Therapeutic index

Key takeaways

Therapeutic index belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Therapeutic index to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Therapeutic index from memory before moving on to harder problems.

Reference excerpt

The therapeutic index (TI; also referred to as therapeutic ratio) is a quantitative measurement of the relative safety of a drug with regard to risk of overdose. It is a comparison of the amount of a therapeutic agent that causes toxicity to the amount that causes the therapeutic effect. 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. In the early days of pharmaceutical toxicology, TI was frequently determined in animals as lethal dose of a drug for 50% of the population (LD50) divided by the minimum effective dose for 50% of the population (ED50). In modern settings, more sophisticated toxicity endpoints are used. For many drugs, severe toxicities in humans occur at sublethal doses, which limit their maximum dose. A higher safety-based therapeutic index is preferable instead of a lower one; an individual would have to take a much higher dose of a drug to reach the lethal threshold than the dose taken to induce the therapeutic effect of the drug. However, a lower efficacy-based therapeutic index is preferable instead of a higher one; an individual would have to take a higher dose of a drug to reach the toxic threshold than the dose taken to induce the therapeutic effect of the drug. 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.

Types Based on efficacy and safety of drugs, there are two types of therapeutic index:

Safety-based therapeutic index

T I safety = L D 50 E D 50 {\displaystyle TI_{\text{safety}}={\frac {LD_{50}}{ED_{50}}}}

It is desirous for the value of LD50 to be as large as possible, to decrease risk of lethal effects and increase the therapeutic window. In the above formula, TIsafety increases as the difference between LD50 and ED50 increases—hence, a higher safety-based therapeutic index indicates a larger therapeutic window, and vice versa.

Efficacy-based therapeutic index In pharmacology, potency (e.g. ED50) and efficacy (maximal effect, Emax) are distinct properties of drug action. The therapeutic index is typically defined using dose-based measures (such as TD50/ED50) and does not incorporate efficacy directly. The use of terms such as "efficacy-based therapeutic index" is uncommon in standard pharmacology texts and may reflect a conflation of efficacy with dose-based safety margins.

T I efficacy = E D 50 T D 50 {\displaystyle TI_{\text{efficacy}}={\frac {ED_{50}}{TD_{50}}}}

Ideally the ED50 is as low as possible for faster drug response and larger therapeutic window, whereas a drugs TD50 is ideally as large as possible to decrease risk of toxic effects. In the above equation, the greater the difference between ED50 and TD50, the smaller the value of TIefficacy. 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.

Protective index = T D 50 E D 50 = 1 T I efficacy {\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 ( T I safety {\displaystyle {TI_{\text{safety}}}} ) is still useful as it can be considered an upper bound of the protective index, and the former also has the advantages of objectivity and easier comprehension. Since the protective index (PI) is calculated as TD50 divided by ED50, it can be mathematically expressed that:

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

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Therapeutic index

Start with the simplest possible case. Write down what Therapeutic index claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Therapeutic index before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Therapeutic index ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Therapeutic index

In research: Therapeutic index appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Therapeutic index in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Therapeutic index is common in secondary-school and first-year university syllabi. It links to neighbouring topics Life sciences industry, Pharmacokinetics, so understanding it makes those chapters shorter.
In everyday life: Look for Therapeutic index outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Therapeutic index in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Therapeutic index means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Therapeutic index out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Therapeutic index in simple terms?

The therapeutic index (TI; also referred to as therapeutic ratio) is a quantitative measurement of the relative safety of a drug with regard to risk of overdose. It is a comparison of the amount of a therapeutic agent that causes toxicity to the amount that causes the therapeutic effect.

Why does Therapeutic index matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Therapeutic index?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Therapeutic index.