analysis when you condition on a collider.
The image below shows three variables: X, Y, and a collider.
In this diagram, X and Y both cause the collider. The relationship between X and Y is unknown and is the estimate of interest (the extent to which X causes Y). If we fit a model that controls for the collider, our estimate of the effect of X on Y will be biased.
It’s helpful to think about this temporally. If X and Y both cause the collider, they must happen before the collider. Given this, the collider can’t cause X or Y. But it will be correlated with both.
Here’s an image that shows what this might look like in a plot (where q is the collider variable):
