Gennings Chris, Carter W Hans, Carney Edward W, Charles Grantley D, Gollapudi B Bhaskar, Carchman Richard A
Department of Biostatistics, Virginia Commonwealth University, Richmond, Virginia 23298-0032, USA.
Toxicol Sci. 2004 Jul;80(1):134-50. doi: 10.1093/toxsci/kfh134. Epub 2004 Apr 14.
Assessing for interactions among chemicals in a mixture involves the comparison of actual mixture responses to those predicted under the assumption of zero interaction (additivity), based on individual chemical dose-response data. However, current statistical methods do not adequately account for differences in the shapes of the dose-response curves of the individual mixture components, as occurs with mixtures of full and partial receptor agonists. We present here a novel extension of current methods, which overcomes some of these limitations. Flexible single chemical concentration-effect curves combined with a common background parameter are used to describe an additivity surface along each axis. The predicted mixture response under the assumption of additivity is based on the constraint of Berenbaum's definition of additivity. Iterative algorithms are used to estimate mean responses at observed mixture combinations using only single chemical parameters. A full model allowing for different maximum response levels, different thresholds, and different slope parameters for each mixture component is compared to a reduced model under the assumption of additivity. A likelihood-ratio test is used to test the hypothesis of additivity by utilizing the full and reduced model predictions. This approach is useful for mixtures of chemicals with threshold regions and whose component chemicals exhibit differing response maxima (e.g., mixtures of full and partial agonists). The methods are illustrated with a combination of six chemicals in an estrogen receptor-alpha (ER-alpha) reporter gene assay.
评估混合物中化学物质之间的相互作用，需要根据单个化学物质的剂量反应数据，将实际混合物反应与在零相互作用（相加性）假设下预测的反应进行比较。然而，当前的统计方法没有充分考虑单个混合物成分剂量反应曲线形状的差异，就像完全和部分受体激动剂的混合物那样。我们在此提出一种当前方法的新扩展，它克服了其中一些局限性。灵活的单化学物质浓度 - 效应曲线与一个共同的背景参数相结合，用于描述沿每个轴的相加性表面。在相加性假设下预测的混合物反应基于贝伦鲍姆相加性定义的约束。迭代算法仅使用单化学物质参数来估计观察到的混合物组合处的平均反应。将一个允许每个混合物成分具有不同最大反应水平、不同阈值和不同斜率参数的完整模型与在相加性假设下的简化模型进行比较。使用似然比检验通过利用完整模型和简化模型的预测来检验相加性假设。这种方法对于具有阈值区域且其成分化学物质表现出不同反应最大值的化学物质混合物（例如完全和部分激动剂的混合物）很有用。通过在雌激素受体 - α（ER - α）报告基因测定中六种化学物质的组合来说明这些方法。
