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 Relative Risk Reduction Formula
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Relative Risk Reduction Formula (Table of Contents)
What is the Relative Risk Reduction Formula?
Relative risk reduction a measure of risk reduced in the experimental group against the control group where no risk reduction measures have been used. It is otherwise defined as a reduction in the likelihood of a bad outcome event after experimenting with a solution as compared to the control group where no experimental treatment has been provided. The concept of relative risk is more accurate as compared to absolute risk.
In absolute risk formula, the difference between bad outcome between experiment group and control group is taken but absolute risk formula doesn’t measure the base at which the reduction happened which is used in this equation. It is mainly used in the clinical industry in which at first bad outcomes percentage is measured in a control group. Then in another group called the experiment group, new medicine or treatment is given and find out the percentage of a bad outcome. The difference between the bad outcome in the experimental group and the control group is known as relative risk reduction.
The formula for RRR is represented as follows,
 CER = Event Rate in Control group
 EER = Event Rate in Experiment Group
Explanation of Relative Risk Reduction Formula
The formula for RRR is
Relative Risk Reduction formula = (CEREER)/CER
With this equation, if the RRR is coming to be negative that means the risk of the outcome has been increased by the treatment because of EER with greater than CER. On the other side if RRR is positive that means the risk of outcome has been reduced by the treatment and this treatment can be further checked and applied for approval.
Examples of Relative Risk Reduction Formula (with Excel Template)
Let’s see some simple to advanced examples of Relative Risk Reduction Formula to understand it better.
Example #1
Let’s say Event rate in Control Group is 50% and the event rate in the experiment group is 40%.
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Below is given data for calculation of Relative Risk Reduction.
RRR = (5040)/50
RRR = 20%
Example #2
Let’s say scientists have found a new cure for cancer. They want to experiment with a certain group of patients and want to find out the result of the operations. For the experiment, they have taken 2 samples of 100 patients each. In one group of patients known as the control group, treatment is provided as usual. With other groups of patients known as the Experiment group, this new treatment is being used. Now patients are observed and were looking for a bad outcome. Let’s say with the control group in which new treatment has not been provided, the death rate of patients is 70%. But with a new treatment, the death rate got reduced to 40%. By this information, we will find out RRR.
Below is given data for calculation of Relative Risk Reduction.
RRR calculation = (7040)/70
RRR = 30/70
RRR will be –
RRR = 42.86%
Example #3
Let’s say Pfizer a leading pharma company in the US has found a treatment by which chances of moving of HIV virus from mother to child would get reduced for a newborn baby. They want to experiment with a certain group of patients and want to find out the result of the operations. For the experiment, they have taken 2 samples of 100 patients each. In one group of patients known as the control group, treatment is provided as usual. With other groups of patients known as the Experiment group, this new treatment is being used. Now patients are observed and were looking for a bad outcome. Let’s say with the control group in which new treatment has not been provided, the transfer rate of the HIV virus is 90%. But with the treatment chances of transfer reduced to 50%. With this information, we will find out RRR.
Following is data for calculation of Relative Risk Reduction of pharma company
Relative Risk Reduction Calculation = (9050)/90
RRR = 40/90
RRR will be –
RRR = 44.44%
Calculator
You can use the following RRR Formula Calculator.
CER  
EER  
Relative Risk Reduction Formula =  
Relative Risk Reduction Formula = 


Relevance and Uses
Relative Risk Reduction is widely used in the medical industry to test the significance of new drug on the group of patients. It is used to check whether actually the medicine is effective and with how much percentage it can reduce the risk of bad outcomes? On the other hand, absolute risk reduction only provides the difference between the bad outcome of the Control group and Experiment group. So absolute risk reduction does not provide the info that at what base the risk reduction happened. But the RRR equation provides that information also. Because it provides the percentage change.
So RRR formula can be used to compare against different populations with different baseline risks.
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