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When computing results for a clinical trial, researchers compare the number of people who experience the studied outcome against those who avoided it in both arms of the study. They often set up a table like the following to keep track of the results. For example, if the outcome is death at 12 months, the table would look like this:
The risk of the studied outcome is the number of people who experienced the outcome as a percentage of all people in that group. For those exposed to the the therapy, the risk of death at 12 months is 300/(300+700) or 30%. The risk of death at 12 months of those not exposed to the therapy is 800/(800+200) or 80%.
Relative Risk Reduction
The Relative Risk Reduction (RRR) achieved by a particular therapy is the difference between the two risks as a percentage of the risk of those not exposed to the therapy. In the example above, the relative risk reduction would be (80%-30%)/80% or 62.5%.
Absolute Risk Reduction
The Absolute Risk Reduction (ARR) achieved by a particular therapy is simply the difference in the two risks. In the above example, the absolute risk reduction is 80%-30% or 50%.
Relative vs. Absolute Risk Reducation
Because it is presented as a percentage of the control group, Relative Risk Reduction does not take into account the size of the initial risk and the actual reduction. In the example below, while the actual reducations vary greatly, the Relative Risk Reduction remains the same.
Although the Absolute Risk Reduction is a more accurate report of the effect of the intervention, it's harder for people to understand the distinction between the two. So EBM pratctitioners came up with another statistic to more clearly represent what the statistics mean.
Number Needed to Treat
The Number Needed to Treat (NNT) is the reciprocal of the Absolute Risk Reduction. If the ARR is expressed as a decimal, the Number Needed to Treat is 1/ARR; if the ARR is expressed as a percentage, the Number Needed to Treat is 100/ARR. In the above example, the Number Needed to Treat is 100%/50% or 2. The Number Needed to Treat tells how many people you need to treat in order to see the desired outcome in one additional patient . In this example, you would need to treat 2 patients to prevent one additional patient from dying at 12 months. The NNT gives you a clear number to use to balance benefits against risks. If you only need to treat 2 patients to see a benefit, you may feel comfortable ignoring extremely mild side effects. However, if you need to treat 2000 patients to see a benefit with a drug that has very severe side effects, you may not feel comfortable recommending this treatment.