Researchers conducted a randomized controlled trial to assess the effectiveness of a new drug to reduce severe cutaneous reactions in patients with rheumatoid arthritis who are treated with adalimumab. Of 150 adults with rheumatoid arthritis who are treated with adalimumab, 75 received the new drug in addition to adalimumab, and 75 received a placebo in addition to adalimumab. Results show that 6 patients in the new drug group developed severe cutaneous reactions, compared to 9 in the placebo group. Which of the following represents the relative risk reduction for severe cutaneous reactions among patients in the new drug group?
Relative risk reduction (RRR) measures how much a given treatment reduces the risk of an unfavorable outcome relative to the control group. RRR may be defined as the difference in risk of the unfavorable outcome in the treatment group (eg, new drug) compared to the control group (eg, placebo):
RRR = (Riskcontrol − Risktreatment) / Riskcontrol
In this example, Riskcontrol (ie, risk of severe cutaneous reactions in the placebo group) is 9/75 = 0.12, and Risktreatment (ie, risk of severe cutaneous reactions in the new drug group) is 6/75 = 0.08. Therefore, RRR for severe cutaneous reactions among patients in the new drug group is:
RRR = (0.12 − 0.08) / 0.12 = 0.33
Alternately, RRR may be calculated using relative risk (RR). When using RR, the formula for RRR is:
RRR = 1 − RR
For this example, RR is the ratio of the risk of severe cutaneous reactions in the new drug group to the risk of severe cutaneous reactions in the placebo group, calculated as follows:
RR = (Risktreatment / Riskcontrol) = (0.08/0.12) = 0.67
Therefore, RRR is:
RRR = 1 − 0.67 = 0.33
(Choice A) 0.08 represents the risk of severe cutaneous reactions in the new drug group (6/75 = 0.08, or 8%), not RRR.
(Choice B) 0.10 represents the risk of severe cutaneous reactions in the entire study (ie, both groups: [6 + 9] / [75 + 75] = 0.10, or 10%).
(Choice C) 0.12 represents the risk of severe cutaneous reactions in the placebo group (9/75 = 0.12, or 12%).
(Choice E) 0.67 represents the RR, the ratio of the risk of severe cutaneous reactions in the new drug group to the risk of severe cutaneous reactions in the placebo group (0.08/0.12 = 0.67, or 67%).
Educational objective:
Relative risk reduction (RRR) measures how much a treatment reduces the risk of an unfavorable outcome. Two methods to calculate it are: