Clinical epidemiology and measures of effect — formative SAQs

SAQ 1 (10 marks)

You are asked to interpret the results of a randomised controlled trial of a preventive therapy in children. The trial reports the outcome in 200 of 1,000 controls and 100 of 1,000 treated children, and the abstract quotes a 50 percent relative risk reduction. ^[1]

1. From the data provided, compute the relative risk, the relative risk reduction, the absolute risk reduction, and the number needed to treat, showing your working. (4) ^{[3] [4]}
2. Explain why quoting only the 50 percent relative risk reduction is misleading, and describe how you would present the benefit accurately to a family. (3) ^{[3] [8]}
3. Explain how the number needed to treat would change if the child's baseline risk were 2 percent rather than 20 percent, and what this implies for applying the result. (3) ^{[3] [4]}

Model answer

The risk in controls is 200 divided by 1,000, which is 0.20 or 20 percent, and the risk in the treated group is 100 divided by 1,000, which is 0.10 or 10 percent. The relative risk is the risk in the treated group divided by the risk in controls, 0.10 divided by 0.20, which is 0.5. The relative risk reduction is one minus the relative risk, which is 0.5 or 50 percent. The absolute risk reduction is the risk in controls minus the risk in the treated group, 0.20 minus 0.10, which is 0.10 or 10 percent. The number needed to treat is the reciprocal of the absolute risk reduction, 1 divided by 0.10, which is 10, rounded up to the next whole person. ^{[3] [4]}

The 50 percent relative risk reduction is misleading because it hides the baseline risk and inflates the perceived benefit. I would present the absolute risk reduction and the number needed to treat alongside the relative figure, explaining that out of ten children treated, one event is prevented, and I would read the confidence interval so the family understands the range compatible with the data. The absolute figure is benefit family can feel, so it should always accompany the relative one. ^{[3] [8]}

If the child's baseline risk were 2 percent rather than 20 percent, the same 50 percent relative risk reduction would produce an absolute risk reduction of 1 percent and a number needed to treat of 100, a tenth of the absolute benefit. This shows that the number needed to treat is only as honest as the baseline risk behind it, so it must be recomputed for the child's own baseline risk rather than borrowed from the trial average. ^{[3] [4]}