The distribution of Levin's measure of attributable risk

Some properties of the sample estimator of attributable risk λ, defined here as the proportion of all cases of disease which may be attributed to a risk factor, are considered for the case-control study situation. It is shown that log (1 −λ^ ) may be expressed in terms of the prevalences of the factor in cases and healthy controls, that the bias of the estimator is minimized when ½ is added to the cell frequencies corresponding to nonexposed persons in the usual 2 × 2 contingency table, and that the distribution of 1−λ^ is asymptotically log normal. Examples of the calculations, and a discussion of the results, are given for a number of risk factors for childhood leukemia.