# Therapeutic index

The therapeutic index (also known as therapeutic ratio) is a comparison of the amount of a therapeutic agent that causes the therapeutic effect to the amount that causes death (in animal studies) or toxicity (in human studies).[1]

Quantitatively, it is the ratio given by the lethal or toxic dose divided by the therapeutic dose.

In animal studies, the therapeutic index is the lethal dose of a drug for 50% of the population (LD50) divided by the minimum effective dose for 50% of the population (ED50).

Lethality is not determined in human clinical trials; instead, the dose that produces a toxicity in 50% of the population (TD50) is used to calculate the therapeutic index.

While the lethal dose is important to determine in animal studies, there are usually severe toxicities that occur at sublethal doses in humans, and these toxicities often limit the maximum dose of a drug. A higher therapeutic index is preferable to a lower one: a patient would have to take a much higher dose of such a drug to reach the lethal/toxic threshold than the dose taken to elicit the therapeutic effect.

$\mbox{Therapeutic ratio} = \frac{\mathrm{LD}_{50}}{\mathrm{ED}_{50}}$ in animal studies, or for humans, $\mbox{Therapeutic ratio} = \frac{\mathrm{TD}_{50}}{\mathrm{ED}_{50}}$

Generally, a drug or other therapeutic agent with a narrow therapeutic range (i.e. having little difference between toxic and therapeutic doses) may have its dosage adjusted according to measurements of the actual blood levels achieved in the person taking it. This may be achieved through therapeutic drug monitoring (TDM) protocols.

The therapeutic index varies widely among substances: most forgiving among the opioid analgesics is remifentanyl, which offers a therapeutic index of 33,000:1; tetrahydrocannabinol, a sedative and analgesic of herbal origin (cannabis), has a safe therapeutic index of 1000:1, while diazepam, a benzodiazepine sedative-hypnotic and skeletal muscle relaxant has a less-forgiving index of 100:1 and morphine, a sedative, antidepressant, and analgesic also of herbal origin (genus Papaver) has an index of 70:1[2] (which, however, is still considered very safe).

Less safe are cocaine, a stimulant and local anaesthetic; ethanol (colloquially, the "alcohol" in alcoholic beverages), a widely available sedative consumed world-wide: the therapeutic indices for these substances are 15:1 and 10:1 respectively. Even less-safe are drugs such as digoxin, a cardiac glycoside; its therapeutic index is approximately 2:1.[3] Other examples of drugs with a narrow therapeutic range, which may require drug monitoring both to achieve therapeutic levels and to minimize toxicity, include: paracetamol (acetaminophen), dimercaprol, theophylline, warfarin and lithium carbonate. Some antibiotics require monitoring to balance efficacy with minimizing adverse effects, including: gentamicin, vancomycin, amphotericin B (nicknamed 'amphoterrible' for this very reason), and polymyxin B.

The effective therapeutic index can be affected by targeting, in which the therapeutic agent is concentrated in its area of effect. For example, in radiation therapy for cancerous tumors, shaping the radiation beam precisely to the profile of a tumor in the "beam's eye view" can increase the delivered dose without increasing toxic effects, though such shaping might not change the therapeutic index. Similarly, chemotherapy or radiotherapy with infused or injected agents can be made more efficacious by attaching the agent to an oncophilic substance, as is done in peptide receptor radionuclide therapy for neuroendocrine tumors and in chemoembolization or radioactive microspheres therapy for liver tumors and metastases. This concentrates the agent in the targeted tissues and lowers its concentration in others, increasing efficacy and lowering toxicity.

Sometimes the term safety ratio is used instead, particularly when referring to psychoactive drugs used for non-therapeutic purposes, e.g. recreational use.[4] In such cases, the "effective" dose is the amount and frequency that produces the desired effect, which can vary, and can be greater or less than the therapeutically effective dose.

A therapeutic index does not consider drug interactions or synergistic effects. For example, the risk associated with benzodiazepines increases significantly when taken with alcohol, opiates, or stimulants when compared with being taken alone.[medical citation needed] Therapeutic index also does not take into account the ease or difficulty of reaching a toxic or lethal dose. This is more of a consideration for recreational drug users, as the purity can be highly variable.

Protective index is a similar concept, except that it uses TD50 (median toxic dose) in place of LD50. For many substances, toxic effects can occur at levels far below those needed to cause death, and thus the protective index (if toxicity is properly specified) is often more informative about a substance's relative safety. Nevertheless, the therapeutic index is still useful as it can be considered an upper bound for the protective index, and the former also has the advantages of objectivity and easier comprehension.