Does collider bias induce non-linear associations?

Collider bias is a common issue in epidemiological studies. It is the underlying mechanism behind many potential sources of bias including stratified sampling, differential loss to follow-up, survivor bias, Berkson’s bias, and index event bias. In each case, bias in the true causal relationship between two variables is induced by conditioning on a common effect (a “collider”) or a variable that is causally downstream of the common effect (a “child” of the collider). In a comprehensive study of collider bias, Gkatzionis et al. (2025) quantified its magnitude in a wide range of settings. Our aim is both to illustrate the results of Gkatzionis et al. and extend them to further non-linear scenarios.