The preparation of radioepidemiologic tables requires extensive mathematical modeling because matters such as sex, size of dose, age at exposure, type of cancer, and age at diagnosis must be taken into account. The limited data require many assumptions about the quantitative relationship between radiation dose and the age-specific incidence rate of cancer. After partitioning a population into reference sets based on age at exposure, size of dose, type of cancer, etc., an assigned share is computed for each reference set and then assigned to all of its members. The assigned share represents the fraction of the cancer cases in the reference set that are attributed to the radiation dose. Because the population can be partitioned in many ways, each individual's assigned share depends on the partition used and will change with different partitions. Options for modeling and limitations in epidemiologic data lead to considerable uncertainties in estimates of assigned charges that have been scientifically evaluated. In contrast, the uncertainties associated with the current approach for determining the likelihood a cancer was caused by radiation have not been appraised but are likely to be even greater than those associated with the tables. (Copyright (c) 1986 Society for Risk Analysis.)