Explain the difference between relative risk reduction and absolute risk reduction.

Explain the difference between relative risk reduction and absolute risk reduction.

• A. RRR = (risk in exposed - risk in control) / risk in control; ARR = risk difference; implications for number needed to treat.
• B. RRR = risk difference; ARR = (risk in control - risk in exposed) / risk in control;
• C. RRR and ARR are identical.
• D. RRR is always smaller than ARR.

Answer: (A)

The key idea is that one measure shows how big the effect is in relative terms, while the other shows the actual, absolute change in risk. Relative risk reduction tells you what fraction of the baseline (control) risk is removed by the treatment. It’s a proportional reduction: you compare the risk in the treated group to the risk in the control group and express how much has dropped relative to the control risk. Absolute risk reduction, on the other hand, is the straightforward difference between the two risks—the actual drop in risk per person (or per 100 people) due to the treatment. For example, if 10% of people in the control group have the event and 6% in the treated group do, the ARR is 4 percentage points (0.10 − 0.06 = 0.04). The relative reduction is 40% (0.04/0.10 = 0.40), since the treated risk is 60% of the control risk (1 − RR with RR = 0.60). This distinction matters for interpretation and for planning, because NNT, the number needed to treat to prevent one event, comes from the ARR: NNT = 1/ARR (when ARR is expressed as a decimal). A treatment can have a large relative reduction if baseline risk is high, but the absolute risk reduction—and thus the NNT—can still be small if baseline risk is low. Why the other ideas don’t fit: the notion that the two measures are identical ignores that one is a proportion of baseline risk while the other is a simple difference. The idea that one is always smaller than the other isn’t accurate, since their magnitudes depend on the baseline risk. And the idea that RRR is simply the risk difference reverses the definitions. So, the best answer reflects that RRR is a proportionate reduction relative to baseline risk, ARR is the risk difference, and NNT derives from ARR.

The key idea is that one measure shows how big the effect is in relative terms, while the other shows the actual, absolute change in risk.

Relative risk reduction tells you what fraction of the baseline (control) risk is removed by the treatment. It’s a proportional reduction: you compare the risk in the treated group to the risk in the control group and express how much has dropped relative to the control risk. Absolute risk reduction, on the other hand, is the straightforward difference between the two risks—the actual drop in risk per person (or per 100 people) due to the treatment.

For example, if 10% of people in the control group have the event and 6% in the treated group do, the ARR is 4 percentage points (0.10 − 0.06 = 0.04). The relative reduction is 40% (0.04/0.10 = 0.40), since the treated risk is 60% of the control risk (1 − RR with RR = 0.60).

This distinction matters for interpretation and for planning, because NNT, the number needed to treat to prevent one event, comes from the ARR: NNT = 1/ARR (when ARR is expressed as a decimal). A treatment can have a large relative reduction if baseline risk is high, but the absolute risk reduction—and thus the NNT—can still be small if baseline risk is low.

Why the other ideas don’t fit: the notion that the two measures are identical ignores that one is a proportion of baseline risk while the other is a simple difference. The idea that one is always smaller than the other isn’t accurate, since their magnitudes depend on the baseline risk. And the idea that RRR is simply the risk difference reverses the definitions.

So, the best answer reflects that RRR is a proportionate reduction relative to baseline risk, ARR is the risk difference, and NNT derives from ARR.