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 epsilon 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.