Fig. 1.

Nine simulation scenarios. E, C, D indicate exposure, matching factor, outcome, respectively. Let variable S indicate whether a person is selected for case-control study or not, the square around S indicates the analysis is conditional on individuals having been selected into the matched case-control study. Dashed line C--D show the colliding bias (i.e., selective bias) due to matching on C. S is a collider on C→S←D. Colliding bias will arise if conditioning on colliding node (i.e., S). a) C is a confounder for the exposure E and the outcome D; b) C is a common cause of E and D with an absence of cause effect between them; c) C is an independent cause of D; d) C is a cause of E, but has no direct causal effect on D; e) C is a common effect (i.e. collider) of E and D; f) C is an effect of outcome D; g) C is an effect of exposure E; h) C is a mediator of causal path from E to D; i) C is an instrumental variable for E and D