Communication of relative and absolute risk reduction

What do percentages really say?

In everyday life you are often confronted with percentages. But what do they really say? Just imagine you are standing in front of the refrigerated section of your local supermarket where you notice two price-reduced yoghurts. Which price reduction helps you save the most?

Click on the appropriate yogurt cup.

ausgabe

Percentages alone are not decisive for the savings effect. The starting price is also important.

Although the red yoghurt has the lower percentual price discount, you save 0,10 more.

50% of 0,40 = 0,20
30% of 1,00 = 0,30

Percentages in health information

Percentages in
health
information

Regarding questions of health, we are not interested in price reductions but rather in risk reductions.

Suppose you are looking for information about cancer early detection tests (screening) and find the following adverts. Which information do you think would convince you more that early detection is important?

Click on the appropriate information.

Percentages can be misleading

You have probably already guessed: The way the benefits are presented, influences your decision. Both statements refer to the same screening test and are statistically correct. However, they differ in their meaningfulness.

First of all, let’s see how the results were obtained.

A study - where the results originate

A randomised-controlled study came to the conclusion that if cancer screening is used, one person less dies of cancer than if screening is not used.

How is it possible that a difference of one person can be represented as 0.1% and 25%?

It is easier to understand if the question is: Percentage of what?

Absolute risk reduction – 0,1% of what?

The 0,1% in our example presents the absolute risk reduction and refers to the actual number of people who benefit from the screening test.

The number of people participating is also taken into account.

The early detection test (screening) saves 1 out of 1000 people (0,1%).

Relative risk reduction – 25% of what?

The 25% in our example presents the relative risk reduction and refers to the number of deaths due to cancer.

The one less death due to early detection (screening) is considered in relation to the four deaths without early detection.

Through early detection 1 out of 4 (25%) deaths can be prevented.

This should be remembered

Relative and absolute risk reduction are two different possibilities of describing the effect of a treatment. However, when interpreting the results, it is important to consider the respective meaningfulness:

The relative risk reduction (25% in our example):

usually assumes larger values and often appears more impressive,
does not give any information about the actual number of people benefiting from the intervention.

The absolute risk reduction (0,1% in our example):

is more significant for decision-making because more reliable conclusions can be drawn about the benefits of the treatment.

The numbers in the example have been taken from the sigmoidoscopy (smaller variant of the colonoscopy) as an early detection test for colon cancer. If you concern yourself with early detection tests, you will probably find even more examples where the relative risk reduction is more impressive than the absolute risk reduction.

If you would like to learn more about early detection tests, you will find an article about their benefits and harm here.

Test your knowledge

Calculate the relative and absolute risk reduction for the following fictitious example:

Relative risk reduction

The treatment prevents 5 cases of illness. Without treatment, 10 people become ill. This means that the treatment protects half of them from the illness. The relative risk reduction is therefore 50%.

Absolute risk reduction

10 out of 100 people become ill without the treatment and 5 out of 100 people with the treatment. With treatment 5 people less out of 100 become ill. Or in other words: 10% - 5% = 5%

The influence of baseline risk

This example deals with the risk of having a first heart attack in the next 10 years. The risk depends on different factors and can vary greatly from person to person.

The graphic shows two groups with different baseline risks. In our example, the baseline risk shows how many people without any treatment at all will have their first heart attack within the next 10 years.

The risk can be reduced relatively by 20% if a certain medication is used.

Let’s now check the influence the individual baseline risk has on the benefit of the treatment.

People with a high baseline risk

Calculate the relative risk reduction:

%

RRR=

=

%

Calculate the absolute risk reduction:

ARR=

%

=

People with a low baseline risk

Calculate the relative risk reduction:

%

RRR=

=

%

Calculate the absolute risk reduction:

ARR=

%

=

Conclusion

Relative risk reduction = 20%

Absolute risk reduction = 4 out of 100

Relative risk reduction = 20%

Absolute risk reduction = 1 out of 100

Although the relative risk reduction was identical in both groups, the benefit for the people differs depending on the baseline risk.

While heart attacks can be prevented by the medication in 4 out of 100 people with a high baseline risk, only 1 out of 100 people with a low baseline risk benefits. The benefit of the medication depends therefore on the risk of having a heart attack.

Therefore, when making decisions you should look for absolute risk reductions in association with the baseline risk.

Exercises

Perhaps you have noticed that the groups in our examples were the same size. This is not always the case. In the following exercises, you will learn how to calculate the absolute and relative risk reductions when the groups are not the same size.

In addition, you will see an example of how doctors can be influenced by advertising from pharmaceutical companies.

The exercises increase in difficulty. If you have no or little experience with calculations, we recommend you start with Exercise No. 1.

Exercise 1

In this exercise, you will learn how to calculate risk reductions for groups of different sizes with the help of event rates.

Start

Exercise 2

Consolidate the calculation of risk reductions using event rates. The special thing about this: The graphic is replaced by a table and new expressions/terminologies are introduced.

Start

Exercise 3

A big pharmaceutical company promotes their new medication in an advert. Calculate what is actually in the 20%.

Start

In this exercise, you will learn how to calculate risk reductions for groups of different sizes with the help of event rates.

Start

Consolidate the calculation of risk reductions using event rates. The special thing about this: The graphic is replaced by a table and new expressions/terminologies are introduced.

Start

A big pharmaceutical company promotes their new medication in an advert. Calculate what is actually in the 20%.

Start

Congratulations on completing the course!

You are now well familiar with interpreting and calculating risk reductions.

We hope that you can benefit from this knowledge in your professional and personal life and wish you every success in applying it.

If you have any questions or suggestions, please do not hesitate to contact us.

Exercise 1

Calculate the relative and absolute risk reduction for the following fictitious example:

Since the groups here have different sizes, we can no longer simply put the number of people who have fallen ill into relationship with each other. So first we have to calculate the event rates. The event rate shows the relative frequency with which the event occurs in the group. In our example, this means the number of people who become ill with or without treatment.

Event rate formula:

Calculate the event rate:

Eventrate

without

=

treatment

Event rate

with

=

treatment