Implications of M bias in epidemiologic studies: a simulation study.

Collider-stratification bias arises from conditioning on a variable (collider) which opens a path from exposure to outcome. M bias occurs when the collider-stratification bias is transmitted through ancestors of exposure and outcome. Previous theoretical work, but not empirical data, has demonstrated that M bias is smaller than confounding bias. The authors simulated data for large cohort studies with binary exposure, an outcome, a collider, and 2 predictors of the collider. They created 178 scenarios by changing the frequencies of variables and/or the magnitudes of associations among the variables. They calculated the effect estimate, percentage bias, and mean squared error. M bias in these realistic scenarios ranged from -2% to -5%. When the authors increased one or both relative risks for the relation between the collider and unmeasured factors to ≥8, the negative bias was more substantial (>15%). The result was substantially biased (e.g., >20%) if an unmeasured confounder that was also a collider was not adjusted to avoid M bias. In scenarios resembling those the authors examined, M bias had a small impact unless associations between the collider and unmeasured confounders were very large (relative risk > 8). When a collider is itself an important confounder, controlling for confounding would take precedence over avoiding M bias.