# Number Needed to Treat

The number needed to treat (NNT) is the number of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship that are needed to treat to prevent 1 additional adverse outcome (e.g., stroke, death). For example, if a drug has an NNT of 10, it means 10 people must be treated with the drug to prevent 1 additional adverse outcome. The NNT is the inverse of the absolute risk reduction Absolute risk reduction Measures of Risk (ARR), which is equal to the rate of adverse outcomes occurring in the control group minus the number of adverse outcomes in the experimental group.

Last updated: Aug 11, 2022

Editorial responsibility: Stanley Oiseth, Lindsay Jones, Evelin Maza

## Prerequisites

In order to comprehend the concept of number needed to treat, some previous knowledge about descriptive and inferential statistics is recommended.

## Definition

The number needed to treat (NNT), also called the number needed to benefit (NNTB); and its analog, the number needed to harm (NNH), are simply other measures of effect sizes, like Cohen’s d Cohen’s d Cohen’s d is the most common (but imperfect) method to calculate ES. Cohen’s d = the estimated difference in the means/(pooled estimated standard deviations). Statistical Power, and help relate an effect size Effect size Effect size is the standardized mean difference between 2 groups, which is exactly equivalent to the “Z-score” of a standard normal distribution. Statistical Power difference back to real-world clinical relevance.

### Number needed to treat

The NNT signifies how many patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship would need to be treated to get 1 additional patient better, who would not have otherwise gotten better without that particular treatment.

• The inverse of the absolute risk reduction Absolute risk reduction Measures of Risk (ARR) = 1/ARR
• NNT is a number between 1 and infinity:
• A lower number indicates more effective treatment.
• Fractions are rounded up to the next whole number.
• A perfect NNT would be 1, meaning that for every patient treated, 1 got better in the trial, who would not have otherwise without that specific treatment.

### Absolute risk reduction Absolute risk reduction Measures of Risk, absolute risk Absolute risk The AR is the risk of developing a disease or condition after an exposure. Measures of Risk difference (ARD), and absolute risk Absolute risk The AR is the risk of developing a disease or condition after an exposure. Measures of Risk excess (ARE)

All terms represent the absolute value of the difference between the proportion (expressed as a percent, fraction, or incidence Incidence The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from prevalence, which refers to all cases in the population at a given time. Measures of Disease Frequency) of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship in the control group (Pc) who had the outcome of interest and the proportion of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship in the experimental group (Pe) with that the outcome of interest:

$${ARR = ARD = ARE = \left | P_{c} – P_{e} \right |}$$

## Characteristics and Interpretation

### Characteristics

• Must be interpreted in context: An isolated NNT point estimate has little value, although approximately 50% of clinical studies do not provide the necessary contextual information.
• NNT uses the ARR and not the relative risk reduction Relative risk reduction Measures of Risk ( RRR ), which tends to overemphasize the benefit.
• RRR = (Pe – Pc)/Pc.
• For example, if the initial risk were 0.2% and drug X lowered this risk to 0.1%, the RRR would still be 50%, but the ARR would be only 0.1%, which is not much of a difference from the baseline.
• As the RRR is directly correlated with the ARR, the NNT is also inversely correlated with the RRR .
• The NNT tells you how many patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship would benefit, but does not tell you how much they may benefit. The answers to the following questions should be provided with the NNT in order to fully interpret it:
• What is the baseline risk of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship in the study?
• What is the comparator? (e.g., no treatment? placebo Placebo Any dummy medication or treatment. Although placebos originally were medicinal preparations having no specific pharmacological activity against a targeted condition, the concept has been extended to include treatments or procedures, especially those administered to control groups in clinical trials in order to provide baseline measurements for the experimental protocol. Epidemiological Studies? another therapy?)
• What is the outcome? (e.g., complete cure? 30% improvement?)
• How long does the study last? (must be included with the NNT)
• What is the confidence interval Confidence interval A confidence interval is the probability that your result falls between a defined range of values. Statistical Tests and Data Representation?

### Interpretation

• The lower the NNT, the better; the larger the NNT, the fewer people will be helped.
• Treatment interventions that have an NNT in the single or low double digits are generally considered effective for treating symptomatic conditions.
• For outcomes with high clinical significance, such as preventing death, an NNT in the lower 100s may also be considered useful.
• For preventive therapies, NNTs can also be high.

## Number Needed to Harm

The NNH is the additional number of individuals who need to be exposed to risk (harmful exposure or treatment) to have 1 extra person develop the disease compared to that in the unexposed group.

• NNH is the inverse of ARE (1/ARE).
• The relationship Relationship A connection, association, or involvement between 2 or more parties. Clinician–Patient Relationship between NNH and NNT: A negative NNT indicates that the treatment has a harmful effect. For example, an NNT of −10 indicates that if 10 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are treated with the new treatment, one additional person would be harmed compared to patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship receiving the standard treatment, i.e., the NNH = 10.
• LIke NNT, the NNH must be interpreted in context.

## Calculating NNT and NNH

### The basis for calculating NNT and NNH

A 2 x 2 contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk uses a binary outcome and 2 groups of subjects to show the basis for calculating NNT and NNH. Each result must be expressed as a proportion, percent, or incidence Incidence The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from prevalence, which refers to all cases in the population at a given time. Measures of Disease Frequency, and not as the actual number of subjects.

If the following is true, the difference in proportions is P treated – P control.

• P treated = the proportion of subjects with a positive outcome in the treated group
• P treated = a/(a + b)
• P control = the proportion of subjects with a positive outcome in the control group
• P control = b/(b + d)

The absolute risk Absolute risk The AR is the risk of developing a disease or condition after an exposure. Measures of Risk difference (ARD) is equal to the ARR, which is calculated as the absolute value of the difference between P treated and P control.

$${ARD = ARR = \left | P_{treated} – P_{control} \right |}$$

So, the NNT can be calculated as:

$${NTT = \frac{1}{\left | P_{treated} – P_{control} \right |}}$$

If the treated or exposed group has a worse outcome than the control, then the ARR is called ARE. In that case, the NNT is called the number needed to harm (NNH). In both cases, the calculation is the same (NNH = 1/ARD).

## Practice Questions

A randomized clinical trial studied the effect of childhood exposure to 2nd-hand smoke on the incidence Incidence The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from prevalence, which refers to all cases in the population at a given time. Measures of Disease Frequency of bronchogenic adenocarcinoma (BA). The study included 100 subjects (50 exposed to childhood 2nd-hand smoke and 50 healthy controls with no childhood exposure) and involved monitoring the lifetime incidence Incidence The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from prevalence, which refers to all cases in the population at a given time. Measures of Disease Frequency of BA. Data from the study are shown in the table below:

### Question 1

What is the NNH?

Answer: NNH = 1/ absolute risk Absolute risk The AR is the risk of developing a disease or condition after an exposure. Measures of Risk difference (called “ARE” when NNH is involved). ARE = Pe – Pc = 18/50 – 7/50 = 0.22. NNH = 1/0.22 = 4.45 ⇾ 5, which means that 5 individuals need to be exposed to childhood 2nd-hand smoke to have 1 extra person develop BA compared to that in the unexposed group.

### Question 2

What is the relative risk increase Relative risk increase Measures of Risk in the study cited in Question 1?

Answer: The relative risk increase Relative risk increase Measures of Risk = (Pe – Pc)/Pc = (18/50 – 7/50)/7/50 = 1.57, which means that individuals exposed to childhood 2nd-hand smoke are 1.57 times more likely to develop BA after exposure to 2nd-hand smoke than those who were not exposed.

## References

1. Peirce, C.S. (1878). Illustrations of the Logic of Science VI. Popular Science Monthly, vol. 13. Popular Science Monthly. Retrieved March 1, 2021, from https://en.wikisource.org/w/index.php?oldid=3592335
2. Clinical Tools and calculators for medical professionals—ClinCalc. Retrieved March 19, 2021, from https://clincalc.com/
3. Power/sample size calculator. Retrieved March 20, 2021, from https://www.stat.ubc.ca/~rollin/stats/ssize/n2.html
4. Interactive statistical calculation pages. Retrieved March 20, 2021, from https://statpages.info/#Power
5. Statistical power calculator using average values. SPH Analytics. Retrieved March 20, 2021, from https://www.sphanalytics.com/statistical-power-calculator-using-average-values/
6. Otte, W.M., Tijdink, J.K., Weerheim, P.L., Lamberink, H.J., Vinkers, C.H. (2018). Adequate statistical power in clinical trials is associated with the combination of a male first author and a female last author. https://doi.org/10.7554/eLife.34412
7. Bland, M. (2015). An Introduction to Medical Statistics. 4th ed., pp. 295–304.
8. Ellis, P.D. (2010). The Essential Guide to Effect Sizes. Statistical Power, Meta-Analysis, and the Interpretation of Research Results, pp. 46–86.
9. Walters, S.J., Campbell, M.J., Machin, D. (2020). Medical Statistics, A Textbook for the Health Sciences. 5th ed, pp. 40–48, 99–133.
10. Citrome, L., Ketter, T.A. (2013). When does a difference make a difference? Interpretation of number needed to treat, number needed to harm, and likelihood to be helped or harmed. International Journal of Clinical Practice, 67(5), 407–411. https://doi.org/https://doi.org/10.1111/ijcp.12142
11. Smith, M.K. (2012). Common mistakes involving power. Retrieved March 21, 2021, from https://web.ma.utexas.edu/users/mks/statmistakes/PowerMistakes.html
12. Ioannidis, J.P., Greenland, S., Hlatky, M.A., et al. (2014). Increasing value and reducing waste in research design, conduct, and analysis. Lancet, 11;383(9912), 166–175.
13. Coe, R. (2002). It’s the effect size, stupid: What effect size is and why it is important. https://www.leeds.ac.uk/educol/documents/00002182.htm
14. Allen, J.C. (2011). Sample size calculation for two independent groups: A useful rule of thumb. Proceedings of Singapore Healthcare, 20(2), 138–140. https://doi.org/10.1177/201010581102000213