Relative Risk Reduction

The proportional reduction in risk associated with a treatment, calculated as one minus the relative risk, expressed as a percentage.

Source: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. Lippincott Williams & Wilkins; 2008.

Relative risk reduction is the proportional drop in risk a treatment produces, calculated as one minus the relative risk and given as a percentage. It can sound more impressive than it is because a large percentage reduction may rest on a tiny absolute change: cutting risk from two in a thousand to one in a thousand is a fifty per cent relative reduction yet spares only one person per thousand. Reporting it without the absolute figures can overstate a treatment's real value. The proportional, not the actual, drop in risk is what it gives. Rothman and colleagues (2008) describe this measure.

Source: Rothman et al. 2008

Relative risk reduction is calculated as one minus the relative risk, where the relative risk is the ratio of the risk in the treated group to the risk in the control group; it is often expressed as a percentage. Equivalently, it is the absolute risk reduction divided by the control-group risk. So relative risk reduction is calculated from the relative risk, or from the absolute risk reduction relative to the baseline risk, giving the proportional reduction in risk achieved by the treatment, which conveys the benefit as a fraction of the control-group risk rather than as an absolute difference.

Source: Rothman, Greenland & Lash 2008

Relative risk reduction is the proportional reduction in risk, a fraction of the control-group risk, while absolute risk reduction is the arithmetic difference in risk between the groups. The relative measure conveys the proportional size of the benefit and the absolute measure its actual magnitude. The same relative risk reduction can correspond to very different absolute reductions depending on the baseline risk. So the two differ in scale: relative risk reduction gives the proportional benefit and absolute risk reduction the practical one, and reporting the absolute reduction alongside prevents the benefit from appearing larger than it is when the baseline risk is low.

Source: Rothman, Greenland & Lash 2008

Relative risk reduction can be misleading because it does not reflect the baseline risk, so a large proportional reduction may correspond to a small absolute benefit when the outcome is rare, making a treatment appear more valuable than it is in practice. A reduction from a very low risk to a slightly lower one can still give a striking relative figure. So relative risk reduction can mislead if reported alone, which is why it should be accompanied by the absolute risk reduction and the baseline risk, since the proportional reduction, however large, must be judged against how common the outcome was to understand the real benefit.

Source: Rothman, Greenland & Lash 2008

Relative risk reduction is used because it conveys the proportional strength of a treatment's benefit in a way that is often relatively stable across populations with different baseline risks, making it useful for summarising and comparing treatment effects across studies. So relative risk reduction is used to express how much a treatment proportionally lowers risk, which is convenient for comparison and often reported in trials, though because it does not convey absolute benefit, it is interpreted alongside the absolute risk reduction and the number needed to treat, since the proportional reduction alone does not tell how much the outcome actually falls for the patients treated.

Source: Rothman, Greenland & Lash 2008