Characterization of U-Shaped Exposure-Response Relationships with Application to a Copper Database

The need to find an acceptable medium between excess and deficiency motivates the characterization of U-shaped exposure-response relationships. Previous work on a copper(Cu) database employed CatReg to model excess and deficiency conditions separately. Interest lies in simultaneously fitting these conditions. Using binary logistic regression, we have developed a methodology that can be used to simultaneously fit observations from excess and deficiency experiments. Capturing excess and deficiency conditions in one well-defined model facilitates the estimation of a U-shape function, with concentration on the horizontal axis and the probability of a non-normal reading on the vertical axis. The bottom of this U-shape function represents the dose of Cu associated with the smallest chance of adverse health effects attributed to an excess or deficient Cu condition, or both. For humans, this dose level is estimated to be 2.73 mg Cu/day with an acceptable range of oral intake between 1.57 and 4.46 mg Cu/day.