Dose-response relationships

Vivian Imbriotis | Jan. 5, 2026

For almost all drugs, there is a monotonic relationship between dose and effect. This can be demonstrated with dose-response curves, either for a graded or quantal response (old terms for continuous or binary outcomes). Quantal curves demonstrate the potency, efficacy, LD50, TD50, and ED50 of the drug. Dose-response curves are modified by the presence of an antagonist.

This is the curve of a continuous measure of drug effect against dose in an individual subject.

This is the curve of a binary measure of drug affect against dose in a population.

The potency of a drug is the dose or concentration required to achieve some effect (usually 50% of the drug's maximally effect, the \(ED_{50}\) or \(EC_{50}\).

The efficacy of a drug is the maximal effect achievable by that drug \(E_{max}\).

The intrinsic activity is the maximum efficacy of a drug as a fraction of the maximum efficacy of a full agonist.

An agonist is a drug that binds to a receptor, induces a conformational change, and thereby a physiological response.

Agonists can bind to the binding site of endogenous ligands ('orthosteric') or to other binding sites ('allosteric').


Full agonists will produce the maximal response the target system can acheive. It has an intrinsic activity of one. E.g. oxycodone.

Partial agonists have a lower efficacy than full agonists, and an intrinsic activity between zero and one. In the presence of a full agonist they will act as an antagonist. E.g. buprenorphine

Inverse agonists have a negative efficacy, they decrease the activity of the receptor below its basal function. E.g. naloxone.

Antagonists have an intrinstic activity of zero, but a nonzero affinity.

A competitive antagonist binds to the same site as the agonist. A sufficient concerntration of agonist can displace it. It reduces the potency of the agonist but not the efficacy.

A noncompetative antagonist binds to some other site, rendering the receptor useless to the agonist. They reduce both the potency and efficacy of the agonist.

Consider a quantal dose-response curve.

The ED50 is the dose at which 50% of subjects achieve the binary therapeutic effect.

The TD50 is the dose at which 50% of subjects achieve the binary toxic adverse effect (note the issues here: DAEs may not be dose-related and may take a long time to emerge e.g. carcinogenesis).

The LD50 is the dose at which 50% of subjects die.

$$\text{therapeutic index} = \frac{TD_{50}}{ED_{50}}$$