Number needed to harm: Difference between revisions

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{{Short description|Measure in epidemiology}}

{{redirect|NNH|the British colonial military force|Natal Native Horse}}

{{Redirect|NNH}}

The '''number needed to harm''' ('''NNH''') is an [[epidemiology|epidemiological]] measure that indicates how many patients on average need to be exposed to a [[risk-factor]] over a specific period to cause harm in an average of one patient who would not otherwise have been harmed.<ref>[http://www.effectivehealthcare.ahrq.gov/index.cfm/glossary-of-terms/?pageaction=showterm&termid=41 Glossary of Terms]</ref> It is defined as the inverse of the [[attributable risk]]. Intuitively, the lower the number needed to harm, the worse the [[risk-factor]], with 1 meaning that, on average, every patient exposed is harmed.

[[File:Number needed to harm plain.svg|alt=Illustration of two groups: one exposed to a risk factor, and one unexposed. Exposed group has larger risk of adverse outcome (NNH = 4).|thumb|Group exposed to a risk factor (left) has increased risk of an adverse outcome (black) compared to the unexposed group (right). 4 individuals need to be exposed for 1 adverse outcome to occur (NNH = 4).]]

In [[medicine]], the '''number needed to harm''' ('''NNH''') is an [[epidemiology|epidemiological]] measure that indicates how many persons on average need to be exposed to a [[risk-factor|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 <math>1/(I_e - I_u)</math>, where <math>I_e</math> is the [[Incidence_(epidemiology) | incidence]] in the treated (exposed) group, and <math>I_u</math> is the incidence in the control (unexposed) group.<ref name=":02">{{Cite book|title=Dictionary of Epidemiology - Oxford Reference|language=en|doi=10.1093/acref/9780199976720.001.0001|year=2014|isbn=9780199976720|last1=Porta|first1=Miquel|last2=Greenland|first2=Sander|last3=Hernán|first3=Miguel|last4=Silva|first4=Isabel dos Santos|last5=Last|first5=John M.}}</ref> 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 [[Numbernumber needed to treat]] (NNT), where NNT usually refers to a positive therapeutic interventionresult and NNH to a detrimental effect or risk factor. NNH is computed with respect to "exposure" and "non-exposure", and can be determined for raw data or for data corrected for [[Confounding variable|confounders]]. A defined endpoint has to be specified. If the [[probability|probabilities]] ''p_exposure'' and ''p_non-exposure'' of this endpoint are known, then the NNH is computed as 1/(''p_exposure''-''p_non-exposure''). This quantity can also be interpreted as the inverse of attributable risk or 1/AR.

Marginal metrics:

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]], [[myocardial infarction|heart attack]]), drugs with a low NNH may still be indicated in particular situations if the [[number needed to treat]], (the converse for [[adverse effect (medicine)|side effect]]s, or the drug's benefit) is less 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.<ref>{{cite journal |author=Hutton JL |title= Misleading Statistics: The Problems Surrounding Number Needed to Treat and Number Needed to Harm |url=http://adisonline.com/pharmaceuticalmedicine/Fulltext/2010/24030/Misleading_Statistics__The_Problems_Surrounding.3.aspx| journal=Pharm Med |volume=24 |issue=3 |pages=145–9 |year=2010 |doi=10.2165/11536680-000000000-00000}}</ref>

* NNT for an additional beneficial outcome ('''NNTB''')

* NNT for an additional harmful outcome ('''NNTH''')

are also used.<ref>{{cite web

|url=https://training.cochrane.org/handbook/current/chapter-15

|accessdate=3 October 2023

|title=Cochrane Handbook for Systematic Reviews of Interventions

|last1=Schünemann

|first1=Holger J

|date=2023<!-- version 6.4 -->

|website=cochrane.org

|publisher=Cochrane Training

|quote=<!-- section 15.4.2 -->[NNH] can easily^{''[citation needed]''} be read to imply the number of people who will experience a harmful outcome if given the intervention ... The preferred alternative is to use phrases such as 'number needed to treat for an additional beneficial outcome' (NNTB) and 'number needed to treat for an additional harmful outcome' (NNTH) to indicate direction of effect.

}}</ref>

__TOC__

==Worked example==

== Relevance ==

The following is an example of calculating number needed to harm.

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]], [[myocardial infarction|heart attack]]), drugs with a low NNH may still be indicated in particular situations if the NNT is smaller than the NNH.{{dubious|reason=risk is exposure times effect; comparing number exposed while neglecting size of effect is statistically clueless|date=October 2023}}{{Citation needed|date=September 2018}} 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.<ref>{{cite journal |author=Hutton JL | authorlink = Jane Hutton |title= Misleading Statistics: The Problems Surrounding Number Needed to Treat and Number Needed to Harm | journal=Pharm Med |volume=24 |issue=3 |pages=145–9 |year=2010 |doi=10.1007/BF03256810| s2cid = 39801240 }}</ref>

==Numerical example==

In a [[cohort study]], individuals with exposure to a risk factor (Exposure&nbsp;+) are followed for a certain number of years to see if they develop a certain disease or outcome (Disease&nbsp;+). A control group of individuals who are not exposed to the risk factor (Exposure&nbsp;&minus;) are also followed . "Follow up time" is the number of individuals in each group multiplied by the number of years that each individual is followed.

{{RCT risk increase example}}

==See also==

Assume there are two unknown rates of the disease incidence per patient per year, <math>\gamma_{+}</math> and <math>\gamma_{-}</math> for the exposed and the unexposed group, respectively. Probability of observing <math>n</math> events in a group of <math>N</math> individuals during the time interval <math>T</math> when the rate of incidence per individual per unit time is <math>\gamma</math> is approximated by the Poisson distribution:

* [[Pharmacoeconomics]]

<math>P(n| N, T, \gamma) = \frac{(\gamma \cdot N \cdot T )^{n} \cdot \exp(-\gamma \cdot N \cdot T) } {n !}</math>

The most likely value of <math>\gamma</math> is then

<math>\gamma \approx \frac{n}{N\cdot T} </math>

Uncertainty of the incidence rate parameter is

<math>\sigma_{\gamma} \approx \frac{\sqrt{n}}{N\cdot T} </math>

For the set of data in the table the values of the incidence rate are:

{| class="wikitable"

|-

!

! Disease +

! Total subjects followed

! Years followed^

! Follow-up time

! Incidence rate (per patient per year)

|-

| Exposure +

| 6054

| 86318

| 13.56^

| 1,170,074

| <math>\gamma_{+} = \frac{6054}{86318\cdot 13.56} = 0.0052( \pm 0.00007) </math>

|-

| Exposure &minus;

| 32

| 516

| 21.84^

| 11,270

| <math>\gamma_{-} = \frac{32}{516 \cdot 21.84} = 0.0028( \pm 0.0005)</math>

|}

^ "Years followed" is a [[weighted average]] of the length of time the patients were followed.

The estimate of the incidence rate with exposure is:

:<math>\gamma_{+} = 0.0052</math>

The estimate of the incidence rate without exposure:

:<math>\gamma_{-} = 0.0028</math>

To determine the [[relative risk]], divide the incidence with exposure by the incidence without exposure:

: <math>\frac{0.0052}{0.0028}= 1.86 </math> [[relative risk]]

To determine [[attributable risk]] subtract incidence without exposure from incidence with exposure:

: <math>\gamma_{+} - \gamma_{-} = 0.0052 - 0.0028 = 0.0024</math> [[attributable risk]] per patient per year

In the context of the example the number needed to harm can be introduced as the estimate of the number of patients needed to observe for one year to detect one patient affected by exposure:

<math>N_{\text{NNH}} ( \gamma_{+} - \gamma_{-}) = 1 </math>

NNH therefore is expressed as the inverse of [[attributable risk]] per patient per year:

: <math>\frac{1}{0.0024} \approx 417 </math> = Number needed to harm

This means that if 417 individuals are exposed to the risk factor for one year, 1 will develop the disease that he of she would not have otherwise.

==Number of exposures needed to harm==

In case there can be more than one exposure in the specific period, the ''number (of patients) needed to harm'' is numerically equal to ''number of exposures needed to harm'' for one person if the risk per exposure isn't significantly altered throughout the specific period or by previous exposure, e.g. when the risk per exposure is very small or the "harm" is a very brief disease that doesn't confer immunity.

==References==

{{reflist}}{{Clinical research studies}}

{{DEFAULTSORT:Number Needed To Harm}}

[[Category:Drug discovery]]