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Epidemiology:
doi: 10.1097/EDE.0b013e318259c31c
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Software for Unbiased Estimation of Attributable Risk

Hamel, Jean-François; Fouquet, Natacha; Ha, Catherine; Goldberg, Marcel; Roquelaure, Yves

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Laboratory of Ergonomics and Epidemiology in Health at Work University of Angers Angers, France jean-francois.hamel@etud.univ-angers.fr (Hamel)

Laboratory of Ergonomics and Epidemiology in Health at Work University of Angers Angers, France Work Health Department Institute of Health Surveillance Saint-Maurice, France (Fouquet)

Work Health Department Institute of Health Surveillance Saint-Maurice, France (Ha)

Inserm U1018 Population-based Cohorts Research Platform Centre for Research in Epidemiology and Population Health Villejuif, France Versailles-Saint Quentin University UMRS, France (Goldberg)

Laboratory of Ergonomics and Epidemiology in Health at Work University of Angers Angers, France (Roquelaure)

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To the Editor:

Attributable risk (AR) provides a measurement of the population burden of a disease associated with a particular exposure. AR can be interpreted as the proportion of disease cases (eg, carpal tunnel syndrome) that could be avoided if the effects of the exposure (eg, work activity) were totally eliminated from the population. Such an index can help in the design of public health prevention strategies by establishing the relative importance of various exposures.1 However, few studies report ARs, and those are usually Levin's unadjusted estimators, which are suitable only for binary exposure factors. A more consistent AR assessment would take into account both the multifactorial nature of diseases and confounding factors.2

Bruzzi et al3 proposed a method based on logistic regression for computing n-dimensional ARs. This method provides estimates of adjusted ARs for combinations of exposures, but not separately for each exposure. Several methods have subsequently been proposed to compute an AR estimate for each exposure from these combined ARs4:

* The “sequential AR method” is based on the assessment of exposure-specific effects by successively removing each exposure from the analysis while simultaneously calculating their respective contribution to the combined AR. This approach depends on the choice of the exposure permutation.5

* The “average AR method” averages the sequential ARs over all the set of possible permutations, and thus allows estimation of AR independent of the order in which exposures are removed.

We briefly illustrate these various methods using data from the Surveillance Program for carpal tunnel syndrome in the Pays de la Loire Region (France). We focus on the main carpal tunnel syndrome exposures for AR estimations: age, sex, obesity, diabetes mellitus, and occupational category for comparing unadjusted, sequential, and average ARs. For the sequential AR estimations, we chose 2 removal sequences: (1) sex, obesity, occupational category, diabetes mellitus, age; and (2) occupational category, diabetes mellitus, obesity, age, sex.

The ARs were highly dependent on the computation method. Crude ARs computed with the Levin formula were overvalued, as demonstrated by the fact that the sum of these ARs (160%) was higher than the possible maximum of 100%. Sequential ARs were slightly dependent on the order of exposures chosen for removal. The sequential ARs were overvalued for the first exposures removed and undervalued for the last exposures removed (Table). (The 2 sequences presented here are just 2 examples among the 5 = 120 possible permutations of the 5 exposures.) In the final method, the average ARs were constant regardless of the order of removal of the exposures, and their sum was less than 100%, which allows them to be interpreted as the proportion of disease cases that could be avoided in the population if the exposure of interest was eliminated.

Table. AR Estimated ...
Table. AR Estimated ...
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Although the average AR method is clearly advantageous, there is no convenient software that allows estimation of average ARs. Standard statistical software, such as The R Project for Statistical Computing, SAS (SAS Institute, Cary, NC) and Stata (StataCorp, College Station, TX), allows AR estimations only for dichotomous exposures.2,6,7 We provide in the appendix a Stata program for estimating average ARs for dichotomous, polytomous, and quantitative exposures (eAppendix, http://links.lww.com/EDE/A593).

Public health prevention strategies should not only highlight risk factors for a given disease but also the consequences of exposure to these risk factors at the population level. These effects should be evaluated in terms of attribution of risk through reliable and unbiased estimators, such as the average AR. We believe that the additional Stata program provided here will facilitate such estimates.

Jean-François Hamel

Laboratory of Ergonomics and

Epidemiology in Health at Work

University of Angers

Angers, France

jean-francois.hamel@etud.univ-angers.fr

Natacha Fouquet

Laboratory of Ergonomics and

Epidemiology in Health at Work

University of Angers

Angers, France

Work Health Department

Institute of Health Surveillance

Saint-Maurice, France

Catherine Ha

Work Health Department

Institute of Health Surveillance

Saint-Maurice, France

Marcel Goldberg

Inserm U1018

Population-based Cohorts Research Platform

Centre for Research in Epidemiology and

Population Health

Villejuif, France

Versailles-Saint Quentin University

UMRS, France

Yves Roquelaure

Laboratory of Ergonomics and

Epidemiology in Health at Work

University of Angers

Angers, France

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REFERENCES

1. Davis CH, MacKinnon DP, Schultz A, Sandler I. Cumulative risk and population attributable fraction in prevention. J Clin Child Adolesc Psychol. 2003;32:228–235.

2. Rückinger S, von Kries R, Toschke AM. An illustration of and programs estimating attributable fractions in large scale surveys considering multiple risk factors. BMC Med Res Methodol. 2009;9:7.

3. Bruzzi P, Green SB, Byar DP, Brinton LA, Schairer C. Estimating the population attributable risk for multiple risk factors using case-control data. Am J Epidemiol. 1985;122:904–914.

4. Eide GE, Gefeller O. Sequential and average attributable fractions as aids in the selection of preventive strategies. J Clin Epidemiol. 1995;48:645–655.

5. Land M, Vogel C, Gefeller O. Partitioning methods for multifactorial risk attribution. Stat Methods Med Res. 2001;10:217–230.

6. Raemsch C. pARccs: estimation of attributable and partial attributable risks (AR and PAR) and visualization of attributable risks from case-control data. R package version 0.2-2. 2010. Available at: http://CRAN.R-project.org/package=pARccs.

7. Lehnert-Batar A. pARtial: pARtial package. R package version 0.1. 2006. Available at: http://cran.r-project.org/src/contrib/Archive/pARtial/.

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© 2012 Lippincott Williams & Wilkins, Inc.

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