Statistics: How to Calculate Absolute and Relative Risk

You will often encounter ratio calculations in medical literature. It is a calculation of probability. Ratio calculations include absolute risk, absolute risk reduction, absolute risk increase, number needed to treat and relative risk.

Risk calculations are especially useful in cohort studies and randomized controlled trials where selected patients are observed over period of time to determine if they will experience a particular outcome. In other words, the probability that they will experience a particular outcome. In other words, their risk of experiencing a particular outcome.

As a practitioner, you may be tasked to perform ratio calculations for your own publications. Most often you will be assessing the ratio calculations of other authors as a way of validating their results. We should make some effort to evaluate literature for use of appropriate data points and the corresponding statistical test. If the data points and/or test are not appropriate no valid information can be derived from a study.

The type of data that is needed for calculation of relative risk is very important. In the unit Statistics: Ratio Data we discussed several important foundational concepts for understanding calculations of risk. I highly recommend reviewing this unit.

Ratio calculations, including relative risk, requires the use of ratio data. Ratio data has 4 properties.

Once we validate data points as ratio data we can proceed to the calculation of risk.

Contingency Tables

To perform ratio calculations we set up contingency tables. These tables organize the observed and non-observed results for each group of patients in a way that allows us to calculate probability.

We have 2 study groups (exposed/intervention) each with one of 2 possible outcomes or results. These 4 values will be placed in their respective position on the contingency table. We will use the following letters to represent each value.

Using our contingency table with letters (ABCD) to represent the outcome for each of the 4 groups, we will set up the equation for calculating absolute risk.

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Absolute Risk

Absolute risk is the probability of an event occurring within ONE group i.e. either the exposed group or non-exposed group. Terminology will start to become very important here as we differentiate between absolute risk and relative risk. Teasing out these differences will take you far in understanding statistics. With absolute risk we are looking at ONE group at a time.

Let us consider our exposure to be: daily exercise for 1 month and our outcome to be: atleast 1 pound weight lose.

Absolute Risk Scenario 1: Exposed

Of all the people who exercised daily for one month what is the probability that they will lose atleast 1 pound (Group A: exposed + outcome). This is the absolute risk for the exposed group (A+B)

Absolute Risk Scenario 2:

Of all the people who did NOT exercise daily for one month what is the probability that they will lose atleast 1 pound (Group C: not exposed + outcome). This is the absolute risk for the non-exposed group (C+D).

Again, when we think about absolute risk, we are considering the probability of a specified outcome in the exposed and non exposed group individually.

Absolute Risk Difference

Once we know the absolute risk for each group there are many other calculations that can be derived from those values.

Absolute risk difference in simply the numerical difference between the absolute risk in each group. This is also sometimes referred to as absolute risk reduction or absolute risk increase (reduction or increase being the two differences that can occur).

From this simple calculation of difference we can derive a very important value: the number needed to treat.

Number Needed to Treat

The number needed to treat (NNT) is the number of persons that need to be exposed in a given time period to see a specified positive outcome or prevent a negative outcome. NNT is calculated as follows.

The number needed to treat give us a sense of the impact an exposure/treatment will have. It is valuable when considering if the cost or complexity of an intervention justifies the outcome we are seeking. It is expressed as the nearest whole number.

Relative Risk

Using the absolute risk values from the exposed group and the non exposed group we are also able to calculate the relative risk. Relative risk is also referred to as risk ratio. The question we are attempting to answer with relative risk: is there a difference in risk between persons exposed and not exposed?

Relative risk compares the risk between the 2 groups. It is the incidence of an event or outcome in the exposed group divided by the incidence in the non-exposed group. Compare this to absolute risk which considers one group at a time. We calculate relative risk by dividing the absolute risk of the treatment group by the absolute risk on the non-exposed group.

When we compare 2 groups using their relative risk we are asking: is the probability of an event occurring greater in the exposed group or the non exposed group?

If the probability of risk is the same in both groups, the absolute risk will be the same for both groups. Any non-zero number divided by itself will have a value of 1. This is why 1 is a critical value in the assessment of ratios. A value of one is the point of significance, it suggests that there is no difference between the exposed and the non exposed groups. Any deviation from one suggests a difference exist between the groups.

Because the absolute risk in the treatment group is the numerator in the calculation of relative risk, a value less than 1 implies there is less risk of outcome in the treatment group. If the relative risk is greater than 1 is implies there is a lower risk out outcome in the non-exposed group.

Calculations

Let us put all of these calculations into an example.

• Absolute Risk Exposed: There is a 45% chance of outcome being observed in the exposed group
• Absolute Risk Non-Exposed: There is a 29% chance of outcome being observed in the non-exposed group
• Absolute Risk Difference: There is 16% increase in risk of occurrence in the exposed group
• Number Needed to Treat: Atleast 6 patients need to be exposed for an outcome to be observed
• Relative Risk: 60% more likely to observe outcome in exposed group relative to non-exposed group.

MedCalc provides a risk calculator. As always, it is best to use these calculators as a tool once you’ve understood the concept.

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