# Relative Risk Reduction Formula

Last Updated :

21 Aug, 2024

Blog Author :

Edited by :

Ashish Kumar Srivastav

Reviewed by :

Dheeraj Vaidya, CFA, FRM

Table Of Contents

## Formula to Calculate Relative Risk Reduction

Relative risk reduction is a relative reduction in the overall business risks due to adverse circumstances of an entity which can be calculated by subtracting the Experimental event rate (EER) from the control event rate (CER) and dividing the resultant with the control event rate (ER).

Relative risk reduction measures risk reduction 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 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 the absolute risk formula, the difference between the lousy outcome between the experimental group and the control group is taken. Still, the total risk formula doesn’t measure the base at which the reduction happened in this formula. It is mainly used in the clinical industry in which, at first, a bad outcome percentage is calculated in a control group. Then in another group called the experiment group, new medicine or treatment is given and determines the rate of a bad outcome. The difference between the wrong result in the experimental group and the control group is relative risk reduction.

**Relative Risk Reduction = (CER-EER)/CER**

- CER = Event Rate in Control group
- EER = Event Rate in Experiment Group

With this formula, if the RRR is coming to be negative, that means the treatment has increased the risk of the outcome because of EER with greater than CER. On the other hand, if RRR is positive, the risk of the product has been reduced by the treatment, and this treatment can be further checked and applied for approval.

##### Table of contents

- The relative risk reduction formula measures the relative reduction in total business risks for an entity due to adverse conditions.
- It is computed by subtracting the control event rate (CER) from the experimental event rate (EER) and then dividing the result by the control event rate (CER).
- The calculation of relative risk reduction compares the risk reduction observed in the experimental group to the absence of any risk reduction measures in the control group.
- The relative risk reduction formula allows researchers and analysts to assess the impact and effectiveness of risk reduction strategies and interventions.

### Examples

#### Example #1

The event rate in the Control Group is 50%, and the event rate in the experiment group is 40%.

Below is given data for the calculation of Relative Risk Reduction.

RRR = (50-40)/50

**RRR = 20%**

#### Example #2

Let’s say scientists have found a new cure for cancer. They want to experiment with a particular group of patients and find out the result of the operations. For the experiment, they have taken two 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 Experimental group, this new treatment is being used. Now patients are observed and are looking for a bad outcome. With the control group in which further treatment has not been provided, the death rate of patients is 70%. But with a new treatment, the death rate got reduced to 40%. With this information, we will find out RRR.

Below is given data for the calculation of Relative Risk Reduction.

RRR calculation = (70-40)/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 HIV from mother to child would be reduced for a newborn baby. They want to experiment with a particular group of patients and find out the result of the operations. For the experiment, they have taken two 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 Experimental group, this new treatment is being used. Now patients are observed and are looking for a bad outcome. With the control group in which further treatment has not been provided, the transfer rate of HIV is 90%. But with the treatment, chances of transfer are reduced to 50%. With this information, we will find out RRR.

The following is data for the calculation of the Relative Risk Reduction of the pharma company.

Relative Risk Reduction Calculation = (90-50)/90

RRR = 40/90

**RRR will be - **

**RRR = 44.44%**

### Relative Risk Reduction Calculator

You can use the following Relative Risk Reduction Calculator.

### Relevance and Uses

The relative Risk Reduction formula is widely used in the medical industry to test the significance of new drugs on patients. It is used to check whether the medicine is useful, 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 harmful effect of the Control group and the Experiment group. So total risk reduction does not provide the info that at what base the risk reduction happened. But the relative risk reduction formula provides that information also because it allows for the percentage change.

So the relative risk reduction formula can be used to compare against different populations with different baseline risks.

### Frequently Asked Questions (FAQs)

**1. What are the limitations of the relative risk reduction technique?**The relative risk reduction technique has certain limitations. One limitation is that it only measures the proportionate reduction in risk between two groups and does not provide information about the absolute risk or baseline risk. Additionally, relative risk reduction does not consider the study's time frame or the incidence rate of the event being studied.

**2. What is relative risk reduction vs. hazard ratio?**RRR measures the relative reduction in risk between two groups, typically a treatment group and a control group, and is expressed as a percentage. On the other hand, the hazard ratio compares the hazard rates or instantaneous risks between two groups over time, providing an estimate of the relative risk of an event occurring.

**3. What is relative risk reduction vs. attributable risk?**Relative risk reduction (RRR) and attributable risk (AR) are measures used to evaluate the effectiveness of interventions or treatments. RRR quantifies the proportionate reduction in risk between two groups. Attributable risk, on the other hand, measures the absolute difference in risk between two groups, representing the proportion of disease or outcome that can be attributed to the exposure or intervention.

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