Critical issues in benchmark calculations from continuous data

The benchmark dose (BMD) is a dose that causes a specified low level of additional risk and is estimated using a statistical dose-response analysis. Regulatory agencies are using a statistical lower bound on the BMD in the place of the NOAEL for establishing exposure limits. However, there are still several issues regarding the BMD for which no clear consensus has emerged, particularly with respect to calculation of BMD from continuous response data. These include: (1) how to define the BMD from continuous data so that they are comparable to BMD derived from binary data, (2) what dose-response models and levels of additional risk should be used to calculate the BMD. The "hybrid" approach (Gaylor and Slikker, 1990; Crump, 1995) expresses the BMD from continuous data in terms that are directly comparable to those obtained using binary data. Several features of the hybrid approach are examined, with the emphasis on application to epidemiological data. The effect on the BMD of converting continuous data to binary form is quantified. Model uncertainty is explored, and the need for controlling this uncertainty by restricting the class of allowable models is demonstrated. Control data, which are often not available in epidemiological studies, are shown to have a limited effect upon the BMD so long as the model for the mean response is linear or convex. Such models are also biologically plausible, at least at low doses. Based on these and other considerations, suggestions are made for selecting a model for applying the hybrid approach and for selecting the level of additional risk on which to base the BMD.