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Biometrika 1995 82(3):633-638; doi:10.1093/biomet/82.3.633
© 1995 by Biometrika Trust
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MISCELLANEA

A note on the bias due to omitted confounders

CHRISTIANA DRAKE and ALLAN McQUARRIE

Division of Statistics, University of California Davis, California 95616, U. S. A

Received for publication 1 November 1992. Revision received 1 December 1994.
  Abstract

In observational studies some confounders may be unknown and therefore omitted from the analysis while others are adjusted for. Approximations to the functions defining the relationship between the parameters in the full and reduced models are proposed leading to asymptotic bias estimates. Numerical calculations for logistic and Poisson regression models show good agreement between asymptotic and simulation bias. A data set containing the relationship between low birth weight and smoking (Hosmer & Lemeshow, 1989) is used as an illustration.

Key Words: Bias • Confounding • Generalised linear model • Omitted covariates


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