Causal Inference
Errors and Their Visualization in the Calculation of the Population Attributable Fraction Etsuji Suzuki* Etsuji Suzuki Eiji Yamamoto
The population attributable fraction (PAF) has been widely used to assess the potential impact of health interventions in epidemiology. One of the common errors in the calculation of the PAF is the use of an “adjusted” risk ratio in the Levin formula (i.e., the “partially adjusted” Levin formula). Although previous studies have addressed the “bias” in this approach, there is some confusion because of the lack of a clear definition of the PAF, and it is important for researchers to understand the concept of the PAF in the counterfactual framework. In this presentation, we discuss the errors in the “partially adjusted” Levin formula and illustrate them visually in wireframes by varying the standardized mortality ratio (SMR) and associational risk ratio (aRR) when the prevalence of exposure is fixed. When SMR > 1, both the true PAF and the “partially adjusted” Levin formula become positive; when SMR = 1, they both become 0; and when SMR 1. When SMR > aRR, the absolute bias is positive and relative bias is larger than 1. Their magnitudes increase as the difference between SMR and aRR increases. By contrast, when SMR < aRR, the absolute bias is negative and the relative bias is smaller than 1. Their magnitudes are relatively small. The patterns of the wireframes did not substantially change when the prevalence of exposure varied. Although the bias of the “partially adjusted” Levin formula may be much smaller than that of the (crude) Levin formula, this does not necessarily justify the use of the “partially adjusted” Levin formula. A comprehensive understanding and accurate interpretation of the PAF requires a clear grasp of its definition in the counterfactual framework. Improper calculations of the PAF frequently occur in the absence of this understanding, and confusion persists regarding the condition under which the Levin formula is valid.