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.
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.
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 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?
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%).
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.
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):
The absolute risk reduction (0,1% in our example):
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.
Calculate the relative and absolute risk reduction for the following fictitious example:
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%.
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%
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.
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.
So, when making decisions look for absolute risk reductions in association with the baseline risk.
We hope that you have now gained a deeper insight into the presentation and calculation of risk reductions. You now have the opportunity to broaden your knowledge even further.
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.
In this exercise, you learn step-by-step how to calculate risk reductions for groups of different sizes with the help of event rates.
Consolidate the calculation of risk reductions using event rates. The special thing about it: The graphic is replaced by a table and new expressions/terminologies are introduced.
A big pharmaceutical company promotes their new medication in an advert. Calculate here what is actually in the 20%.
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.
Formula for relative risk reduction:
Calculate the relative risk reduction:
Formula for absolute risk reduction:
Calculate the absolute risk reduction:
Calculate the relative and absolute risk reduction for the following fictitious example:
| Group | No. of affected people | No. of unaffected people | Total no. of people examined |
|---|---|---|---|
| Control group | 23 | 184 | 197 |
| Intervention group | 17 | 186 | 203 |
The results are now shown in a table instead of in a clearly designed graphic. In addition, the names of the groups have been changed. The control group received no treatment. The intervention group received treatment.
Calculate the relative risk reduction:
Formula for relative risk reduction:
Calculate the absolute risk reduction:
Formula for absolute risk reduction:
A big pharmaceutical company is promoting one of their new medications. The new medication reduces mortality due to cardiovascular diseases in people with cardiac insufficiency (heart failure) by 20%. In a study, the new medication (Entresto) was compared with a well-established drug (Enalapril) with the following results:
| Probands who died from cardiovascular disease | Probands who did not die from cardiovascular disease | Total no. of probands | |
| Treated with Entresto | 558 probands | 3629 probands | 4187 probands |
| Treated with Elanapril | 693 probands | 3519 probands | 4212 probands |
You have probably guessed already: The 20% mentioned is the relative risk reduction.
Calculate the absolute risk reduction from the figures in the table. What do you notice?
Once again, the absolute risk reduction is significantly lower than the impressive relative risk reduction of 20%.
The results presented in the advert are taken from the study mentioned below. In the study, a hazard ratio of 0,8 was calculated. From this, the relative risk reduction was derived to simplify matters.
McMurray, J. J. V., Packer, M., Desai, A. S., Gong, J., Lefkowitz, M. P., Rizkala, A. R., Zile, M. R. (2014). Angiotensin-neprilysin inhibition versus enalapril in heart failure. The New England Journal of Medicine, 371(11), 993–1004. doi: 10.1056/NEJMoa1409077
Here is the link to the study.
Prof. Dr. Anke Steckelberg
E-Mail: anke.steckelberg@medizin.uni-halle.de
Tel.: 0049-(0)345-557 4106
Sandro Zacher
E-Mail: sandro.zacher@medizin.uni-halle.de
Tel.: 0049-(0)345-577 4478
Martin-Luther-Universität Halle-Wittenberg
Medizinische Fakultät
Institut für Gesundheits- und Pflegewissenschaft
Magdeburger Str. 8
06112 Halle
Prof. Dr. Anke Steckelberg
Martin-Luther-Universität Halle-Wittenberg
Medizinische Fakultät
Institut für Gesundheits- und Pflegewissenschaft
Magdeburger Str. 8
06112 Halle
Tel.: 0049-(0)345-5571220 (Sekretariat)
www.medizin.uni-halle.de/pflegewissenschaft/
Anke Steckelberg (Anschrift wie oben)
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Berechnen Sie die relative Risikoreduktion (RRR) für das folgende Beispiel. In einer randomisierten-kontrollierten Studie wurden zwei Gruppen mit jeweils 100 Personen über einen längeren Zeitraum beobachtet. Die Personen in der Kontrollgruppe erhielten keine Behandlung. Die Personen in der Interventionsgruppe erhielten eine neuartige Behandlung. Ziel der Studie war es herauszufinden wie viele Personen in den Gruppen erkranken. Bis auf die Behandlung sind sich die Personen in beiden Gruppen ähnlich (z.B. Geschlecht und Alter).
Gruppe ohne Behandlung
(Kontrollgruppe)
10 von 100 Personen erkranken.
Gruppe mit Behandlung
(Interventionsgruppe)
5 von 100 Personen erkranken.
Mit der der Behandlung werden 5 Erkrankungen verhindert. Ohne Behandlung erkranken 10 Personen. Mit der Behandlung wird also die Hälfte vor der Erkrankung geschützt. Die relative Risikoreduktion liegt also bei 50%.
| erkrankte Personen | nicht erkrankte Personen | Gesamtanzahl untersuchter Personen | |
| Kontrollgruppe | 23 | 184 | 197 |
| Interventionsgruppe | 17 | 186 | 203 |
Berechnen Sie die absolute Risikoreduktion (ARR) für das folgende Beispiel. In einer randomisierten-kontrollierten Studie wurden zwei Gruppen mit jeweils 100 Personen über einen längeren Zeitraum beobachtet. Die Personen in der Gruppe A (Kontrollgruppe) erhielten keine Behandlung. Die Personen in Gruppe B (Interventionsgruppe) erhielten eine neuartige Behandlung. Ziel der Studie war es herauszufinden, wie viele Personen in den Gruppen erkranken. Bis auf die Behandlung sind sich die Personen in beiden Gruppen ähnlich (z.B. Geschlecht und Alter).
Gruppe ohne Behnadlung
(Kontrollgruppe)
10 von 100 Personen erkranken.
Gruppe mit Behnadlung
(Interventionsgruppe)
5 von 100 Personen erkranken.
Es erkranken 10 von 100 Personen ohne Behandlung und 5 von 100 Personen mit Behandlung. Mit Behandlung erkranken also 5 von 100 Personen weniger. Anders ausgedrückt: 10% - 5% = 5%
| erkrankte Personen | nicht erkrankte Personen | Gesamtanzahl untersuchter Personen | |
| Kontrollgruppe | 23 | 184 | 197 |
| Interventionsgruppe | 17 | 186 | 203 |
Wir hoffen, dass Sie durch das Tool einen tieferen Einblick in die Darstellung und Berechnung von Risikoreduktionen erhalten haben.
Werfen Sie einen Blick in die Quellen und erfahren Sie woher die Zahlen für die Beispiele in diesem Tool
stammen.
Klicken Sie auf "Weiterführende Links" um mehr zum Thema zu erfahren.
