Therapeutic index

The therapeutic index (TI; also referred to as therapeutic ratio) is a quantitative measurement of the relative safety of a drug. It is a comparison of the amount of a therapeutic agent that causes toxicity to the amount that causes the therapeutic effect.^[1] The related terms therapeutic window or safety window refer to a range of doses optimized between efficacy and toxicity, achieving the greatest therapeutic benefit without resulting in unacceptable side-effects or toxicity.

Classically, for clinical indications of an approved drug, TI refers to the ratio of the dose of the drug that causes adverse effects at an incidence/severity not compatible with the targeted indication (e.g. toxic dose in 50% of subjects, TD₅₀) to the dose that leads to the desired pharmacological effect (e.g. efficacious dose in 50% of subjects, ED₅₀). In contrast, in a drug development setting TI is calculated based on plasma exposure levels.^[2]

In the early days of pharmaceutical toxicology, TI was frequently determined in animals as lethal dose of a drug for 50% of the population (

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 its blood levels in the person taking it. This may be achieved through therapeutic drug monitoring (TDM) protocols. TDM is recommended for use in the treatment of psychiatric disorders with lithium due to its narrow therapeutic range.^[3]

Types

Based on

Safety-based therapeutic index

• ${\displaystyle TI_{\text{safety}}={\frac {LD_{50}}{ED_{50}}}}$

LD₅₀ is ensured to be as high as possible to decrease risk of lethal effects (often leading to death), and for larger therapeutic window. In the above formula, LD₅₀ is taken in the numerator and ED₅₀ is taken in the denominator because the higher the LD₅₀ and the lower the ED₅₀, the higher the ${\displaystyle TI_{\text{efficacy}}}$, the higher the difference between ED₅₀ and LD₅₀. Hence, a higher safety-based therapeutic index indicates a larger therapeutic window.

Efficacy-based therapeutic index

• ${\displaystyle TI_{\text{efficacy}}={\frac {ED_{50}}{TD_{50}}}}$

ED₅₀ is ensured to be as low as possible for faster drug response and larger therapeutic window, whereas TD₅₀ is ensured to be as high as possible to decrease risk of toxic effects of drugs. In the above formula, ED₅₀ is taken in the numerator and TD₅₀ is taken in the denominator because the lower the ED₅₀ and the higher the TD₅₀, the lower the ${\displaystyle TI_{\text{efficacy}}}$, the higher the difference between ED₅₀ and TD₅₀. Hence, a lower efficacy-based therapeutic index indicates a larger therapeutic window.

Protective index

Similar to safety-based therapeutic index, the protective index uses TD₅₀ (median toxic dose) in place of LD₅₀.

• ${\displaystyle {\text{Protective index}}={\frac {TD_{50}}{ED_{50}}}={\frac {1}{TI_{\text{efficacy}}}}}$

For many substances, toxicity can occur at levels far below lethal effects (that cause death), and thus, if toxicity is properly specified, the protective index is often more informative about a substance's relative safety. Nevertheless, the safety-based therapeutic index (${\displaystyle {TI_{\text{safety}}}}$) is still useful as it can be considered an

Since the protective index (PI) is calculated as TD₅₀ divided by ED₅₀, it can be mathematically expressed that:

${\displaystyle TI_{\text{efficacy}}={\frac {1}{\text{Protective index}}}}$

which means that ${\displaystyle TI_{\text{efficacy}}}$ is a reciprocal of protective index.

All the above types of therapeutic index can be used in both

A review published by Muller and Milton in Nature Reviews Drug Discovery critically discusses TI determination and interpretation in a translational drug development setting for both small molecules and biotherapeutics.^[2]

Range of therapeutic indices

The therapeutic index varies widely among substances, even within a related group.

For instance, the

Even less safe are drugs such as digoxin, a cardiac glycoside; its therapeutic index is approximately 2:1.^[11]

Other examples of drugs with a narrow therapeutic range, which may require drug monitoring both to achieve therapeutic levels and to minimize toxicity, include dimercaprol, theophylline, warfarin and lithium carbonate.

Some antibiotics and antifungals require monitoring to balance efficacy with minimizing adverse effects, including: gentamicin, vancomycin, amphotericin B (nicknamed 'amphoterrible' for this very reason), and polymyxin B.

Cancer radiotherapy

Radiotherapy aims to shrink tumors and kill cancer cells using high energy. The energy arises from

The Certain Safety Factor, also referred to as the Margin of Safety (MOS), is the ratio of the lethal dose to 1% of population to the effective dose to 99% of the population (LD₁/ED₉₉).^[16] This is a better safety index than the LD₅₀ for materials that have both desirable and undesirable effects, because it factors in the ends of the spectrum where doses may be necessary to produce a response in one person but can, at the same dose, be lethal in another.

${\displaystyle {\text{Certain safety factor}}=\mathrm {\frac {LD_{1}}{ED_{99}}} }$

Synergistic effect

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.

Therapeutic window

The therapeutic window (or pharmaceutical window) of a drug is the range of drug dosages which can treat disease effectively without having toxic effects.^[17] Medication with a small therapeutic window must be administered with care and control, frequently measuring blood concentration of the drug, to avoid harm. Medications with narrow therapeutic windows include theophylline, digoxin, lithium, and warfarin.

Optimal biological dose

Optimal biological dose (OBD) is the quantity of a drug that will most effectively produce the desired effect while remaining in the range of acceptable toxicity.

Maximum tolerated dose

The maximum tolerated dose (MTD) refers to the highest dose of a radiological or

MTD is an essential aspect of a drug's profile. All modern healthcare systems dictate a maximum safe dose for each drug, and generally have numerous safeguards (e.g. insurance quantity limits and government-enforced maximum quantity/time-frame limits) to prevent the prescription and dispensing of quantities exceeding the highest dosage which has been demonstrated to be safe for members of the general patient population.

Patients are often unable to tolerate the theoretical MTD of a drug due to the occurrence of side-effects which are not innately a manifestation of toxicity (not considered to severely threaten a patient's health) but cause the patient sufficient distress and/or discomfort to result in non-compliance with treatment. Such examples include emotional "blunting" with antidepressants,

See also

• Drug titration – process of finding the correct dose of a drug
• Effective dose
• EC50
• IC50
• LD50
• Hormesis

References