# Number Needed to Treat

### Study Outcome

#### Group 2 IncidenceEvent Rate

###### (Experimental Group)

Events per

Press 'Calculate' to view calculation results.

Number Needed to Treat (NNT) represents the number of patients over a given time period that one would need to treat to achieve one additional study endpoint.

As an example, in the PROSEVA trial of patients with severe ARDS, prone positioning decreased 28-day all-cause mortality compared to supine positioning (16% vs. 32.8%) with a NNT of 6. In other words, 6 patients with severe ARDS would need to be treated with prone positioning (and not supine positioning) in order for one additional patient to not die within a 28-day period.

#### NNT Calculation 1

When a study outcome is expressed as a percent, the number needed to treat (NNT) is the inverse of the absolute risk reduction (ARR) expressed as a decimal. The example below compares an event rate of 26% versus 16%:

$$\\ ARR = (Control\;event\;rate) - (Experimental\;event\;rate) \\ ARR = 0.26 - 0.16 = 0.1 \\ NNT = 1/ARR \\ NNT = 1/0.1 = 10\;patients$$

Similarly, when a study outcome is based on time of exposure (patient-years), the NNT is calculated based on cumulative event proportions. The example below compares 12 events per 1000 patient-years versus 4 events per 1000 patient-years:2

$$\\ R_0 = 1-e^{(-Control\;Events/Time)} = 1-e^{(-12/1000)} \\ R_1 = 1-e^{(-Experimental\;Events/Time)} = 1-e^{(-4/1000)} \\ NNT = 1/(R_0-R_1) \\ NNT = 1/(0.0119 - 0.00399) = 126\;patients$$

If a time-based study outcome is relatively rare, the following shorter equation may be used for person-time data:2

$$\\ ARR = (Control\;event\;rate) - (Experimental\;event\;rate) \\ ARR = 12 - 4 = 8 \\ NNT = (Patient\;Years) / ARR \\ NNT = 1000/8 = 125\;patients$$

#### Number Needed to Harm (NNH)

When an experimental treatment is detrimental, the term 'number needed to harm' (NNH) is often used. The equations and approach are identical to those described above, except that NNH will have a negative absolute risk reduction (which is ignored when expressing NNH).

#### Weaknesses of the NNT Metric3,2

The idea of NNT provides clinicians with a method of explaining the relative benefit or harm of a given therapy for a patient. Because of its simplicity, NNT has the following weaknesses:

• It is usually described as a point estimate instead of a confidence interval of the observed therapeutic effect. This has led some authors to report NNT with a corresponding confidence interval (eg, NNT 5 (95% CI 3 to 9))
• As with other descriptions of benefit, NNT does not account for a patient's baseline risk. If a patient's individual risk is higher or lower than that studied in a trial, his or her NNT will be lower or higher, respectively.
• When describing NNT, the comparator is an essential component. The NNT of a given treatment will be very different when describing the value versus placebo instead of another active therapy.
• The time frame of a given study is important and the benefit of a treatment is usually not linear over time. For example, if a treatment was conducted over a mean of 4 years, its NNT should be expressed with the same time component (eg, 12 patients need to be treated over about 4 years...).

1. Wen L, Badgett R, Cornell J. Number needed to treat: a descriptor for weighing therapeutic options. Am J Health Syst Pharm. 2005;62(19):2031-6. PMID 16174840.
2. Stang A, Poole C, Bender R. Common problems related to the use of number needed to treat. J Clin Epidemiol. 2010;63(8):820-5. PMID 19880287.
3. McAlister FA. The "number needed to treat" turns 20--and continues to be used and misused. CMAJ. 2008;179(6):549-53. PMID 18779528.