# NNT Calculator

Created by Luis Fernando
Last updated: Jul 02, 2022

If you were searching for how to calculate NNT, this calculator is what you need! Apart from calculating the number needed to treat, this tool calculates the ARR (absolute risk reduction).

NNT measures the effectiveness of a health intervention. This calculator can find it for you in the blink of an eye, but if you want to know the NNT formula behind it, read on. Be sure to check the 20/20 vision calculator as well that focuses on your eyesight!

## How to use this NNT calculator

1. Select how your outcome is presented:
• Some scientists provide data as a percentage - i.e., group A had a 15% response to the treatment.
• Other times, they provide them in terms of exposure data or patient-years - i.e., the study lasted six years, and seven patients survived in group A, while only two patients could do it in group B.
2. Enter the data of both the control and the experimental group.
3. If you click on the "advanced mode" of the NNT calculator, the ARR value will show up.

Now that you know how to calculate NNT with the calculator let's see how to do it with the formula.

## ARR and NNT formula

### Formula in terms of percentage.

First, we must understand the risk difference (RD) concept. RD refers to the difference between the risk of an outcome between an experimental (Iₑ) and a control group (I꜀).

RD = Iₑ - I꜀

In the previous formula, Iₑ is the incidence rate in the control group, while Ic is the incidence rate in the experimental group. The incidence rate is a measure of the probability of occurrence of a given medical condition.

Risk difference can be a negative number, although, depending on the response to the risk, scientists can invert the terms to get a positive value:

• If exposure causes a risk increase (for example, by exposure to a virus or radiation), we use the term absolute risk increase (ARI)
ARI = Iₑ - I꜀

• If exposure causes a risk reduction (for example, by starting a pharmacological treatment or a healthy lifestyle), we use the term absolute risk reduction (ARR); the formula is:
ARR = I꜀ - Iₑ

Now that we know the absolute risk reduction formula, we're ready for the formula to calculate the number needed to treat (NNT), which is just is just the inverse of the ARR:

 NNT = 1/(I꜀ - Iₑ)

### Formula in terms of patient-years.

In this case, we don't use incidence rates, but absolute values of numbers of events. The NNT and absolute risk reduction formula, in this case, are:

$\ ARR = e^{-\frac{\text{Experimental\ group}}{\text{Patient-years}}} - e^{-\frac{\text{Control\ group}}{\text{Patient-years}}} \\\ \\\ NNT = 1/ARR$

where control group and patient-years refer to the number of events during a given time for each group. ARR grows exponentially with the control group and decreases exponentially with the experimental group, while the opposite occurs for NNT.

Patient-years is the product of the number of patients participating in the study by the duration of the study. For example, if 150 patients participated in the study for five years, the study would have involved 750 patient-years (150 * 5).

Luis Fernando
Percentage
Control group
%
Experimental group
%
NNT
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