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Additive Dose Response Models: Explicit Formulation and the Loewe Additivity Consistency Condition.

ABSTRACT: High-throughput techniques allow for massive screening of drug combinations. To find combinations that exhibit an interaction effect, one filters for promising compound combinations by comparing to a response without interaction. A common principle for no interaction is Loewe Additivity which is based on the assumption that no compound interacts with itself and that two doses from different compounds having the same effect are equivalent. It then should not matter whether a component is replaced by the other or vice versa. We call this assumption the Loewe Additivity Consistency Condition (LACC). We derive explicit and implicit null reference models from the Loewe Additivity principle that are equivalent when the LACC holds. Of these two formulations, the implicit formulation is the known General Isobole Equation (Loewe, 1928), whereas the explicit one is the novel contribution. The LACC is violated in a significant number of cases. In this scenario the models make different predictions. We analyze two data sets of drug screening that are non-interactive (Cokol et al., 2011; Yadav et al., 2015) and show that the LACC is mostly violated and Loewe Additivity not defined. Further, we compare the measurements of the non-interactive cases of both data sets to the theoretical null reference models in terms of bias and mean squared error. We demonstrate that the explicit formulation of the null reference model leads to smaller mean squared errors than the implicit one and is much faster to compute.

SUBMITTER: Lederer S

PROVIDER: S-EPMC5808155 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Additive Dose Response Models: Explicit Formulation and the Loewe Additivity Consistency Condition.

Lederer Simone S Dijkstra Tjeerd M H TMH Heskes Tom T

Frontiers in pharmacology 20180206

High-throughput techniques allow for massive screening of drug combinations. To find combinations that exhibit an interaction effect, one filters for promising compound combinations by comparing to a response without interaction. A common principle for no interaction is Loewe Additivity which is based on the assumption that no compound interacts with itself and that two doses from different compounds having the same effect are equivalent. It then should not matter whether a component is replaced ...[more]

PMID: 29467650

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Project description:Endocrine disruption from environmental contaminants has been linked to a broad spectrum of adverse outcomes. One concern about endocrine-disrupting xenobiotics is the potential for additive or synergistic (i.e., greater-than-additive) effects of mixtures. A short-term dosing model to examine the effects of environmental mixtures on thyroid homeostasis has been developed. Prototypic thyroid-disrupting chemicals (TDCs) such as dioxins, polychlorinated biphenyls (PCBs), and polybrominated diphenyl ethers have been shown to alter thyroid hormone homeostasis in this model primarily by up-regulating hepatic catabolism of thyroid hormones via at least two mechanisms. Our present effort tested the hypothesis that a mixture of TDCs will affect serum total thyroxine (T4) concentrations in a dose-additive manner. Young female Long-Evans rats were dosed via gavage with 18 different polyhalogenated aromatic hydrocarbons [2 dioxins, 4 dibenzofurans, and 12 PCBs, including dioxin-like and non-dioxin-like PCBs] for 4 consecutive days. Serum total T4 was measured via radioimmunoassay in samples collected 24 hr after the last dose. Extensive dose-response functions (based on seven to nine doses per chemical) were determined for individual chemicals. A mixture was custom synthesized with the ratio of chemicals based on environmental concentrations. Serial dilutions of this mixture ranged from approximately background levels to 100-fold greater than background human daily intakes. Six serial dilutions of the mixture were tested in the same 4-day assay. Doses of individual chemicals that were associated with a 30% TH decrease from control (ED30), as well as predicted mixture outcomes were calculated using a flexible single-chemical-required method applicable to chemicals with differing dose thresholds and maximum-effect asymptotes. The single-chemical data were modeled without and with the mixture data to determine, respectively, the expected mixture response (the additivity model) and the experimentally observed mixture response (the empirical model). A likelihood-ratio test revealed statistically significant departure from dose additivity. There was no deviation from additivity at the lowest doses of the mixture, but there was a greater-than-additive effect at the three highest mixtures doses. At high doses the additivity model underpredicted the empirical effects by 2- to 3-fold. These are the first results to suggest dose-dependent additivity and synergism in TDCs that may act via different mechanisms in a complex mixture. The results imply that cumulative risk approaches be considered when assessing the risk of exposure to chemical mixtures that contain TDCs.

Dataset Information

Additive Dose Response Models: Explicit Formulation and the Loewe Additivity Consistency Condition.

Publications

Additive Dose Response Models: Explicit Formulation and the Loewe Additivity Consistency Condition.

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