The problem of optimal dosage estimation arises in diverse scientific domains, from pharmacology and toxicology to aquaculture and environmental studies. Statistical modeling of nonlinear dose-response relationships is essential to quantify biological effects and determine response-optimal levels. This paper introduces a flexible Bayesian fractional polynomial (BFP) framework for modeling such relationships, allowing for model uncertainty quantification and robust prediction through Bayesian model averaging. Extensive simulation results demonstrate that the proposed BFP approach yields accurate estimation of optimal dose levels, outperforming benchmarks significantly. The approach is demonstrated on real data from fish nutrient requirement experiments.

翻译：最优剂量估计问题广泛出现在从药理学、毒理学到水产养殖和环境研究等不同科学领域中。对非线性剂量-反应关系进行统计建模，对于量化生物效应和确定反应最优水平至关重要。本文引入了一个灵活的贝叶斯分数多项式框架来建模此类关系，通过贝叶斯模型平均实现模型不确定性量化和稳健预测。大量模拟结果表明，所提出的贝叶斯分数多项式方法能够准确估计最优剂量水平，显著优于基准方法。该方法在鱼类营养需求实验的真实数据上得到了验证。