## Prerequisites

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

### Related videos

## 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, and help relate an effect size difference back to real-world clinical relevance.

### Number needed to treat

The NNT signifies how many patients 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 (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 difference (ARD), and absolute risk excess (ARE)

All terms represent the absolute value of the difference between the proportion (expressed as a percent, fraction, or incidence) of patients in the control group (Pc) who had the outcome of interest and the proportion of patients 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 (RRR), which tends to overemphasize the benefit.
- RRR = (Pe – Pc)/c.
- 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 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 in the study?
- What is the comparator? (e.g., no treatment? placebo? 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?

### 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 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 are treated with the new treatment, one additional person would be harmed compared to patients 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 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, and not as the actual number of subjects.

Outcome | Treated group | Control group |
---|---|---|

Positive | a | b |

Negative | c | d |

Total | a + c | b + d |

NNT: number needed to treat

NNH: number needed to harm

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 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 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 of BA. Data from the study are shown in the table below:

Outcome | Exposed group | Control group |
---|---|---|

BA present | 18 | 7 |

BA not present | 32 | 43 |

Total | 50 | 50 |

### Question 1

**What is the NNH?**

**Answer: **NNH = 1/absolute 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 in the study cited in Question 1?**

**Answer: **The relative risk increase = (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

- 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
- Clinical Tools and calculators for medical professionals—ClinCalc. Retrieved March 19, 2021, from https://clincalc.com/
- Power/sample size calculator. Retrieved March 20, 2021, from https://www.stat.ubc.ca/~rollin/stats/ssize/n2.html
- Interactive statistical calculation pages. Retrieved March 20, 2021, from https://statpages.info/#Power
- Statistical power calculator using average values. SPH Analytics. Retrieved March 20, 2021, from https://www.sphanalytics.com/statistical-power-calculator-using-average-values/
- 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
- Bland, M. (2015). An Introduction to Medical Statistics. 4th ed., pp. 295–304.
- Ellis, P.D. (2010). The Essential Guide to Effect Sizes. Statistical Power, Meta-Analysis, and the Interpretation of Research Results, pp. 46–86.
- Walters, S.J., Campbell, M.J., Machin, D. (2020). Medical Statistics, A Textbook for the Health Sciences. 5th ed, pp. 40–48, 99–133.
- 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
- Smith, M.K. (2012). Common mistakes involving power. Retrieved March 21, 2021, from https://web.ma.utexas.edu/users/mks/statmistakes/PowerMistakes.html
- 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.
- 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
- 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