dosisrespons

The dose-response relationship describes how the magnitude of a biological effect changes with varying doses or concentrations of a substance. It is a central concept in pharmacology, toxicology, and environmental health, used to predict effects, compare potencies, and set exposure limits. Responses can be graded within individuals or binary across individuals.

Graded dose-response curves show continuous changes in a measured effect (such as enzyme activity or blood pressure) as dose rises, frequently forming a sigmoidal shape. Quantal dose-response curves describe an all-or-none outcome across a population, enabling estimates of the dose that affects a given proportion of individuals, such as ED50 or LD50.

Models such as the Hill equation or logistic functions describe the relationship. Key parameters include Emax (maximum effect), EC50 (concentration for half-maximal effect), ED50 (dose for half-maximal effect), and LD50 (lethal dose). Potency refers to the dose required for a given effect; efficacy refers to the maximal achievable effect.

Applications include guiding clinical dosing, assessing drug safety, and establishing regulatory limits. The therapeutic index or margin (for example, TD50/ED50 or LD50/ED50) provides a rough measure of safety.

Limitations include biological variability, time-dependent kinetics, and non-monotonic responses in some systems. Extrapolation across species or populations carries uncertainty, and non-linear dynamics can complicate interpretation. The concept is often associated with Paracelsus’ principle "the dose makes the poison."