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Probability of Causation and the Attributable Proportion Risk

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  • Louis Anthony Cox

Abstract

A uranium miner who smokes develops lung cancer: what is the probability that radiation, rather than tobacco, caused it? This paper briefly explains the principles and limits of probability models for which this question makes sense, and then shows how principles of risk accounting can be applied to obtain a solution to the general problem of attributing risk in the presence of joint, possibly interacting, causes. A procedure for calculating each factor's “share” in a jointly caused risk is proposed, and shown to be a generalization of the “probability of causation” concept. Problems of implementation and interpretation for the proposed attribution procedure are discussed, and illustrative error bounds are derived for a simple decision rule, in which probability of causation or attributable risk share calculations are made using aggregate data as a proxy for unknown individual data.

Suggested Citation

  • Louis Anthony Cox, 1984. "Probability of Causation and the Attributable Proportion Risk," Risk Analysis, John Wiley & Sons, vol. 4(3), pages 221-230, September.
    • Handle: RePEc:wly:riskan:v:4:y:1984:i:3:p:221-230
    DOI: 10.1111/j.1539-6924.1984.tb00142.x
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    References listed on IDEAS

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    1. Leonard J. Mirman & Dov Samet & Yair Tauman, 1983. "An Axiomatic Approach to the Allocation of a Fixed Cost Through Prices," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 139-151, Spring.
    2. Louis J. Billera & David C. Heath, 1982. "Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 32-39, February.
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    Cited by:

    1. Louis Anthony Cox & Paolo F. Ricci, 1992. "Reassessing Benzene Cancer Risks Using Internal Doses," Risk Analysis, John Wiley & Sons, vol. 12(3), pages 401-410, September.
    2. Vincent M. Brannigan & Vicki M. Bier & Christine Berg, 1992. "Risk, Statistical Inference, and the Law of Evidence: The Use of Epidemiological Data in Toxic Tort Cases," Risk Analysis, John Wiley & Sons, vol. 12(3), pages 343-351, September.
    3. Louis Anthony Cox, 1987. "Statistical Issues in the Estimation of Assigned Shares for Carcinogenesis Liability," Risk Analysis, John Wiley & Sons, vol. 7(1), pages 71-80, March.
    4. Louis Anthony Cox, 1986. "Technical and Policy Issues in Assigned Share Calculations: A Comment on Lagakos and Mosteller," Risk Analysis, John Wiley & Sons, vol. 6(3), pages 373-375, September.
    5. Zhihong Cai & Manabu Kuroki, 2005. "Variance Estimators for Three “Probabilities of Causation”," Risk Analysis, John Wiley & Sons, vol. 25(6), pages 1611-1620, December.
    6. Stephen W. Lagakos & Frederick Mosteller, 1986. "Assigned Shares in Compensation for Radiation‐Related Cancers," Risk Analysis, John Wiley & Sons, vol. 6(3), pages 345-357, September.
    7. Bertram Price & Michael MacNicoll, 2015. "Multiple Interacting Risk Factors: On Methods for Allocating Risk Factor Interactions," Risk Analysis, John Wiley & Sons, vol. 35(5), pages 931-940, May.
    8. Fritz A. Seiler, 1986. "Assigned Shares and Combined Insults," Risk Analysis, John Wiley & Sons, vol. 6(3), pages 371-372, September.
    9. Jonathan B. Wiener, 2020. "Learning to Manage the Multirisk World," Risk Analysis, John Wiley & Sons, vol. 40(S1), pages 2137-2143, November.

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