Glossary
Collider bias
What is Collider Bias?
Collider bias occurs when a statistical analysis conditions on a shared consequence of other variables, potentially creating or distorting an association. The relevant causes need not be the treatment and outcome themselves; they may also be causes of those variables.
How it works
In a causal diagram, or directed acyclic graph, a collider is a variable with two arrows pointing into it: A → C ← B. Conditioning on it (including it as a control variable or restricting the sample to it) opens a path between its causes that would otherwise be blocked. This can create an association where none existed, or alter the size or direction of an existing association. Griffith and colleagues explain how sampling through testing, hospitalization, or voluntary participation can create this problem.
Applied example: selection creates a relationship
Consider a hypothetical program that admits applicants who have either a strong art portfolio or a strong music audition. In a pool of 400 applicants, assume the two skills are independent: 100 qualify in both, 100 in art only, 100 in music only, and 100 in neither. Before selection, half of those with strong art skills have strong music skills, and so do half of those without strong art skills.
The program admits the first three groups and excludes the fourth. Among admitted applicants without strong art skills, all have strong music skills: that was their only route in. Among admitted applicants with strong art skills, only half also have strong music skills. Looking only at admitted applicants therefore creates a negative association between the two skills, even though they were independent in the full pool.
The diagram is art qualification → admission ← music qualification. Admission is the collider. Restricting the analysis to admitted applicants conditions on it. This particular “either qualifies” rule produces the negative relationship; a different selection process can produce a different distortion. The example illustrates the mechanism; these hypothetical numbers do not describe real admissions or clinical findings.
Why it matters
Adding more control variables does not automatically improve an analysis. A variable that looks useful can introduce bias if it is a shared consequence. Think through the causal relationships before adjusting for it or using it to select the sample.