mathematics

Number needed to harm

Number needed to harm is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Number needed to harm rather than just read about it. In short: In medicine, the number needed to harm (NNH) is an epidemiological measure that indicates how many persons on average need to be exposed to a risk factor over a specific period to cause harm in an average of one person who would not otherwise have been harmed. It is defined as the inverse of the absolute risk increase, and computed as 1 / ( I e − I u ) {\displaystyle 1/(I_{e}-I_{u})} , where I e {\displaystyle I_{e}…

Key takeaways

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

Reference excerpt

In medicine, the number needed to harm (NNH) is an epidemiological measure that indicates how many persons on average need to be exposed to a risk factor over a specific period to cause harm in an average of one person who would not otherwise have been harmed. It is defined as the inverse of the absolute risk increase, and computed as 1 / ( I e − I u ) {\displaystyle 1/(I_{e}-I_{u})} , where I e {\displaystyle I_{e}} is the incidence in the treated (exposed) group, and I u {\displaystyle I_{u}} is the incidence in the control (unexposed) group. Intuitively, the lower the number needed to harm, the worse the risk factor, with 1 meaning that every exposed person is harmed. NNH is similar to number needed to treat (NNT), where NNT usually refers to a positive therapeutic result and NNH to a detrimental effect or risk factor. Marginal metrics:

NNT for an additional beneficial outcome (NNTB) NNT for an additional harmful outcome (NNTH) are also used.

Relevance The NNH is an important measure in evidence-based medicine and helps physicians decide whether it is prudent to proceed with a particular treatment which may expose the patient to harms while providing therapeutic benefits. If a clinical endpoint is devastating enough without the drug (e.g. death, heart attack), drugs with a low NNH may still be indicated in particular situations if the NNT is smaller than the NNH. However, there are several important problems with the NNH, involving bias and lack of reliable confidence intervals, as well as difficulties in excluding the possibility of no difference between two treatments or groups.

Numerical example

Illustrations

Worked examples

Example 1 — a first encounter with Number needed to harm

Start with the simplest possible case. Write down what Number needed to harm claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Number needed to harm 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 Number needed to harm 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 Number needed to harm

In research: Number needed to harm appears in mathematics 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 Number needed to harm 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: Number needed to harm is common in secondary-school and first-year university syllabi. It links to neighbouring topics Drug discovery, Epidemiology, Evidence-based medicine, so understanding it makes those chapters shorter.
In everyday life: Look for Number needed to harm 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.

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How to study Number needed to harm in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Number needed to harm 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 Number needed to harm out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Number needed to harm in simple terms?

Why does Number needed to harm matter?

Because it connects several mathematics 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 Number needed to harm?

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 Number needed to harm.