doseresponse

Dose-response, or doseresponse, is the relationship between the dose of a chemical, drug, or other agent and the magnitude of the biological response it elicits. It is a core concept in pharmacology, toxicology, and risk assessment, used to understand potency, efficacy, and safety across populations and systems.

Responses may be graded, increasing continuously with dose, or quantal, where a defined effect occurs or does not occur in individuals. Graded dose-response curves are commonly sigmoidal and can be described by the Hill equation, with Emax representing the maximum effect and EC50 the dose producing half of that maximum. The slope reflects cooperativity or allosteric effects. Some agents show nonmonotonic dose-response relationships.

Quantitative endpoints include LD50 or TD50 for toxic or lethal effects, NOAEL and LOAEL for observed effects, and EC50 for pharmacologic potency. In pharmacology the dose at which half-maximal effect is reached helps compare drugs; in toxicology the risk increases with dose, often informing safety margins.

Applications span drug development, regulatory risk assessment, pesticide and chemical exposure limits, and environmental health policy. Dose-response data underpin potency and efficacy assessments, help set exposure limits, and support benefit-risk analyses.

Limitations include interindividual variability, species differences, and time- or duration-dependent kinetics that affect target-site exposure. Extrapolation from animal models to humans introduces uncertainty, and nonmonotonic, adaptive, or mixture effects can complicate interpretation.