*A. Introduction*

Reasonable people arc likely to differ considerably on how to assess the value of a cancer claim. As more is learned about the process by which radiation induces cancer, better judgements should be possible. Since there is a latent period of some years after the accident before cancer claims are expected, there is plenty of time to form the proposed PSA. The PSA could assemble the then-current information and propose a fair method for settling claims. However, the Commission felt a responsibility to illustrate how the proposed method might work, given the tools for mass tort claims processing presently available and consistent with the present level of knowledge for radiogenic cancers.

The examples in this Appendix rely heavily on information obtained from the recently released BEIR V report. That report concludes that the risks of cancer from a radiation exposure of 0.1 Sv (10 rem) or greater may be three or more times higher than stated in previous reports. This conclusion has not yet received widespread acceptance. It is used here, however, in sample calculations because its conclusions will project higher numbers of cancers, which is in the conservative direction. The Commission does not comment on the validity of BEIR V.

The BEIR V report gives (*inter alia*) the expected excess cancer mortalities over the lifetime for a group of 100,000 men and 100,000 women for a single exposure of 0.1 Sv (10 rem). The age distribution of the groups matches that of the U.S. population. Table H.1 reproduces part of Table 4.2 of that report. For the range of interest to this report, the response is very nearly linear. Using a linear assumption,

Table H.2 shows the excess cancer fatalities expected for the two groups as a function of effective dose. These figures can be interpolated to obtain the expected “all cancer” excess for any dose desired. The response becomes quite nonlinear above about 4 Sv (400 rem). Note that the normal rate in males is about 20 percent higher than in females.

*B. The Probability of Causation Method*

As indicated in several places in the report, those analytical techniques most widely accepted at the time of the accident should be utilized in dealing with latent injury issues. In this report, the PC method (sometimes called the assigned share method), which currently appears to be the best technique available, was used to illustrate the manner in which a large number of latent claims might be handled equitably.

To understand the theory behind the PC method, consider two groups of the same number of people of the same composition, e.g., age, sex, race, etc. Group 1 is not exposed to any radiation in excess of the normal background and normal medical exposure. Group 2 receives an extra whole body dose due to the accident. For each of these groups, functions h_{1}(t) and h_{2}(t), respectively, are defined, where h(t), usually called the hazard function, is the probability that they will have a diagnosed, and eventually fatal, cancer in year t following the accident. Thus the number of cancers we would expect to be diagnosed in the 1-year period between the 9th and 10th anniversary of the accident for Group 2 would be:

h_{2}(10) x N(9) = number of cancers diagnosed [in 10th year] which prove to be fatal

where N(9) is the population of the group at t = 9 years. Thus, h(t) is just the probability that any individual who is not diagnosed to have fatal cancer at the beginning of a particular year will develop one during that year. It is well known that h(t) changes with time. Although there is some uncertainty in the exact form of h(t), the exposed group can be expected to have a time variation of the type shown in Figure H.1.

The latent period 0 to t_{L}, is a period following the accident during which the normal cancer rate shows no statistically significant increase. Thus, in this time interval, h_{1}(t) equals h_{2}(t). At a much later time, t_{c} (cut off time), the value of h_{2}(t) once again returns to its normal level. For cancers of the hematological system such as leukemias, the latency period is about 3 to 5 years, while for solid tumors (e.g., of the lung, bone, thyroid, etc.), it tends to be about 10 years. The cut off time tends to be about 40 years, but is very difficult to measure. Note that in Figure H.1, the normal incidence of cancer remains constant. This would, in fact, not be true for most age groups.

From Figure H.1, it may be seen that there is a period of time between the end of the latent period and the cut off where Group 2 has a significantly higher probability of getting a cancer than Group 1. This effect has been expressed several ways in the literature. Two such definitions of PC are:

where P_{1}(t) and P_{2}(t) are the total number of people having a diagnosed fatal cancer between t = 0 and t = t years for each group. Note that if h_{1}(t) and h_{2}(t) were constants (i.e., not functions of time), then the two expressions would be mathematically identical. This would be equivalent to replacing the function h_{2}(t) by its average value over the entire time span. This in fact is what is suggested be done in some cases because there is rather limited data available on excess cancers, and when a population is divided into groups by age, sex, race. personal habits, such as smoking, diet, etc., and then into 40 groups representing the time since the exposure, there are so many categories and the data in each category is so sparse that a significant statistical uncertainty results. Thus, Equation H.2 could be used to determine PC or assigned share^{1} for those cases where the data do not permit a more accurate determination of the function h_{2}(t).

A well recognized problem with the above procedure is that it assumes that the increase in cancer caused by the radiation is independent of the factors causing the natural background rate of cancer occurrence. For example, in Equation H.2 P_{1}(t) is subtracted from P_{2}(t) to get the excess cancers caused by radiation. This procedure implies the above assumption. In certain cases^{2} there is enough evidence to suggest that there may be a synergistic effect rather than independent causation. For example, suppose a group of smokers showed an increase of 20 percent in the incidence of lung cancers over nonsmokers. Suppose a group of uranium miners received enough extra radiation dose to the lungs to increase their lung cancer risk by 20 percent above the normal rate. If the smokers went to work in the uranium mines, one would expect the resultant increase in cancer to be 40 percent using the additive model or 44 percent using the multiplicative model. However, what has been inferred in some cases is that the cancer rate is much larger than either of these projections.^{3} Such synergistic effects are suspected to occur between other carcinogenic agents, but in most cases there has been no experimental evidence to prove it. The question then arises, to which cause does one assign the increase above 40 percent? Since knowledge of the causes of cancer is so limited, this question cannot be answered today. Thus, it is suggested that the assumption of independence be used and that the excess risk of the irradiated group all be assigned to the exposure caused by the accident.

From the data in Table H.1 and H.2, the PC for any given equivalent dose can now be calculated. For example, suppose a group of 100,000 females receive a dose of 1.99 Sv (199 rem). Interpolating from Table H.2 gives an excess of cancer fatalities of 16,150 over the lifetime of the population. However, from Table H.1 the normal expectation would be 16,150 cancers from natural causes. Thus, the value of P_{2} is the sum of the excess plus the natural cancers. Thus P_{2} = 16,150 + 16,150 = 32,300, P_{1} = 16,150 so:

The values of PC versus equivalent dose are included in Table H.2. Note that although the dose-effect relationship is assumed to be linear, the PC dose relation is not.

The calculation in Equation H.3 illustrates another problem with the use of PC. Note that the difference in the numerator gets quite small as the dose received decreases. The effect is that, in the calculation of PC at low doses, the numerator is a small difference of large numbers. Since these large numbers in the numerator would be expected to be statistically distributed, the result is that the uncertainty of PC calculated in this way becomes very large. Thus, one should be very careful in using values of PC below about 0.1 (effective dose of about 30 rem) because the uncertainty is very large at that level and below.

The BEIR V report contains the basic information to update the relations for groups of varying age (at exposure and, in some cases, age at manifestation of disease or for certain minimum latency periods) and sex for a variety of different cancers given in the NIH Radioepidemiological Tables.^{4} For those cases where enough data am available to generate a curve h_{2}(t) (as in Figure H.1), then the definition of PC expressed by Equation H.1 should be used. Where the data are inadequate to do this, then the approximation given by Equation H.2 should be used. Table H.2 gives the probability of causation as a function of equivalent dose. The data for Table H.2 come from Table H.1 and the assumption of linearity in dose response from higher to lower doses.

A procedure to compensate for latent illnesses that would combine PC with proportionate recovery might begin by defining two PC values, PC(A) and PC(B). The higher of these, PC(A), would define a level above which a cancer that has actually appeared is mom likely than not to have been caused by the radiation dose resulting from the accident. 'Me value of PC(A) could be set at approximately 0.5. PC(A) would be substantially above this if it were the proxy for expert medical opinion as to causation “to a reasonable medical certainty.” Persons with a diagnosed cancer that could be radiogenic and who received a dose equal to or greater than PC(A) would receive a full cancer claim payment of $V. What that payment might cover is discussed in Chapters 3 and 4, i.e., reimbursement of pecuniary losses (such as medical expenses and lost income) plus scheduled amounts for nonpecuniary losses.^{5}

In the range between PC(A) and PC(B), the cause is less likely to have been the exposure to radiation, so the proposed award might be set at some fraction of $V related to the dose received. A logical way to do this might be a linear interpolation between $V at PC(A) and the cutoff value, and a corresponding fraction of $V at PC(B). Here again, the fraction might be applied to pecuniary and non-pecuniary losses as described in Chapter 3 or, if Congress so elects, to a uniform payment. In either event, given the widely shared perception that medical expenses are a special case, a higher percentage of medical costs might be allowed at a given PC value than would be allowed for lost income or applied to the scheduled payment for pain and suffering.

The value of equivalent dose for a particular claimant would inmost cases^{6} be determined from a blood sample taken shortly after the accident. Then the appropriate version of Table H.2 for a particular cancer based on the applicable age at exposure (and, in some cases, age at manifestation of disease), latency period, and sex would be used to obtain a value for PC if the data permitted. However, at present, the definition of Equation H.2 may be more practicable in many cases because of limited data, as explained earlier.^{7}

Those for whom the probability P falls below PC(B), in these examples, would not receive direct financial payments if cancer appears. However, the Commission has recommended that a threshold dose be selected for eligibility for free medical examinations. This threshold dose might vary by age and, perhaps, sex, taking into account PC(B), if established at the time, but might be considerably lower than an “all cancer” dose corresponding to PC(B). The threshold dose should be selected in light of the uncertainties involved, including cancers that have a relatively high risk at relatively low doses for certain members of the population, such as those exposed *in utero*. In the range below this threshold, expected excess cancer fatalities would be small, as excess fatalities would probably be offset by early detection through free cancer screening.

The values of PC(A), PC(B) and $V are clearly a matter to be decided by the Congress or, under appropriate guidelines, the court. The doses corresponding to “all cancer” values of PC or increased risk based on BEIR V are shown on Table H.2 for a group of U.S. males and a similar group of U.S. females.

It is intended that claims would be paid for nonfatal cancers (morbidity) as well as deaths. However, all the data used from the BEIR V report was for cancer fatalities. Since some cancers are cured and hence do not lead to a cancer fatality, the number of cancers observed will be larger than the number of cancer fatalities. If, however, the fraction of radiogenic cancers cured is the same as the fraction from other causes that are cured, as is now believed,^{8} then the probability of causation will not be changed. For example, suppose that, on the average, one-third of cancers of all origins were cured. Then, the number of excess cancers observed following a dose of I Sv (100 rem) (see Table H.2) would become 1.5 x 7,700 = 11,550. The number of cancers observed in the unexposed population would also increase by the non-fatal ones (a factor of 1.5) so their number would be 1.5 x 20,510 = 30,765. Thus,

and is unchanged from the PC for cancer fatalities.

*Examples*

In the following examples, three variations are discussed for illustrative purposes only. The first variation (Example 1) would pay the full amount for any diagnosed cancer where the PC is .5 or greater, and a declining amount down to a cutoff of PC =.2, at which compensation would be 20 percent of a full award. It will be observed that these values of PC(A) and PC(B) seem to be consistent with the corresponding values used in the process under the BNFL/UKAEA agreement with their unions as discussed in Appendix G. The full $V benefit should at least equal the cost of treatment of an “average” cancer.

The second variation (Example 2) would pay the full amount for any diagnosed cancer where the PC is .5 or greater, and a declining amount down to a PC of .20, at which compensation would be 30 percent of a full award. The third, which is called Example 3, would simply pay the same scheduled benefit to anyone in the affected area with a diagnosed cancer whose radiation exposure indicated a PC that the exposure induced the cancer of 20 percent or greater. Tables H.3 through H.5 show how the payout for claims might be structured for the region between PC(A) and PC(B).

A review of tort principles applicable to proof of latent health effects from radiation exposure shows that, in general, claimants need to show that radiation was the causative agent by a preponderance of the evidence. Further, the standard for expert medical opinion on the issue of causation may well be ”reasonable medical certainty," a standard that likely exceeds a bare preponderance of the evidence considered by the expert. In some courts, the standard for statistical evidence requires a 95 percent confidence level. (See Appendix D.) These two considerations imply that a claimant seeking to use PC to establish causation in fact would have to show that the PC value was above 0.5. If it is assumed that a claimant, to be assured of success using PC under current law, would have to show a PC level somewhat greater than 0.5 (for example, 0.6), few claimants would prevail on a PC basis under cur-rent law even in the case of a very severe accident.

Using the results of a typical risk assessment (Figure VI-18 of WASH 1400) for the largest postulated release of radioactivity and average weather and population density, somewhere between 100 and 1,000 (say, 500) members of the public would receive a dose that would yield a PC greater than 0.6. Thus, using PC with current principles, the total payout would be about 500 persons times $Av (where $Av is the average value of the total loss suffered by claimants of this type).

Since the total number of cancers calculated to result from such an accident greatly exceeds the number of people with PC greater than 0.6, the total payout by the above method would be a small fraction of the total liability that would result if one could actually determine which of all cancers that developed in the exposed population were, in fact, due to the accident and which were not. As noted earlier, this cannot be done. Since the Commission's interpretation of the intent of the Price-Anderson law is that the exposed population should be fully compensated for its loss, the Commission concludes that the present practice of the law would not fully internalize the cost. For this reason, the Commission has formulated a method based on PC that the Commission has concluded is the best proxy for direct proof of causation currently available. Coupled with proportional recovery, this yields a process illustrated in the first two examples described above.

One of the advantages of this approach is that those in charge of it (i.e., the Congress or the courts) can control total payout through the selection of the values of PC(A), PC(B), and $V to be used in processing claims, taking into account the estimated cost of latent illnesses on a consistent basis. Thus, after the accident had been evaluated, it would be possible to estimate (using risk coefficients developed by experts) the total number Of excess cancers that might be expected. This number times the average loss per cancer would be one way of determining the size of the pool of money to be made available for cancer claims. Using the PC/proportionate recovery method, the Congress or the courts could set the value of PC(A), PC(B), and $V that they felt could most fairly distribute these funds to the parties most likely to have sustained latent injuries.

For purposes of illustration, suppose the average cost of fully reimbursing a claimant for losses due to a latent cancer were $Av. Then, if the court's judgments were based upon existing standards even using PC at 0.6 as postulated earlier, the payout for the extreme accident described above would be:

500 x $Av = 500 $Av

For that same accident, WASH 1400 would predict a population dose of about 100,000 person-SV (10 million person rem) leading to about 7,700 fatal cancers (See Table H. 1) or about 7,700 X 1.5 = 11,550 total cancers (7,700 fatal plus 3,850 nonfatal ones). Assuming that the value of a non-fatal cancer claim is about one-third of a fatal one, in this case, society would have incurred a cost of

7,700 x $Av + 3,850 x 1/3 $Av = 9,000 $Av

On these assumptions, the estimated cost incurred by society is about 18 times the amount that would be expected to be recovered under standard tort principles if the above assumptions are correct. The great advantage of the proportionate recovery method is that it would allow the court to estimate the total cost, choose appropriate values of PC(A), PC(B), and $V on a consistent basis, and then fairly distribute the corresponding funds to the people most deserving of compensation.

It would be valuable to calculate the total cost of latent cancer claims. When this was tried, it was found that very large variations in the answer were obtained depending on the assumptions made. Of course, the larger the assumption of consequences, the smaller the likelihood of the event. What such a calculation amounts to, then, is an assumption of just what probability one wishes to use. If one takes the results of NUREG 1150 (2nd Draft, see Appendix B), an accident as rare as about 1 in 1 billion (which has a return period of about the age of the earth) would produce about 10,000 cancer fatalities in a period of about 30 years, 10 to 40 years following the accident. Taking a value of $250,000 for an average cancer claim^{9} gives about $2.5 billion for the total value of cancer fatality claims. Note that the money would be paid out over a 40-year period, so the cost of an annuity policy to cover the claims purchased shortly after the accident would be substantially less than $2.5 billion. From these types of calculations, the Commission concluded that the total claims from latent effects would be a fraction of the direct losses associated with property damage and direct costs of relocation and decontamination.

Thus, it was concluded that latent health effects claim in an extreme (i.e., very unlikely) accident could be sizeable but in trial calculations were never more than 10 or 20 percent of an estimate for other types of claims.