Q&A: Relative Risk and Relative Risk Reduction

In epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk of an adverse event in the exposed group compared to an unexposed group.

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In this article:
What is relative risk and relative risk reduction?
MCQ exam: clinical scenario
MCQ exam: answer
MCQ exam: explanation

What is relative risk and relative risk reduction?

How do you interpret the results of a randomised controlled trial? A common measure of a treatment is to look at the frequency of bad outcomes of a disease in the group being treated compared with those who were not treated. For instance, supposing that a well-designed randomised controlled trial in children with a particular disease found that 20 per cent of the control group developed bad outcomes, compared with only 12 per cent of those receiving treatment. Should you agree to give this treatment to your child? Without knowing more about the adverse effects of the therapy, it appears to reduce some of the bad outcomes of the disease. But is its effect meaningful?

This is where you need to consider the risk of treatment versus no treatment. In healthcare, risk refers to the probability of a bad outcome in people with the disease.

Absolute risk reduction (ARR) – also called risk difference (RD) – is the most useful way of presenting research results to help your decision-making. In this example, the ARR is 8 per cent (20 per cent - 12 per cent = 8 per cent). This means that, if 100 children were treated, 8 would be prevented from developing bad outcomes. Another way of expressing this is the number needed to treat (NNT). If 8 children out of 100 benefit from treatment, the NNT for one child to benefit is about 13 (100 ÷ 8 = 12.5).

For technical reasons, some other measures are often used. The relative risk (RR) of a bad outcome in a group given intervention is a proportional measure estimating the size of the effect of a treatment compared with other interventions or no treatment at all. It is the proportion of bad outcomes in the intervention group divided by the proportion of bad outcomes in the control group. In this hypothetical case, the RR is 0.6 (12 per cent ÷ 20 per cent = 0.6).

When a treatment has an RR greater than 1, the risk of a bad outcome is increased by the treatment; when the RR is less than 1, the risk of a bad outcome is decreased, meaning that the treatment is likely to do good. For example, when the RR is 2.0 the chance of a bad outcome is twice as likely to occur with the treatment as without it, whereas an RR of 0.5 means that the chance of a bad outcome is twice as likely to occur without the intervention. When the RR is exactly 1, the risk is unchanged. For example, a report may state ‘The relative risk of blindness in people given drug T was 1.5’. This shows that the drug increased the risk of blindness. Another measure that is used is the odds ratio. For practical purposes, assume that the odds ratio is the same as the relative risk. Sometimes the outcome is a good one and the interpretation of relative risk is the opposite of what we have just outlined.

Relative risk reduction (RRR) tells you by how much the treatment reduced the risk of bad outcomes relative to the control group who did not have the treatment. In the previous example, the relative risk reduction of fever and rash in the group of the children on the intervention was 40 per cent (1 – 0.6 = 0.4 or 40 per cent).

The RR (and therefore the RRR) is often the same in people irrespective of their level of risk, which means that the ARR will be greatest in those at greatest risk, as shown in Table 18.1. The greater your risk, the more you stand to gain from the intervention.

MCQ exam: clinical scenario

A random controlled trial (RCT) of acute asthma treatment was performed in the emergency department wherein patients were discharged with oral corticosteroids plus either budesonide (an inhaled corticosteroid) or placebo. The main outcome event was relapse, defined as an unscheduled visit for worsening asthma symptoms within 21 days of discharge.

Of the 100 patients randomized to budesonide, 25 relapsed. Conversely, 50 of the 94 patients randomized to placebo relapsed.

What is the relative reduction in 21-day relapse from asthma in the treated patients?

a) 7.5%
b) 12.5%
c) 17.5%
d) 25%
e) 50%

MCQ exam: answer

The correct answer is E
The relative reduction from asthma in the treated patients is 50%

MCQ exam: explanation

The relative risk reduction (RRR) is a quantification of how much the treatment reduces the risk of the outcome relative to the baseline outcome event rate. Wherein the baseline risk of an outcome event is the event rate in the control group defined by C/(C + D), the RRR is the difference in outcome event rates between the control and treatment groups divided by the outcome event rate in the control group.

The relative risk reduction = (0.50 - 0.25) / 0.50 = 0.50

We convert these numbers to percent by simply multiplying by 100 to arrive at
The relative risk reduction = 50%

Reference(s)
1). Wikipedia: Relative risk reduction. Available online: https://en.wikipedia.org/wiki/Relative_risk_reduction
2). Irwig L, Irwig J, Trevena L, et al. Chapter 18: Relative risk, relative and absolute risk reduction, number needed to treat and confidence intervals. London: Hammersmith Press; 2008. Available online: https://www.ncbi.nlm.nih.gov/books/NBK63647/