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A General Approach to Modeling Biphasic Relationships

机译：建立两相关系的通用方法

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Biphasic relationships can be found throughout the sciences, especially in the dose-response relationships of pharmacology, toxicology, agriculture, and nutrition. Accurate modeling of biphasic dose-response is an essential step in establishing effective guidelines for the protection of human and ecosystem health, yet currently-used biphasic mathematical models lack biological rationale and fit only limited sets of biphasic data. To model biphasic relationships more closely over wider ranges of exposures, we suggest a simple, general, biologically reasonable modeling approach leading to a family of mathematical models that combine log-logistic functions: at least one for the upslope and one forthe downslope of the biphasic relationship. All parameters employed are meaningfully interpretable. These models can be used to test for the presence of biphasic effects, and they simplify to a standard log-logistic model in the special case where no biphasic effect can be detected. They offer the promise of improvement in assessment of the safety and efficacy of Pharmaceuticals and nutrients as well as in determination of the toxicity of contaminants. Additionally, they may be useful in modeling nonmonotonic cause-effect relationships in other scientific disciplines.
机译：在整个科学领域都可以发现两相关系，特别是在药理学，毒理学，农业和营养学的剂量反应关系中。建立两相剂量反应的准确模型是建立保护人类和生态系统健康的有效指南的重要步骤，但是目前使用的两相数学模型缺乏生物学依据，仅适合有限的两相数据集。为了在更广泛的暴露范围内更紧密地建模双相关系，我们建议一种简单，通用，生物学上合理的建模方法，从而产生一系列结合对数逻辑函数的数学模型：至少一个用于双相的上坡和一个用于双相的下坡关系。所采用的所有参数都可以有意义地解释。这些模型可用于测试双相效应的存在，在无法检测到双相效应的特殊情况下，它们可简化为标准对数逻辑模型。它们有望改善药物和营养素的安全性和功效评估，以及确定污染物的毒性。此外，它们在其他科学学科中对非单调因果关系建模中可能很有用。

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