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Determining a Robust D-Optimal Design for Testing for Departure from Additivity in a Mixture of Four Perfluoroalkyl Acids.
Citation:
Carr, C., C. Gennings, C. LAU, J. Schmid, L. BURGOON, W. Wan, AND B. D. ABBOTT. Determining a Robust D-Optimal Design for Testing for Departure from Additivity in a Mixture of Four Perfluoroalkyl Acids. Presented at Society of Toxicology (SOT) Annual Meeting, Washington, DC, March 06 - 10, 2011.
Impact/Purpose:
Our objective is to determine an optimal experimental design for a mixture of perfluoroalkyl acids (PFAAs) that is robust to the assumption of additivity
Description:
Our objective is to determine an optimal experimental design for a mixture of perfluoroalkyl acids (PFAAs) that is robust to the assumption of additivity. PFAAs are widely used in consumer products and industrial applications. The presence and persistence of PFAAs, especially in human body fluids, have raised concern about this class of compounds. Of particular focus to this research project is whether an environmentally relevant mixture of four PFAAs with long half-lives (in years: PFOA, PFOS, PFNA, and PFHxS) act synergistically. PFAAs are thought to activate peroxisome proliferator-activated receptor alpha (PPARa) to produce liver toxicity and developmental effects. The first phase of study included evaluating the ability of PFAAs to bind PPARa in in vitro studies of a transfected-cell model. Using the resulting data, a non-linear logistic additivity model was employed to predict relative luciferase units (RLU) at an environmentally relevant mixing ratio. The mixing ratio was estimated from NHANES (2005-2006) data. We used a maximin D-optimal design criterion to select from a large set of specified designs. The candidate seven point designs (control plus six dose groups) were generated by varying the total dose locations and shape of the dose-response curve with the additivity curve used as a reference. A total of 6,006 designs were considered with seven dose groups along with 13 different dose-response shapes. A D-optimal design (i.e., the location of the seven dose groups) robust to misspecification of the resulting dose-response shape was found with a minimum D-efficiency of 92%. The proposed design has good statistical properties over a band of possible dose-response curves including synergistic, additive and antagonistic associations among the four PFAAs. (This research was partially supported by NIEHS T32ES007334 and does not reflect USEPA policy.)