Number needed to harm
Encyclopedia
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. 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
pexposure and pnon-exposure of this endpoint are known, then the NNH is computed as 1/(pexposure-pnon-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 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.
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:
^ "Years followed" is a weighted average of the length of time the patients were followed.
The incidence with exposure is:
The incidence without exposure:
To determine the relative risk
, divide the incidence with exposure by the incidence without exposure:
To determine attributable risk
subtract incidence without exposure from incidence with exposure:
The number needed to harm is the inverse of the attributable risk
, or:
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.)
Epidemiology
Epidemiology is the study of health-event, health-characteristic, or health-determinant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive...
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. It is defined as the inverse of the attributable risk
Attributable risk
In epidemiology, attributable risk is the difference in rate of a condition between an exposed population and an unexposed population.. Attributable risk is mostly calculated in cohort studies, where individuals are assembled on exposure status and followed over a period of time. Investigators...
. Intuitively, the lower the number needed to harm, the worse the risk-factor.
NNH is similar to Number needed to treat
Number needed to treat
The number needed to treat is an epidemiological measure used in assessing the effectiveness of a health-care intervention, typically a treatment with medication. The NNT is the average number of patients who need to be treated to prevent one additional bad outcome...
(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
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
pexposure and pnon-exposure of this endpoint are known, then the NNH is computed as 1/(pexposure-pnon-exposure).
The NNH is an important measure in evidence-based medicine
Evidence-based medicine
Evidence-based medicine or evidence-based practice aims to apply the best available evidence gained from the scientific method to clinical decision making. It seeks to assess the strength of evidence of the risks and benefits of treatments and diagnostic tests...
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
Death
Death is the permanent termination of the biological functions that sustain a living organism. Phenomena which commonly bring about death include old age, predation, malnutrition, disease, and accidents or trauma resulting in terminal injury....
, heart attack
Myocardial infarction
Myocardial infarction or acute myocardial infarction , commonly known as a heart attack, results from the interruption of blood supply to a part of the heart, causing heart cells to die...
), drugs with a low NNH may still be indicated in particular situations if the number needed to treat
Number needed to treat
The number needed to treat is an epidemiological measure used in assessing the effectiveness of a health-care intervention, typically a treatment with medication. The NNT is the average number of patients who need to be treated to prevent one additional bad outcome...
, (the converse for side effect
Adverse effect (medicine)
In medicine, an adverse effect is a harmful and undesired effect resulting from a medication or other intervention such as surgery.An adverse effect may be termed a "side effect", when judged to be secondary to a main or therapeutic effect. If it results from an unsuitable or incorrect dosage or...
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.
Worked example
The following is an example of calculating number needed to harm.In a cohort study
Cohort study
A cohort study or panel study is a form of longitudinal study used in medicine, social science, actuarial science, and ecology. It is an analysis of risk factors and follows a group of people who do not have the disease, and uses correlations to determine the absolute risk of subject contraction...
, 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:
The incidence without exposure:
To determine the relative risk
Relative risk
In statistics and mathematical epidemiology, relative risk is the risk of an event relative to exposure. Relative risk is a ratio of the probability of the event occurring in the exposed group versus a non-exposed group....
, divide the incidence with exposure by the incidence without exposure:
-
relative riskRelative riskIn statistics and mathematical epidemiology, relative risk is the risk of an event relative to exposure. Relative risk is a ratio of the probability of the event occurring in the exposed group versus a non-exposed group....
To determine attributable risk
Attributable risk
In epidemiology, attributable risk is the difference in rate of a condition between an exposed population and an unexposed population.. Attributable risk is mostly calculated in cohort studies, where individuals are assembled on exposure status and followed over a period of time. Investigators...
subtract incidence without exposure from incidence with exposure:
- 0.0043 − 0.0028 = 0.0015 = 0.15% = attributable riskAttributable riskIn epidemiology, attributable risk is the difference in rate of a condition between an exposed population and an unexposed population.. Attributable risk is mostly calculated in cohort studies, where individuals are assembled on exposure status and followed over a period of time. Investigators...
The number needed to harm is the inverse of the attributable risk
Attributable risk
In epidemiology, attributable risk is the difference in rate of a condition between an exposed population and an unexposed population.. Attributable risk is mostly calculated in cohort studies, where individuals are assembled on exposure status and followed over a period of time. Investigators...
, or:
-
= 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.)