Sühnel J
Institut für Molekulare Biotechnologie, Jena, Germany.
Bull Math Biol. 1998 Mar;60(2):197-213. doi: 10.1006/bulm.1997.0009.
A possible experimental design for combination experiments is to compare the dose-response curve of a single agent with the corresponding curve of the same agent using either a fixed amount of a second one or a fixed dose ratio. No interaction is then often defined by a parallel shift of these curves. We have performed a systematic study for various types of dose-response relations both for the dose-additivity (Loewe additivity) and for the independence (Bliss independence) criteria for defining zero interaction. Parallelism between dose-response curves of a single agent and those of the same agent in the presence of a fixed amount of another one is found for the Loewe-additivity criterion for linear dose-response relations. For nonlinear relations, one has to differentiate between effect parallelism (parallel shift on the effect scale) and dose parallelism (parallel shift on the dose scale). In the case of Loewe additivity, zero-interaction dose parallelism is found for power, Weibull, median-effect and logistic dose-response relations, given that special parameter relationships are fulfilled. The mechanistic model of competitive interaction exhibits dose parallelism but not effect parallelism for Loewe additivity. Bliss independence and Loewe additivity lead to identical results for exponential dose-response curves. This is the only case for which dose parallelism was found for Bliss independence. Parallelism between single-agent dose-response relations and Loewe additivity mixture relations is found for examples with a fixed dose-ratio design. However, this is again not a general property of the design adopted but holds only if special conditions are fulfilled. The comparison of combination dose-response curves with single-agent relations has to be performed taking into account both potency and shape parameters. The results of this analysis lead to the conclusion that parallelism between zero interaction combination and single-agent dose-response relations is found only for special cases and cannot be used as a general criterion for defining zero-interaction in combined-action assessment even if the correct potency shift is taken into account.
联合实验的一种可能的实验设计是，使用固定量的第二种药物或固定剂量比，将单一药物的剂量-反应曲线与同一药物在相应情况下的曲线进行比较。然后，通常通过这些曲线的平行移动来定义无相互作用。我们针对各种类型的剂量-反应关系，对用于定义零相互作用的剂量相加性（洛伊相加性）和独立性（布利斯独立性）标准进行了系统研究。对于线性剂量-反应关系的洛伊相加性标准，发现单一药物的剂量-反应曲线与在存在固定量的另一种药物时该药物的剂量-反应曲线之间存在平行性。对于非线性关系，必须区分效应平行性（效应尺度上的平行移动）和剂量平行性（剂量尺度上的平行移动）。在洛伊相加性的情况下，对于幂函数、威布尔、中位效应和逻辑剂量-反应关系，在满足特殊参数关系时可发现零相互作用剂量平行性。竞争相互作用的机制模型对于洛伊相加性表现出剂量平行性，但没有效应平行性。对于指数剂量-反应曲线，布利斯独立性和洛伊相加性得出相同的结果。这是发现布利斯独立性存在剂量平行性的唯一情况。对于固定剂量比设计的示例，发现单一药物剂量-反应关系与洛伊相加性混合关系之间存在平行性。然而，这同样不是所采用设计的一般特性，仅在满足特殊条件时才成立。在比较联合剂量-反应曲线与单一药物关系时，必须同时考虑效价和形状参数。该分析结果得出结论，仅在特殊情况下才能发现零相互作用联合与单一药物剂量-反应关系之间的平行性，并且即使考虑了正确的效价变化量，也不能将其用作联合作用评估中定义零相互作用的一般标准。
