Journal
RISK ANALYSIS
Volume 37, Issue 2, Pages 265-279Publisher
WILEY
DOI: 10.1111/risa.12603
Keywords
Copper toxicity; deficiency; excess; severity scoring; U-shaped exposure-response curve
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada (NSERC)
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Essential elements such as copper and manganese may demonstrate U-shaped exposur-response relationships due to toxic responses occurring as a result of both excess and deficiency. Previous work on a copper toxicity database employed CatReg, a software program for categorical regression developed by the U.S. Environmental Protection Agency, to model copper excess and deficiency exposure-response relationships separately. This analysis involved the use of a severity scoring system to place diverse toxic responses on a common severity scale, thereby allowing their inclusion in the same CatReg model. In this article, we present methods for simultaneously fitting excess and deficiency data in the form of a single U-shaped exposure-response curve, the minimum of which occurs at the exposure level that minimizes the probability of an adverse outcome due to either excess or deficiency ( or both). We also present a closed-form expression for the point at which the exposure-response curves for excess and deficiency cross, corresponding to the exposure level at which the risk of an adverse outcome due to excess is equal to that for deficiency. The application of these methods is illustrated using the same copper toxicity database noted above. The use of these methods permits the analysis of all available exposure-response data from multiple studies expressing multiple endpoints due to both excess and deficiency. The exposure level corresponding to the minimum of this U-shaped curve, and the confidence limits around this exposure level, may be useful in establishing an acceptable range of exposures that minimize the overall risk associated with the agent of interest.
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