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.
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