Risk Ratio

What is the Risk Ratio?

Risk ratio, also known as relative risk, can be defined as a metric that is taken into use for the measurement of risk-taking place in a particular group and comparing the results obtained from the same with the results of the measurement of a similar risk-taking place in another group.


This can be said to be a ratio of the probabilities of risk in one group compared to the possibilities of an occurrence of risk in another group. It is commonly taken into use to present the outcomes of various groups. These are also termed as a relative risk.


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Source: Risk Ratio (wallstreetmojo.com)

Risk Ratio Formula

The formula is as follows:

Risk Ratio Formula = Incidence in Exposed / Incidence in Unexposed


Risk Ratio = (a / (a + b)) / (c / (c + d)


Risk Ratio = CIe / CIu


  • CI = Cumulative Incidence,
  • e = exposed group, and
  • u = unexposed group,


Risk Ratio = Risk of Event in A Group / Risk of Event in B Group


(Se / Ne) / (SC / Nc)


  • e = experimental group (A group), and
  • c = control group (B group).

How to Calculate the Risk Ratio?

  • From the above formula, it is clear that the calculation of risk ratio takes the incidence or risk of the event taking place in one group (experimental group) and draws a comparison with the incidence or risk of the event taking place in another group (control group).
  • This is performed by examining two variables. One of the variables shall be used for measuring the incidence of an event (exposed vs. Unexposed), and the second variable shall be used for measuring both the groups (Group A vs. Group B).
  • It will then require the analyst to divide an exposed event for group A or the experimental group by the incidence of an unexposed event for group B or control group. This is calculated by taking percentages into use.
  • When the values equal to 0, it means that there was not even a single case falling in group A had the incidence taking place whereas the “x” number of case/s in group B had the incidence taking place. When the values equal to 1, it means that the results are neutral. In other words, the probability of an event taking place in one group shall be the same for the possibility of an event taking place in different groups.


You can download this Risk Ratio Excel Template here – Risk Ratio Excel Template

Example #1

RR, in this case, can be determined by using the formula-

Had Sports SurgeryYesNo
Any Post-Surgery Infection (A)8125
No Post-Surgery Infection (B)279
  • R.R = CIE / CIu
  • = 6.02% / 2.47%
Risk Ratio Example 1-2
  • R.R. = 2.436

Example #2

Had Sports SurgeryYesNo
Cancer (A)93
No Signs of Cancer (B)12680

RR, in this case, can be determined by using the formula-

  • R.R = CIE / CIu
  • = 6.67% / 3.61%
Example 2-2
  • R.R. = 1.844


  1. This is as important as the calculation of the same. The results of the risk ratio can be equal to zero or one or greater or lower than 1. When the results are more significant than zero, it signifies merely that none of the incidences in the experimental group or group A had the probability of the event taking place whereas ‘x’ no. of incidences in the control group or group B had the likelihood of the event taking place.
  2. When the results are equal to one, then it is regarded as neutral, or in other words, the incidences in an experimental group are the same as the incidences in a control group.
  3. When the result is more significant than one, it means that the risk in the exposed group is greater than the risk in the unexposed group. Similarly, when the result is lower than one, then it signifies that the risk in the exposed group is lower than the risk in the unexposed group.


This is also regarded as a relative risk. These methods are commonly taken into use for drawing useful comparisons between two groups. The comparisons between the two groups are performed based on the likelihood or probability of an event that can take place in these groups.

One of the two groups is regarded as an experimental group, whereas the other is considered the control group. It should not be deemed an inferential statistic since it is a descriptive statistic, and it does not evaluate the significance of a particular statistic.

This can be determined using the formula stated below:

Risk Ratio = Incidence in Experimental Group / Incidence in the Control Group.

A risk ratio equals to one means that the outcomes of both the groups are identical. On the other hand, a rate higher or lower than one would indicate the underlying factor that is responsible for increasing or decreasing the risks in either or both of the groups.

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