Therapeutic index explained: TD50 / ED50

Why a little too much matters for some drugs and not others

Give a patient a little too much penicillin and usually very little happens. Give a little too much lithium and the patient can be in trouble. Both drugs work, so what is different?^[4][5]

The answer is the therapeutic index: a number that compares the dose that causes toxicity with the dose that gives the wanted effect. This lesson shows how to calculate it and why narrow-index drugs need monitoring.^[1]

The quantal curve: ED50, TD50 and LD50

A graded dose-response curve measures how big an effect is. A quantal curve asks a different question: what fraction of patients respond? The effect is all-or-none, present or absent in each person.^[2]

Plot the dose against the cumulative percentage of patients showing the effect and you again get an S-shaped curve. Three doses are read from such curves.^[1][2]

The ED50 here is the quantal median effective dose: the dose at which half of individuals show the specified effect. It is a different use of the term from the ED50 on a graded curve, which is covered in the lesson on graded dose-response curves.^[1][2]

The therapeutic index: TD50 / ED50

1. Read the ED50The dose that works in half of patients.
2. Read the TD50The dose that causes the defined toxic effect in half of patients.
3. Divide toxic by effectiveTD50 / ED50. A bigger number means a wider safety margin.

A big ratio means the toxic curve sits far to the right of the effective curve: a wide safety margin. A small ratio means the two curves sit close together. It is a ratio, not a difference.^[1][3]

This lesson uses TD50 / ED50, the usual exam convention.^[1] Some sources define the index slightly differently, for example as a minimum toxic concentration over a median effective concentration.^[3]

Worked example: same potency, very different safety

Take two drugs, both with a median effective dose of 5 mg. They have the same potency.

Same potency, very different safety. Drug A has a wide margin; drug B has a narrow one. The index uses the doses on both curves, not the ED50 alone, so potency and safety margin are independent properties.^[1]

Drug B is the lithium-type problem: its toxic curve sits close to its effective curve, so little dose change separates a working dose from a toxic one. Drug A behaves like penicillin, where the toxic curve sits far to the right.^[1][4][5]

The therapeutic window

The therapeutic window is the practical cousin of the index: the range of doses, or blood concentrations, between the minimum that works and the minimum that is toxic.^[1][11]

With a narrow window, a small change in dose, or in how the body handles the drug, can tip a patient from ineffective to toxic. Kidney function, age and interacting drugs can all do it.^[3][7][8]

Monitoring narrow-index drugs, and a population caution

That is why narrow-index drugs are monitored more closely. Warfarin is monitored by the INR and lithium by its blood level. Digoxin and phenytoin are other narrow-index drugs.^{[1][6][8][11]}

Kidney function, age or an interacting drug can change how the body handles the drug, so for a narrow-window drug the level or effect is checked rather than assumed.^[1][3][7][8]

Penicillin, with a wide margin, forgives moderate differences in blood level.^[4][9][10]