title: Modeling U-Shaped Exposure-Response Relationships for Agents that Demonstrate Toxicity Due to Both Excess and Deficiency.
abstract: Essential elements such as copper and manganese may demonstrate U-shaped exposure-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.
authors.affiliation: Carleton University, School of Mathematics and Statistics, Ottawa, Ontario, Canada.
authors.forename: Brittany
authors.initials: B
authors.lastname: Milton
authors.affiliation: Carleton University, School of Mathematics and Statistics, Ottawa, Ontario, Canada.|RS McLaughlin Centre for Population Health Risk Assessment, University of Ottawa, Ottawa, Ontario, Canada.
authors.forename: Patrick J
authors.initials: PJ
authors.lastname: Farrell
authors.affiliation: School of Epidemiology, Public Health and Population Medicine, Ottawa, Ontario, Canada.|RS McLaughlin Centre for Population Health Risk Assessment, University of Ottawa, Ottawa, Ontario, Canada.
authors.forename: Nicholas
authors.initials: N
authors.lastname: Birkett
authors.affiliation: Carleton University, School of Mathematics and Statistics, Ottawa, Ontario, Canada.|School of Epidemiology, Public Health and Population Medicine, Ottawa, Ontario, Canada.|RS McLaughlin Centre for Population Health Risk Assessment, University of Ottawa, Ottawa, Ontario, Canada.
authors.forename: Daniel
authors.initials: D
authors.lastname: Krewski
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003300:Copper / Q000633:toxicity*; D016208:Databases, Factual; D004305:Dose-Response Relationship, Drug; D004781:Environmental Exposure; D006801:Humans; D016013:Likelihood Functions; D051379:Mice; D051381:Rats; D012044:Regression Analysis; D018570:Risk Assessment / Q000379:methods*; D013045:Species Specificity
chemical_list: D003300:Copper
keywords: Copper toxicity; U-shaped exposure-response curve; deficiency; excess; severity scoring