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Relationship between collider bias and interactions on the log-additive scale.

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Summary

Collider bias, caused by conditioning on a common effect, can distort exposure-outcome associations. This study quantifies this bias, showing interaction terms in collider models inform its magnitude.

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Causal Inference

Background:

  • Collider bias arises from conditioning on a common effect of two variables.
  • Selection bias due to colliders can distort observed associations between exposures and outcomes.
  • Understanding and quantifying collider bias is crucial for accurate causal inference in observational studies.

Purpose of the Study:

  • To quantify collider bias in the estimated association between an exposure and an outcome.
  • To investigate the role of interaction terms in measuring collider bias under different regression models.
  • To discuss implications for methods adjusting for collider bias, like inverse probability weighting.

Main Methods:

  • Mathematical derivation of collider bias magnitude.
  • Analysis under logistic, linear, and Poisson regression models for exposure-outcome association.
  • Numerical illustrations to assess the informativeness of interaction terms.

Main Results:

  • Collider bias magnitude is proportional to the strength of interaction between exposure and confounder in a log-additive collider model.
  • This proportionality holds for logistic, linear, and Poisson regression models.
  • Interaction terms in collider models provide information about bias magnitude, even if the model is misspecified.

Conclusions:

  • The strength of interaction in a collider's model is a key determinant of collider bias.
  • Methods adjusting for collider bias should consider interactions, particularly in inverse probability weighting.
  • Accurate quantification of collider bias is essential for valid epidemiological research.