Skip to main content
Top
Published in:

Open Access 03-01-2024 | ESSAY

Bias assessment and correction for Levin’s population attributable fraction in the presence of confounding

Authors: John Ferguson, Alberto Alvarez, Martin Mulligan, Conor Judge, Martin O’Donnell

Published in: European Journal of Epidemiology | Issue 2/2024

Login to get access

Abstract

In 1953, Morton Levin introduced a simple approach to estimating population attributable fractions (PAF) depending only on risk factor prevalence and relative risk. This formula and its extensions are still in widespread use today, particularly to estimate PAF in populations where individual data is unavailable. Unfortunately, Levin’s approach is known to be asymptotically biased for the PAF when the risk factor-disease relationship is confounded even if relative risks that are correctly adjusted for confounding are used in the estimator. Here we describe a simple re-expression of Miettinen’s estimand that depends on the causal relative risk, the unadjusted relative risk and the population risk factor prevalence. While this re-expression is not new, it has been underappreciated in the literature, and the associated estimator may be useful in estimating PAF in populations when individual data is unavailable provided estimated adjusted and unadjusted relative risks can be transported to the population of interest. Using the re-expressed estimand, we develop novel analytic formulae for the relative and absolute asymptotic bias in Levin’s formula, solidifying earlier work by Darrow and Steenland that used simulations to investigate this bias. We extend all results to settings with non-binary valued risk factors and continuous exposures and discuss the utility of these results in estimating PAF in practice.
Appendix
Available only for authorised users
Footnotes
1
Note that if Y is an indicator for incident disease over a period of time, rather than prevalent disease, in a cohort of healthy individuals at baseline, the PAF as defined by (1) would be interpreted as the proportion of incident disease in the cohort over that period of time that would have been avoided if the entire cohort were risk-factor unexposed. For simplicity, in this manuscript we will interpret PAFs in terms of decreases in prevalent, rather than incident, disease.
 
2
\(\widehat{R{R}_{C}}\) may be biased for the true causal relative risk, \(R{R}_{C}\), due to residual confounding. However, a discussion of ensuing bias in the estimated PAF due to residual confounding is beyond the scope of this manuscript, where we are solely concerned with the difference in the estimands \(PA{F}_{L}\) and \(PA{F}_{M}\).
 
3
Note that (5) is technically the relative discrepancy (or error) between the estimands \(PA{F}_{L}\) and \(PAF\). However, if statistically consistent estimates of \(R{R}_{C}\) and \(\pi\) are plugged in to Levin’s formula, (5) will represent the asymptotic bias of the resulting estimator. As a result, we will (somewhat informally) refer to (5) and comparable quantities as biases throughout the manuscript.
 
4
Being a measure of the total disease burden attributable to an exposure or risk factor, defining PAF necessitates consideration of hypothetical populations (such as a world without air pollution) that may be unachievable under realistic public health interventions. This distinguishes PAF from the related idea of impact fractions which can be loosely defined as the relative decrease in disease prevalence achievable from a practically implementable intervention on a risk factor.
 
Literature
1.
go back to reference Doll R. On the aetiology of cancer of the lung. Acta Unio Int Contra Cancrum. 1951;7(1 Spec. No.):39–50.PubMed Doll R. On the aetiology of cancer of the lung. Acta Unio Int Contra Cancrum. 1951;7(1 Spec. No.):39–50.PubMed
2.
go back to reference Liu K et al. Modifiable risk factors and incidence of gout: estimation of population attributable fraction in the US. In: Seminars in Arthritis and Rheumatism. Elsevier; 2022. Liu K et al. Modifiable risk factors and incidence of gout: estimation of population attributable fraction in the US. In: Seminars in Arthritis and Rheumatism. Elsevier; 2022.
3.
go back to reference Borelli WV, et al. Preventable risk factors of dementia: population attributable fractions in a Brazilian population-based study. Lancet Reg Health Am. 2022;11: 100256.PubMedPubMedCentral Borelli WV, et al. Preventable risk factors of dementia: population attributable fractions in a Brazilian population-based study. Lancet Reg Health Am. 2022;11: 100256.PubMedPubMedCentral
4.
go back to reference Tybjerg AJ, et al. Updated fraction of cancer attributable to lifestyle and environmental factors in Denmark in 2018. Sci Rep. 2022;12(1):1–11.CrossRef Tybjerg AJ, et al. Updated fraction of cancer attributable to lifestyle and environmental factors in Denmark in 2018. Sci Rep. 2022;12(1):1–11.CrossRef
6.
go back to reference Tran KB, et al. The global burden of cancer attributable to risk factors, 2010–19: a systematic analysis for the Global Burden of Disease Study 2019. Lancet. 2022;400(10352):563–91.CrossRef Tran KB, et al. The global burden of cancer attributable to risk factors, 2010–19: a systematic analysis for the Global Burden of Disease Study 2019. Lancet. 2022;400(10352):563–91.CrossRef
7.
go back to reference Levin ML. The occurrence of lung cancer in man. Acta Unio int Contra Cancrum. 1953;9:531–941.PubMed Levin ML. The occurrence of lung cancer in man. Acta Unio int Contra Cancrum. 1953;9:531–941.PubMed
8.
go back to reference Khosravi A, Mansournia MA. Issues with incorrect computing of population attributable fraction (PAF) in a global perspective on coal-fired power plants and burden of lung cancer. Environ Health. 2019;18(1):1–2.CrossRef Khosravi A, Mansournia MA. Issues with incorrect computing of population attributable fraction (PAF) in a global perspective on coal-fired power plants and burden of lung cancer. Environ Health. 2019;18(1):1–2.CrossRef
10.
go back to reference Darrow LA, Steenland NK. Confounding and bias in the attributable fraction. Epidemiology. 2011;22:53–8.CrossRefPubMed Darrow LA, Steenland NK. Confounding and bias in the attributable fraction. Epidemiology. 2011;22:53–8.CrossRefPubMed
12.
go back to reference Hernan MA, Robins JM. Causal inference. Boca Raton: CRC Press; 2023. Hernan MA, Robins JM. Causal inference. Boca Raton: CRC Press; 2023.
13.
go back to reference Miettinen OS. Proportion of disease caused or prevented by a given exposure, trait or intervention. Am J Epidemiol. 1974;99(5):325–32.CrossRefPubMed Miettinen OS. Proportion of disease caused or prevented by a given exposure, trait or intervention. Am J Epidemiol. 1974;99(5):325–32.CrossRefPubMed
14.
go back to reference Suzuki E, Yamamoto E. Attributable fraction and related measures: conceptual relations in the counterfactual framework. J Causal Inference. 2023;11(1):20210068.MathSciNetCrossRef Suzuki E, Yamamoto E. Attributable fraction and related measures: conceptual relations in the counterfactual framework. J Causal Inference. 2023;11(1):20210068.MathSciNetCrossRef
15.
go back to reference Welberry HJ, Tisdell CC, Huque MH, Jorm LR. Have We Been Underestimating Modifiable Dementia Risk? An Alternative Approach for Calculating the Combined Population Attributable Fraction for Modifiable Dementia Risk Factors. Am J Epidemiol, 2023;192(10):1763–1771. Welberry HJ, Tisdell CC, Huque MH, Jorm LR. Have We Been Underestimating Modifiable Dementia Risk? An Alternative Approach for Calculating the Combined Population Attributable Fraction for Modifiable Dementia Risk Factors. Am J Epidemiol, 2023;192(10):1763–1771.
16.
go back to reference Ferguson J, et al. Population attributable fractions for continuously distributed exposures. Epidemiol Methods. 2020;9(1):20190037.CrossRef Ferguson J, et al. Population attributable fractions for continuously distributed exposures. Epidemiol Methods. 2020;9(1):20190037.CrossRef
17.
go back to reference Bruzzi P, et al. Estimating the population attributable risk for multiple risk factors using case-control data. Am J Epidemiol. 1985;122(5):904–14.CrossRefPubMed Bruzzi P, et al. Estimating the population attributable risk for multiple risk factors using case-control data. Am J Epidemiol. 1985;122(5):904–14.CrossRefPubMed
18.
go back to reference Abreo A, et al. The impact of modifiable risk factor reduction on childhood asthma development. Clin Transl Med. 2018;7(1):1–12.CrossRef Abreo A, et al. The impact of modifiable risk factor reduction on childhood asthma development. Clin Transl Med. 2018;7(1):1–12.CrossRef
19.
go back to reference Lee M, et al. Variation in population attributable fraction of dementia associated with potentially modifiable risk factors by race and ethnicity in the US. JAMA Netw Open. 2022;5(7):e2219672–e2219672.MathSciNetCrossRefPubMedPubMedCentral Lee M, et al. Variation in population attributable fraction of dementia associated with potentially modifiable risk factors by race and ethnicity in the US. JAMA Netw Open. 2022;5(7):e2219672–e2219672.MathSciNetCrossRefPubMedPubMedCentral
Metadata
Title
Bias assessment and correction for Levin’s population attributable fraction in the presence of confounding
Authors
John Ferguson
Alberto Alvarez
Martin Mulligan
Conor Judge
Martin O’Donnell
Publication date
03-01-2024
Publisher
Springer Netherlands
Published in
European Journal of Epidemiology / Issue 2/2024
Print ISSN: 0393-2990
Electronic ISSN: 1573-7284
DOI
https://doi.org/10.1007/s10654-023-01063-8