Formulation and Validation of an Extended Sigmoid Emax Model in Pharmacodynamics

Drug concentration–response curves (DRCs) are crucial in pharmacology for assessing the drug effects on biological systems. The widely used sigmoid Emax model, which accounts for response saturation, relies heavily on the effective drug concentration ( \(E{D}_{50}\) $E{D}_{50}$ ). This reliance can lead to validation errors and inaccuracies in model fitting. The Emax model cannot generate multiple DRCs, raising concerns about whether the dataset is fully utilized.

This study formulates an extended Emax (eEmax) model designed to overcome these limitations. The eEmax model generates multiple DRCs from a single dataset by using various estimated \({\alpha }^{\prime}\text{s}\in \left[\text{0,100}\right]\) ${\alpha }^{\prime }\text{s}\in \left[\text{0,100}\right]$ , while keeping \(E{D}_{\alpha }\) $E{D}_{\alpha }$ fixed, rather than estimating an \(E{D}_{50}\) $E{D}_{50}$ value as in the Emax model.

This model effectively captures a broader range of concentration–response behavior, including non-sigmoidal patterns, thus providing greater flexibility and accuracy compared to the Emax model. Validation using various drug-response data and PKPD frameworks demonstrates the eEmax model’s improved accuracy and versatility in handling concentration–response data.

The eEmax model provides a robust and flexible method for drug concentration–response analysis, facilitating the generation of multiple DRCs from a single dataset and reducing the possibility of validation errors. This model is particularly valuable for its ease of use and its capability to fully utilize datasets, providing its potential in PKPD modeling and drug discovery.