Relative and absolute risk reduction

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In medicine , relative and absolute risk reduction are different measures to describe the effectiveness of a (new) therapy compared to another therapy. They relate to the respective change in the relative risk (RR) or the absolute risk (AR).

Relative risk reduction

The relative risk reduction (RRR, English relative risk reduction ) indicates what percentage is to the ratio in each case less (relatively) the existing risk by an intervention.

A change in mortality from 2% to 1.6%, for example, corresponds to a reduction in the relative risk by a fifth or 20%; RRR = 20%.

Calculation:

  • Relative risk of the comparator therapy (control group): by definition 1 = 100%
  • Relative risk (RR) of verum therapy: 1.6 / 2.0 = 0.8 = 80%
  • Relative risk reduction (RRR) of the verum group = 1-RR = 1-0.8 = 0.2 = 20%

This level, which pharmaceutical companies like to quote in specialist advertising , is sometimes viewed critically, as the reader or listener tends to significantly overestimate the effect achieved. This is illustrated by the "extreme example" below.

This type of presentation of the therapy benefit, which is still common, is therefore increasingly being supplemented by other more descriptive statistical values ​​that take into account the basic proportion of the disease: the number of treatments required (NNT), the absolute risk reduction (ARR) or the increase in life expectancy are all part of this.

Absolute risk reduction

The absolute risk reduction (ARR, English absolute risk reduction ) indicates by (absolute) respectively reduced to all examinees the existing risk by an intervention as received many percentage points.

A change in mortality from 2% to 1.6%, for example, corresponds to a reduction in the absolute risk of 0.4 percentage points; ARR = 0.4%.

Calculation:

  • Absolute risk of the comparator therapy (control group): 2.0
  • Absolute risk of verum therapy: 1.6
  • Absolute risk reduction (ARR) of the verum group = 2.0-1.6 = 0.4

Examples of the relationship between relative and absolute risk reduction

Example 1:

In a collective of 1000 test persons, therapy changes the number of deaths from 10 (comparative therapy, e.g. with placebo) to 4 (verum therapy). The relative risk under the verum therapy is 4/10 = 0.4 = 40%, the RR of the control group according to definition 1. The mortality risk decreases significantly in the verum group. The relative risk reduction is 0.6 = 60%

In contrast, the absolute risk (AR) of death is 0.004 (= 0.4%) in the verum group and 0.01 (= 1.0%) in the comparison group (control group). The absolute risk reduction (ARR) is the difference, ie it is “only” 0.006 (= 0.6%). The ARR can also be expressed as NNT .

Example 2:

Therapy changes the number of deaths from 6 to 4 out of 1,000 people, that is 2 out of 1,000 - The ARR is 0.2% - The relative risk reduction here would be 2 out of 6 or 33%.

Extreme example:

Therapy group and control group each comprise 10,000 people from the general population. The aim is to test whether a drug reduces the risk of dying from a certain disease. In the therapy group 1 in 10,000 dies of the disease, in the control group 2 in 10,000 people. The manufacturer can now say with good mathematical right that his drug reduces the risk of dying from the disease by 50% - based on the relative risk reduction. In practice, however, such a difference would hardly be relevant.

Related topics

Individual evidence

  1. ↑ aerzteblatt.de: Deutsches Ärzteblatt: Archive "Clinical Studies: How" Correct "Statistics Can Deceive" (April 1, 2005) , accessed on July 7, 2010