Attributable risk, probability of causation, assigned shares, and uncertainty

Calculations of attributable risks, probabilities of causation, and assigned shares attracted increasing interest recently, particularly since the enactment of the Orphan Drug Act. Although efforts have been limited mostly to radiation as the toxic agent, the concept is general to all toxicants. In this paper, the systematic and random uncertainties in calculations of assigned shares are reviewed globally, and possibilities for their reduction are discussed. In addition, an algebraic study is made of the influence of random uncertainties in the input parameters on the random error of the assigned shares. Three dose-effect functions, appropriate for the low-dose, low-effects regions that are of interest here, are chosen for this investigation, and the algebraic properties of the random errors of the assigned shares are discussed. For shares near 0 and 1, the errors are shown to be small and to depend linearly on the value of the shares; the errors are largest for values of the shares near 50%, that is, in the region of almost equal or equal shares.