Simple Formulae for Evaluating the Potential Impact of Confounding Bias

Abstract

Unmeasured confounding is a common problem in observational studies. This article presents simple formulae that can set the bounds of the confounding risk ratio under three standard populations of the exposed, unexposed, and total groups. The bounds are derived by considering the confounding risk ratio as a function of the prevalence of a covariate, and can be constructed using only information about either the exposure–confounder or the disease–confounder relationship. The formulae can be extended to the confounding odds ratio in case–control studies, and the confounding risk difference is discussed. The application of these formulae is demonstrated using an example in which estimation may suffer from bias due to population stratification. The formulae can help to provide a realistic picture of the potential impact of bias due to confounding.

Keywords:

• Confounding risk ratio
• Epidemiologic methods
• Population stratification
• Standardization

Mathematics Subject Classification:

• 62P10
• 92B15

Acknowledgment

The author thanks the reviewers for their constructive comments that substantially improved this manuscript.