Relative risk

Risk indicators
absolute risk relative risk (RR) attributable risk (AR) absolute risk reduction (ARR) relative risk reduction (RRR) number of necessary treatments (NNT) chance (O) chance ratio (OR)

The relative risk (RR), risk ratio or risk ratio is a term used in descriptive statistics . It indicates the relation of a risk in two different groups, which differ in the presence of one or more characteristics. This can lead to an increase (RR> 1) as well as a decrease in the risk (RR <1).

calculation

The following data situation often arises in medical statistics :

	Number of people with risk factor	Number of people without a risk factor
Number of sick people	a	b
Number of not sick people	c	d

The relative risk is calculated here as follows

{\ displaystyle RR = {\ frac {a / (a ​​+ c)} {b / (b + d)}}}

or formally expressed using the conditional probability :

{\ displaystyle RR: = {\ frac {P ({\ text {Disease}} \ \ mid \ {\ text {with risk factor}})} {P ({\ text {Disease}} \ \ mid \ {\ text {without risk factor}})}}}

A distinction is made between cumulative incidence and incidence rate . The probability corresponds to the cumulative incidence of the group exposed to the risk factor and the cumulative incidence of the group not exposed. The relative risk can only be calculated if information on the cumulative incidence is known. If information on the incidence is missing, the odds ratio is used. It is between relative risk or risk ratio ( English risk ratio ), and rate ratio ( English rate ratio ) distinguished. Is used to calculate the incidence rate before, you can not be interpreted as probabilities numerator and denominator, which is why you (from a rate ratio English rate ratio ) but (English often or relative rate of relative risk not risk ratio should be called) speak. The cumulative incidence or incidence rate is known in prospective studies ( cohort studies and randomized controlled studies ), but not in retrospective studies ( cross-sectional or case-control studies ), which is why the odds ratio is used in the latter. ${\ displaystyle a / (a + c)}$ ${\ displaystyle b / (b + d)}$

The relative risk assumes values between 0 and infinity. A value of 1 means that the risk is the same in both groups. Accordingly, there is no evidence of a connection between the disease examined and the risk factor. If the value is greater than 1, this is an indication of a possible positive connection between a risk factor such as smoking and an illness. If the relative risk is below 1, the exposure has a protective effect, as is the case, for example, with vaccinations.

The extent to which a relative risk of over 1 is to be assessed critically for the risk factor carrier depends on various factors and must therefore be considered more closely. Heart attacks are a common illness and cause of death in Germany. “Smokers are about 2.5 times as likely to have a heart attack as non-smokers.” The risk factor smoking makes a common cause of illness and death even more frequent and relevant. Another meaning has a high relative risk, in cases where the risk of non-exposed persons is very small. For example, trained runners 30 minutes after a marathon have a 15 times higher risk of cardiac death than in everyday life. However, since the overall risk is very low, a high relative risk must not be overestimated. Compared to the relative risk, the attributable risk therefore also takes into account how common a disease is.

An example with fictitious data

Suppose you want to investigate the relationship between the occurrence of heart attacks and smoking. You watch 10,000 patients and determine whether they smoke or not and whether they have ever had a heart attack. The result is the following crosstab:

	Number of people who smoke	Number of people who do not smoke
Number of people with a heart attack	130	70
Number of people without a heart attack	1870	7930

The relative risk is as follows

{\ displaystyle RR = {\ frac {130 / (130 + 1870)} {70 / (70 + 7930)}} \ approx 7 {,} 4}

.

This means that the risk of suffering a heart attack is about 7.4 times higher among smokers than among non-smokers. The same result is obtained if the probability of a heart attack of smokers (P = 130/2000 = 6.5%) is divided by the probability of heart attack of non-smokers (P = 70/8000 = 0.875%).

use

The change in the relative risk due to a certain treatment is often used in medicine to make statements more impressive.

For example, in the examinations for the early detection of diseases, the change in the relative risk is indicated. During the discussion of mammography screening for the early detection of breast cancer , studies showed a 20% reduction in the relative risk. That means the investigation prevented one in five deaths. In relation to all women examined, however, the examination prevented only one death per 1000 women examined.

Connection with the odds ratio

Difference between opportunities ratio and relative risk with the example above

The relative risk is related to the opportunity ratio . Unlike the odds ratio, however, the relative risk can only be calculated if the marginal probabilities in the frequency table are random. I.e. the number of sick people must not be fixed by the study design. If the likelihood of getting sick is low, the odds ratio and relative risk are roughly the same.

literature

Leon Gordis: Epidemiology. Fourth edition. Sauders Elsevier, Philadelphia 2009
Robert H. Fletscher, Suzanne W. Fletscher. Clinical epidemiology. Basics and application. 2nd Edition. Publisher Hans Huber, Bern 2007
Oliver Razum, Jürgen Breckenkamp, Patrick Brzoska: Epidemiology for Dummies. WILEY-VCH Verlag, Munich 2009

Individual evidence

^ ^A ^b Stefan Weinmann: Evidence-based Psychiatry: Methods and Application . W. Kohlhammer Verlag, 2007, ISBN 978-3-17-018855-6 , pp. 63 ( limited preview in Google Book search).

↑ Alexander Krämer, Ralf Reintjes: Infection epidemiology: methods, modern surveillance, mathematical models, global public health . Springer-Verlag, 2013, ISBN 978-3-642-55612-8 , pp. 50 ( limited preview in Google Book search).

↑ ^a ^b Final spurt preclinical: PsychSoz: The scripts for the Physikum . Thieme, 2015, ISBN 978-3-13-166743-4 , pp. 20 ( limited preview in Google Book search).

↑ Siegfried Weyerer, Horst Bickel: Epidemiology of mental illnesses in old age . W. Kohlhammer Verlag, 2006, ISBN 978-3-17-016835-0 , pp. 33 ( limited preview in Google Book search).

↑ Marcus Müllner: Successful scientific work in the clinic: Evidence Based Medicine . Springer-Verlag, 2013, ISBN 978-3-7091-3755-0 , pp. 47–50 ( limited preview in Google Book search).

^ ^A ^b Matthias Egger, Oliver Razum: Public Health: Social and preventive medicine compact . Walter de Gruyter, 2014, ISBN 978-3-11-033606-1 , p. 34 ( limited preview in Google Book search).

↑ Flexikon: Relative Risk , accessed June 29, 2020

↑ O. Wegwarth, Breast Cancer Early Detection - Correctly Communicating Benefits and Risks in Der Gynäkologe 2018 (51), pp. 370–379 (2018).

[:0-1] A ^b Stefan Weinmann: Evidence-based Psychiatry: Methods and Application . W. Kohlhammer Verlag, 2007, ISBN 978-3-17-018855-6 , pp. 63 ( limited preview in Google Book search).

[2] Alexander Krämer, Ralf Reintjes: Infection epidemiology: methods, modern surveillance, mathematical models, global public health . Springer-Verlag, 2013, ISBN 978-3-642-55612-8 , pp. 50 ( limited preview in Google Book search).

[:1-3] Final spurt preclinical: PsychSoz: The scripts for the Physikum . Thieme, 2015, ISBN 978-3-13-166743-4 , pp. 20 ( limited preview in Google Book search).

[4] Siegfried Weyerer, Horst Bickel: Epidemiology of mental illnesses in old age . W. Kohlhammer Verlag, 2006, ISBN 978-3-17-016835-0 , pp. 33 ( limited preview in Google Book search).

[5] Marcus Müllner: Successful scientific work in the clinic: Evidence Based Medicine . Springer-Verlag, 2013, ISBN 978-3-7091-3755-0 , pp. 47–50 ( limited preview in Google Book search).

[:2-6] A ^b Matthias Egger, Oliver Razum: Public Health: Social and preventive medicine compact . Walter de Gruyter, 2014, ISBN 978-3-11-033606-1 , p. 34 ( limited preview in Google Book search).

[7] Flexikon: Relative Risk , accessed June 29, 2020