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Methods Inf Med 2006; 45(04): 404-408
DOI: 10.1055/s-0038-1634095
Original Article
Schattauer GmbH

The Attributable Risk in a Multifactorial Situation

Evaluation of Different Methods of Partitioning
C. Rabe
1   Department of Medical Informatics, Biometry and Epidemiology, Friedrich Alexander University Erlangen-Nuremberg, Erlangen, Germany
,
O. Gefeller
1   Department of Medical Informatics, Biometry and Epidemiology, Friedrich Alexander University Erlangen-Nuremberg, Erlangen, Germany
› Author Affiliations
Further Information

Publication History

Publication Date:
06 February 2018 (online)

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Summary

Objectives: Different approaches to partition the attributable risk into exposure-specific components are methodologically evaluated.

Methods: Two methods of partitioning the attributable risk in a multifactorial situation have been suggested. One is based on a solution adopted from game theory, the Shapley value, whereas the other recently suggested approach uses a heuristically motivated proportional weighting scheme. These two concepts are reviewed and compared in a situation with three exposure factors. A hypothetical numerical example is discussed illustrating differences in the case of complex interaction structures.

Results: The two methods are found to differ in two critical features that affect the outcome of partitioning: i) including or ignoring the full interaction structure between exposure factors involved in the partitioning, ii) using an equal or proportional weighting scheme for the marginal excess risks of the exposures. As a result, not only the individual partial attributable risks for the exposure factors may be quantitatively different between the methods, but also their ranking depends on the partitioning approach.

Conclusions: The epidemiologic properties of the partitioning procedure based on the Shapley value are known and fit to the needs of epidemiologic applications. The alternative approach recently suggested can lead to considerably different results. As long as its epidemiologic properties are not fully understood, the traditional partitioning method should be given preference in practical applications.

Keywords

Attributable fraction - partial attributable risk - Shapley value - proportional risk allocation
 

  • References

  • 1 Levin ML. The occurrence of lung cancer in man. Acta Unio Int Contr 1953; 9: 531-41.
    PubMedGoogle Scholar
  • 2 Basu S, Landis JR. Model-based estimation of population attributable risk under cross-sectional sampling. American J Epidemiol 1995; 142 (012) 1338-43.
    PubMedGoogle Scholar
  • 3 Benichou J. A Review of adjusted estimators of attributable risk. Stat Methods Med Res 2001; 10: 195-216.
    CrossrefPubMedGoogle Scholar
  • 4 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 (05) 904-14.
    CrossrefPubMedGoogle Scholar
  • 5 Greenland S, Drescher K. Maximum likelihood estimation of the attributable fraction from logistic models. Biometrics 1993; 49 (03) 865-72.
    CrossrefPubMedGoogle Scholar
  • 6 Vogel C, Gefeller O. Implications of nondifferential misclassification on estimates of attributable risk. Methods Inf Med 2002; 41 (04) 342-8.
    Article in Thieme ConnectPubMedGoogle Scholar
  • 7 Eide GE, Gefeller O. Sequential and average attributable fractions as aids in the selection of preventive strategies. J Clin Epidemiol 1995; 48 (05) 645-55.
    CrossrefPubMedGoogle Scholar
  • 8 Llorca J, Delgado-Rodriguez M. A new way to estimate the contribution of a risk factor in populations avoided nonadditivity. J Clin Epidemiol 2004; 57: 479-83.
    CrossrefPubMedGoogle Scholar
  • 9 McElduff P, Attia J, Ewald B, Cockburn J, Heller R. Estimating the contribution of individual risk factors to disease in a person with more than one risk factor. J Clin Epidemiol 2002; 55: 588-92.
    CrossrefPubMedGoogle Scholar
  • 10 Cox JLA. A new measure of attributable risk for public health application. Managment Sci 1985; 31 (07) 800-13.
    PubMedGoogle Scholar
  • 11 Gefeller O, Land M, Eide GE. Averaging attributable fractions in the multifactorial situation: assumptions and interpretation. J Clin Epidemiol 1998; 51 (05) 437-41.
    CrossrefPubMedGoogle Scholar
  • 12 Land M, Vogel C, Gefeller O. A multifactorial variant of the attributable risk for groups of exposure variables. Biometrical J 2001; 43 (04) 461-81.
    CrossrefPubMedGoogle Scholar
  • 13 Shapley L. A value for n-person games. In Kuhn H, Tucker A. (eds.) Contributions to the theory of games II. Annals of Mathematics Studies 1953; 28: 307-17.
    PubMedGoogle Scholar
  • 14 Land M, Gefeller O. A game-theoretic approach to partitioning attributable risks. Biometrical J 1997; 39 (07) 777-92.
    CrossrefPubMedGoogle Scholar
  • 15 Ramroth H, Dietz A, Becher H. Interaction effects and population-attributable risks for smoking and alcohol on laryngeal cancer and its subsites. A case-control study from Germany. Methods Inf Med 2004; 43 (05) 499-504.
    Article in Thieme ConnectPubMedGoogle Scholar
  • 16 Land M, Vogel C, Gefeller O. Partitioning methods for multifactorial risk attribution. Stat Methods Med Res 2001; 10: 217-30.
    CrossrefPubMedGoogle Scholar
  • 17 Rothman K. Causes. Am J Epidemiol 1976; 104: 587-92.
    CrossrefPubMedGoogle Scholar