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Confounding and Bias in the Attributable Fraction

Darrow, Lyndsey A.; Steenland, N. Kyle

doi: 10.1097/EDE.0b013e3181fce49b
Methods: Original Article

Inappropriate methods are frequently used to calculate the population attributable fraction (AF) for a given exposure of interest. This commonly occurs when authors use adjusted relative risks (RRs) reported in the literature (the “source” data), without access to the original data. In this analysis, we examine the relationship between the direction and magnitude of confounding in the source data and resulting bias in the attributable fraction when incorrect methods are used. We assess confounding by the confounding risk ratio, which is the ratio of the crude RR to the adjusted RR. We assess bias in the AF by the ratio of the incorrectly calculated AF to the correctly calculated AF. Using generated data, we examine the relationship between confounding and AF bias under various scenarios of population prevalence of exposure and strength of the exposure-disease association. For confounding risk ratios greater than 1.0 (ie, crude RR >adjusted RR), the AF is underestimated; for confounding risk ratios less than 1.0 (ie, crude RR <adjusted RR), the AF is overestimated. Bias in the AF increases as the magnitude of the confounding increases, and is dependent on the prevalence of exposure in the total population, with bias greatest at the lowest prevalence of exposure. Bias in the AF is also higher when the exposure-disease association is weaker. Results of these analyses can assist interpretation of incorrectly calculated attributable fraction estimates commonly reported in the epidemiologic literature.


From the Department of Environmental Health, Rollins School of Public Health, Emory University, Atlanta, GA.

Submitted 1 April 2010; accepted 14 July 2010; posted 25 October 2010.

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Correspondence: Lyndsey Darrow, Department of Environmental Health, Rollins School of Public Health, Emory University, 1518 Clifton Road NE, Atlanta, GA 30322. E-mail:

© 2011 Lippincott Williams & Wilkins, Inc.