doserelationship

A dose–response relationship is a foundational concept in pharmacology and toxicology that describes how the magnitude of a biological or clinical response varies with the amount of a substance administered. It characterizes how a drug or toxin produces effects across a range of doses.

There are two main types of dose–response data. Graded dose–response curves depict continuous, measurable effects (such as blood pressure or enzyme activity) within a single subject as the dose increases. Quantal dose–response curves describe binary outcomes (such as sleep or no sleep) across a population, used to determine percentages of responders at each dose.

The curves are often sigmoidal and can be described by models such as the Hill equation. Key parameters include Emax, the maximum achievable effect; EC50, the dose that produces half of Emax and a measure of potency; and the Hill coefficient, which reflects the curve’s steepness. In quantal analyses, endpoints such as ED50 (the dose effective in 50% of individuals) and TD50 or LD50 (toxic or lethal dose for 50%) are used. The therapeutic index or margin of safety is often expressed as TD50/ED50 or LD50/ED50.

Applications of dose–response analysis include guiding dose selection in drug development, informing clinical dosing guidelines, and conducting risk assessments. Limitations arise from variability among individuals due to genetics, age, disease, concomitant medications, and pharmacokinetic factors that can shift or flatten the curve. Environmental factors and receptor sensitivity changes can also modify the relationship, underscoring the need for cautious interpretation in real-world settings.