Dose–response and therapeutic index !

How effect grows with dose, the difference between a more potent and a more effective drug, and how close the toxic dose is to the useful one.

Updated 2026-11-01

Dose–response curves describe how effect changes with dose or concentration. They separate two ideas that are often confused: potency (how much drug is needed) and efficacy (how big the maximum effect can be). Comparing the curves for the wanted effect and for toxicity gives the therapeutic index, which decides how carefully a drug must be dosed and monitored.

Graded dose–response

Plotted against the logarithm of concentration, the response usually forms an S-shaped curve. The left-right position shows potency (a lower EC50 means more potent). The top of the curve shows efficacy. Fentanyl is far more potent than morphine, but both are full agonists at the mu-opioid receptor with similar maximal analgesia.

Quantal dose–response

In a population, each person has a threshold dose for a response. The cumulative curve gives the ED50 (median effective dose) and the TD50 (median toxic dose). The spread of the curve reflects variation between people, which is why a dose that suits most patients can be too much for some.

Therapeutic index and therapeutic window

The therapeutic index compares toxic and effective doses. The therapeutic window is the clinical version: the range of levels that works without unacceptable toxicity. The warfarin label calls it a drug with a narrow therapeutic range that needs INR monitoring; the digoxin label notes toxicity can occur even at levels usually thought safe, especially with low potassium or magnesium.

Wide index: most penicillins, many antihistamines
Narrow index: warfarin, digoxin, aminoglycosides, lithium, phenytoin, ciclosporin, tacrolimus

What it changes in practice

For narrow-index drugs, brand or formulation switches, interactions, kidney function and illness matter more. Monitoring of levels (digoxin, aminoglycosides, lithium) or of effect (INR for warfarin), and teaching patients to report early signs of toxicity, are the safety net.

Test yourself

Think of the answer, then tap the question to see it.

Drug A has a lower EC50 than drug B but the same Emax. What does that mean?

Drug A is more potent (less is needed) but not more efficacious: both reach the same maximum effect.

How is the therapeutic index calculated?

As the ratio of the toxic dose to the effective dose in half of the population (TD50 / ED50); in animal studies the lethal dose (LD50) may be used.

Why does digoxin need careful monitoring?

It has a narrow margin between effective and toxic levels, and toxicity is more likely with low potassium or magnesium or reduced kidney function.

Is fentanyl more efficacious than morphine?

No. Fentanyl is more potent, but both are full mu-opioid agonists with similar maximal effect.

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Example drugs

← All of pharmacology

Educational content on how drugs work; not a prescribing guide and no substitute for a health professional's advice. No doses are given.

Sources: DailyMed - WARFARIN SODIUM tablet (DailyMed (U.S. National Library of Medicine), 2026); DailyMed - DIGOXIN tablet (DailyMed (U.S. National Library of Medicine), 2026); Therapeutic Drug Monitoring (MedlinePlus (U.S. National Library of Medicine), 2026).

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Representative model, for educational purposes only.