Number needed to harm

The number needed to harm (NNH) is an epidemiological measure that indicates how many patients need to be exposed to a risk-factor over a specific period to cause harm in one patient that would not otherwise have been harmed.^[1] It is defined as the inverse of the attributable risk. Intuitively, the lower the number needed to harm, the worse the risk-factor.

NNH is similar to Number needed to treat (NNT), where NNT usually refers to a therapeutic intervention 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 confounders. A defined endpoint has to be specified. If the probabilities p_exposure and p_non-exposure of this endpoint are known, then the NNH is computed as 1/(p_exposure-p_non-exposure).

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 number needed to treat, (the converse for side effects, 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.^[2]

Worked example

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

In a cohort study, individuals with exposure to a risk factor (Exposure +) are followed for a certain number of years to see if they develop a certain disease or outcome (Disease +). A control group of individuals who are not exposed to the risk factor (Exposure −) 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:

	Disease +	Total subjects followed	Years followed^	Follow-up time	Incidence
Exposure +	5054	86318	13.56^	1,170,074	0.0043
Exposure −	32	516	21.84^	11,270	0.0028

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

The incidence with exposure is:

$\frac{5054}{1,170,074} = 0.0043$

The incidence without exposure:

$\frac{32}{11,270} = 0.0028$

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

$\frac{0.0043}{0.0028}= 1.54 = {}$ relative risk

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

0.0043 − 0.0028 = 0.0015 = 0.15% = attributable risk

The number needed to harm is the inverse of the attributable risk, or:

$\frac{1}{0.0015} = 667$ = Number needed to harm

This means that if 667 individuals are exposed to the risk factor, 1 will develop the disease that would not have otherwise.

Note that these calculations can be affected enormously by roundoff error. (If no roundoff is used in the intermediate calculations above, the final figure for the NNH is 676.)

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

^ Glossary of Terms
^ Hutton JL (2010). "Misleading Statistics: The Problems Surrounding Number Needed to Treat and Number Needed to Harm". Pharm Med 24 (3): 145–149. http://adisonline.com/pharmaceuticalmedicine/Fulltext/2010/24030/Misleading_Statistics__The_Problems_Surrounding.3.aspx.