# Probability of Causation: its use in compensation schemes. Richard Wilson Mallinckrodt Research Professor of Physics Harvard University

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2 Rothman, 1986, p 38). Calculation of POC The Probability of Causation that an outcome O is caused by exposure E s to a specified substance s, can be expressed in an equation: POC = (The risk calculated from the estimated exposure to the substance s) divided by (The risk from all causes) All causes include both the natural incidence and the risk calculated from exposure to the substance. If the risk from all causes can be expressed as a sum of risks from a number of k different substances i, the calculation follows at once from the theorem, attributed to the Reverend Thomas Bayes in the 18 th century, that describes how to change a probability when new information is available. Inserting the exposure variable E i and the outcome O instead of the variables used in the textbooks: POC = P (E i O) = P(E i )P (O E i )/Σ i=1 k P(E i )P(O E i ) It must be recognized that both the numerator and the denominator vary with a number of characteristics of the person: is he a smoker? Male or female? What is his diet? Is he genetically sensitive? young or old? Although we ask for the POC for an individual, in most cases we can only obtain values of the quantities averaged over a population. This inevitably leads to approximations. The National Cancer Institute (NCI) has prepared, and is updating, a set of epidemiological tables for such situations (NCI, 1985; 2001). They define excess risk [ERR(O E i )] as the increase in probability of the outcome due to the dose s divided by the incidence averaged throughout the USA (from the [Surveillance, Epidemiology and End Results ] SEER data). The numerator is derive from models depending mostly ion tumor rates in Japan.. Then they express POC in terms of the Excess Risk defined by the formula: POC = P (E i O) = ERR(O E i )/[1 + ERR(O E i )] To be precise, the excess risk must be derived from a population with the same characteristics as the person under study. But data inevitably are averages, and in this case the numerator and the denominator come from countries with different racial characteristics. NCI calculates POC for a person who received a radiation dose D at age t and developed a cancer at age T. But there is a much more important assumption in the preparation of these tables. At low doses of radiation, these tables assume that the response to the radiation dose is linear (linear-no-threshold - the LNT hypothesis). Just as the risk of the adverse response is uncertain when the dose is small, so is the Probability of Causation. This raises the new issue of what to do when the POC is so uncertain. That makes it essential for scientists and technologists to understand what society is deciding and to use their especial expertise to influence the procedure. Various authors have discussed the details and approximations in discussing these concepts and deriving the relevant values of excess risk and other parameters from epidemiological data (Lagakos and Mosteller, 1986; Cox, 1987; Greenland and Robins, 1988; Robins and Greenland, 1989). For example, the formula for POC is negative if the risk calculated for the exposure E is negative (corresponding to a beneficial effect), whereas no probability can be negative. When the risk is negative, (meaning that the exposure is beneficial) it can be set equal to zero in the equation. Nonetheless, these details complicate the picture somewhat, and several authors have suggested that the words, assigned share be used instead of Probability of Causation. Even this runs into difficulties, however, when synergistic effects of two substances, such as asbestos and smoking are considered (Grimson 1987). Each POC calculated from the equation is still below unity, as required for a probability, but the sum of the POC for the two possible causes can exceed unity, because the two are not independent. The sum of two assigned shares cannot

7 Congress (1988) Radiation-Exposed Veterans Compensation Act of 1988" Public Law Congress (1990) Radiation Exposure Compensation Act Public Law Congress (2000) National Defense Authorization Act" Public Law Cox, L.A. (1987) "Statistical Issues in the Estimation of Assigned Shares for Carcinogenesis Liability" Risk Analysis 7: " ()*+*,-)\$+&.-/0&1//2//#2%34&B+"CDE4CCD"FGHHIJ! Crump, K.S., Hoel, D.G., Langley, C.H., and Peto, R. (1976) "Fundamental Carcinogenic Processes and their Implications for Low Dose Risk Assessment" Cancer Research 36:2973. DOE (2000) < Greenland S. and J.M. Robins (1988) "Conceptual Problems in the Definition and Interpretation of Attributable Fractions" American Journal of Epidemiology 128: Grimson, R.C., (1987). Apportionment of risk among environmental exposures: application to asbestos exposure and cigarette smoking. J. Occup. Medicine 29: Guess, H., Crump, K. and Peto, R. (1977) "Uncertainty Estimates for Low Dose Rate Extrapolation of Animal Carcinogenicity Data." Cancer Research 37: K%\$L6\$"M!+"%,)"N;<176\$O%,"5!+"FGHHIJ"P*6)/?%0"#%<1%7/(,"Q,%081/1"K6<\$/17/?1R Journal of Occupational and Environmental Medicine!""CSFIJ9ETT4ESI Lagakos S.W. and F. Mosteller (1986) "Assigned Shares in Compensation for RadiationcRelated cancer" Risk Analysis 6: Mettler, F.A. and A. C. Upton (1995) Medical Effects of Ionizing Radiation, 2nd edition. W.B. Saunders, Philadelphia. NIH (1985) The report of the ad hoc working group to develop the Radioepidemiological Tables. NIH publication U.S. Department of Health and Human Services, Washington D.C. NIH (2001) Update to NIH (1985) in preparation Price B., and R. Wilson (2001) "Trends in Mesothelioma Incidence and Asbestos Exposure Evaluation", Canadian Mineralogist Special Publication 5 (2001) Robins J. and S. Greenland (1989) 'The Probability of Causation Under a Stochastic Model for individual Risk" 45: Rothman K.J. (1986) Modern Epidemiology (1986) Rutherford v. Owens-Illinois, Inc., (1997) 16 Cal.4th 953, 67 Cal.Rptr.2d 16, 941 P.2d 1203.

8 Schneiderman, M.A. and N. Mantel, (1973) "The Delaney Clause and a scheme for rewarding good experiments" Preven. Med. 2:165 Shihab-Eldin, A., A.S. Shlyakhter and R. Wilson (1992) Is there a Large Risk of Radiation? A Critical review of Pessimistic Claims Environment International, 18, Upton A. and R. Wilson (2000) "Compensating government workers exposed to radiation" Risk in Perspective 8 (7) September Vasiliev, A., V. Demin, V. Kutkov, E. Ivanov, and A. Tsyb (2001) Analysis of the Regulation and Remedial Measures on the Radioactive Contaminated Territories to be published Wakeford, R., Antell, B.A., and Leigh, W.J.: (1998). A review of probability of causation and its use in a compensation scheme for nuclear industry workers in the United Kingdom. Health Phys. 74: 1-9. Wilson, R., and J.D. Spengler Eds. (1996) Particles in Our Air: Concentrations and Health Effects Harvard University Press

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