Section VI: Not Mathematically Valid?

In some ways, Pigford's charge that the method in Appendix C is not mathematically valid is a very surprising one to remain standing after the work of the committee was complete. Even more astonishing, Pigford has stated that none of the members of the committee or any of the reviewers even responded to his claim of the mathematical invalidity of the method during the course of the study. (9) The lack of a response to such a basic charge is most unusual and raises serious questions about the integrity of the scientific process by which the committee majority decided that its recommendation of a new, complex, and untried method in radiation protection was a workable one. Therefore, I explore the matter at some length here.

The essence of Pigford's claim of mathematical invalidity is that the method in Appendix C does not result in a critical group that corresponds to a critical group as defined by the ICRP, as the committee would claim. This is because Step 7 of the calculational process divides the "region into subareas, with no homogeneity requirement for the subarea." This means the doses to individuals within the subarea can be very different. A few individuals with high doses could be averaged in with a large number of individuals with low doses, resulting in a low average dose (or risk) for the area.

ICRP recommendations require that the individuals with the highest dose (or risk) be part of the critical group. But in the method of Appendix C, the averaging process over a subarea could result in the highest exposed individuals being in a subarea that has a low average dose. This could result in their exclusion from the critical group defined in Step 8 of Appendix C because there may be many subareas with a higher average dose (or risk), but which do not include the individuals with the highest dose (or risk).

The disagreement has not been resolved. My own preliminary conclusion is that Pigford's is right to conclude that Appendix C is not a mathematically valid approach to creating a critical group in conformity with ICRP's recommendations. While Pigford was a minority of one in the committee, the widespread use of the subsistence farmer approach and its clear conformity with the ICRP method shows that he is, in fact, in the majority in the scientific world at large on this issue.

While disagreements about policy abound, and there is wide room for legitimate debate about how future generations ought to be protected from what we do today, the lack of a clear resolution to the mathematical question is very troubling.

A first reading of the report led me to the conclusion that despite some differences of detail, the method in Appendix C had a close relationship to that described in a report by the Electric Power Research Institute (EPRI). The EPRI report, cited by Pigford in his dissent but not in Appendix C, shows calculations based on one variant of the probabilistic critical group method. (10) This variant is not in conformity with the ICRP critical group method and is not claimed to be.

I had assumed that the calculations by EPRI were an adequate description of possible results of actually trying out the suggested approach to risk evaluation. However, in a review of an early draft of this article, NAS committee chairman Fri explicitly denied the connection:

...it is simply untrue to suggest that the approach in Appendix C derives from an EPRI report. If it is the report I think you may have in mind, any careful comparison of the calculations involved would quickly show no relationship. (11)

• Part VII: Implications Beyond High-Level Waste Disposal
  
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Institute for Energy and Environmental Research

Comments to Outreach Coordinator, Pat Ortmeyer: ieer@ieer.org
Takoma Park, Maryland, USA

Revised March 21, 1996