PharmacologyTier 1Medical Sciences concept

Therapeutic index calculation (TD50/ED50)

Core concept

Quantal (all-or-none) dose-response curves give two population medians
- ED50 - dose producing the desired effect in 50% of the population
- TD50 - dose producing toxicity in 50%; LD50 - dose lethal to 50% (animal data)

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Therapeutic index (TI) = TD50 / ED50 (or LD50 / ED50)

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Higher TI = wider safety margin
The ratio depends on the separation of the two curves, not on either curve alone
Certain safety factor = TD1 / ED99 - a stricter and more clinically honest measure, because it uses the tails rather than the medians
- Two drugs can share a TI while one has overlapping tails and the other does not

Narrow TI (TDM usually needed)	Wide TI
Digoxin, lithium, phenytoin, warfarin, theophylline, gentamicin, vancomycin, ciclosporin, tacrolimus, methotrexate	Penicillins, most SSRIs, PPIs, paracetamol at therapeutic dose

Narrow TI drugs share the same practical consequences
- Therapeutic drug monitoring, defined target ranges
- Small dose increments, and dosing by weight or renal function
- Interactions matter disproportionately - a 30% clearance change is clinically trivial for amoxicillin and dangerous for tacrolimus
- Bioequivalence/brand substitution matters (phenytoin, ciclosporin, levothyroxine, warfarin)
TI is a population statistic and says nothing about an individual; the pharmacogenomic and interaction notes are how you individualise it
Related pharmacodynamic terms
- Potency - the dose needed (position of the curve, EC50); efficacy - the maximum achievable effect (Emax)
- A high therapeutic index is not the same as high potency - a very potent drug can have a narrow index (digoxin) and a weak drug a wide one
Paracetamol illustrates the limitation: a wide TI at therapeutic dose but a steep, unforgiving toxicity curve above it

The narrow-TI list is effectively the therapeutic drug monitoring list - know which drugs need levels and when to take them
- Digoxin >=6 h post dose; lithium 12 h post dose; vancomycin by AUC; gentamicin by post-dose level or nomogram; tacrolimus/ciclosporin trough
Any narrow-TI drug in a patient with AKI, a new interacting drug, or a change in weight needs a level and often a dose change
Do not substitute brands of a narrow-TI drug without rechecking a level - the classic examples are phenytoin, ciclosporin and levothyroxine
In toxicology, the concept becomes the risk assessment: what dose in this patient produces toxicity, and how far above the therapeutic dose is it

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