Yang Linqian, Wang Jiaying, Cheke Robert A, Tang Sanyi
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, China.
Natural Resources Institute, the University of Greenwich, UK.
Dose Response. 2021 Dec 15;19(4):15593258211062785. doi: 10.1177/15593258211062785. eCollection 2021 Oct-Dec.
Dose-response curves, which fit a multitude of experimental data derived from toxicology, are widely used in physics, chemistry, biology, and other fields. Although there are many dose-response models for fitting dose-response curves, the application of these models is limited by many restrictions and lacks universality, so there is a need for a novel, universal dynamical model that can improve fits to various types of dose-response curves.
We expand the hormetic Ricker model, taking the delay inherent in the dose-response into account, and develop a novel and dynamic delayed Ricker difference model (DRDM) to fit various types of dose-response curves. Furthermore, we compare the DRDM with other dose-response models to confirm that it can mimic different types of dose-response curves.
By fitting various types of dose-response data sets derived from drug applications, disease treatment, pest control, and plant management, and comparing the imitative effect of the DRDM with other models, we find that the DRDM fits monotonic dose-response data well and, in most circumstances, the DRDM has a better imitative effect to non-monotonic dose-response data with hormesis than other models do.
The MSE of fits of the DRDM to S-shaped dose-response data (DS2-G) is not lower than those for four other models, but the MSE of fits to U-shaped (DS7) and inverted U-shaped dose-response data (DS10) were lower than for two other models. This means that the imitative effect of the DRDM is comparable to other models of monotonic dose-response data, but is a significant improvement compared to traditional models of non-monotonic dose-response data with hormesis.
We propose a novel dynamic model (DRDM) for fitting to various types of dose-response curves, which can reflect the dynamic trend of the population growth compared with traditional static dose-response models. By analyzing data, we have confirmed that the DRDM provides an ideal description of various dose-response observations and it can be used to fit a wide range of dose-response data sets, especially for hormetic data sets. Therefore, we conclude that the DRDM has a good universality for dose-response curve fitting.
剂量反应曲线适用于源自毒理学的大量实验数据，在物理、化学、生物学及其他领域广泛应用。尽管有许多用于拟合剂量反应曲线的剂量反应模型，但这些模型的应用受到诸多限制且缺乏通用性，因此需要一种新颖、通用的动力学模型来改善对各类剂量反应曲线的拟合。
我们扩展了兴奋效应里克模型，考虑到剂量反应中固有的延迟，开发了一种新颖的动态延迟里克差分模型（DRDM）来拟合各类剂量反应曲线。此外，我们将DRDM与其他剂量反应模型进行比较，以确认它能模拟不同类型的剂量反应曲线。
通过拟合源自药物应用、疾病治疗、害虫防治和植物管理的各类剂量反应数据集，并将DRDM的模拟效果与其他模型进行比较，我们发现DRDM能很好地拟合单调剂量反应数据，且在大多数情况下，与其他模型相比，DRDM对具有兴奋效应的非单调剂量反应数据具有更好的模拟效果。
DRDM对S形剂量反应数据（DS2-G）拟合的均方误差不低于其他四个模型，但对U形（DS7）和倒U形剂量反应数据（DS10）拟合的均方误差低于其他两个模型。这意味着DRDM对单调剂量反应数据的模拟效果与其他模型相当，但与具有兴奋效应的非单调剂量反应数据的传统模型相比有显著改进。
我们提出了一种用于拟合各类剂量反应曲线的新颖动态模型（DRDM），与传统静态剂量反应模型相比，它能反映种群增长的动态趋势。通过数据分析，我们已确认DRDM对各类剂量反应观测提供了理想描述，它可用于拟合广泛的剂量反应数据集，尤其是兴奋效应数据集。因此，我们得出结论，DRDM在剂量反应曲线拟合方面具有良好的通用性。
