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 the benefit the 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]

SAQ 2 (10 marks)

A colleague shows you a case-control study of a childhood outcome that affects about 30 percent of the population. The study reports an odds ratio of 4, and your colleague tells a family the outcome is "four times more likely" in the exposed. [5]

1. Explain why interpreting the odds ratio of 4 as a relative risk of 4 is unsafe in this study. (4) [5] [6]
2. Describe how you would correct the overclaim for the family and what measure you would prefer where the data allow. (3) [5] [8]
3. A separate survival analysis reports a hazard ratio of 0.7. Explain what this means and what you would check before acting on it. (3) [7]

Model answer

The odds ratio approximates the relative risk only when the outcome is rare, under about 10 percent. When the outcome is common, as it is here at 30 percent, the odds grow faster than the risk, so the odds ratio is always further from 1 than the relative risk and overstates the strength of the association. Reading the odds ratio of 4 as a four-fold relative risk therefore exaggerates the true magnitude of the link, because the actual relative risk is closer to 1. The odds ratio is the correct relative measure for a case-control study, since that design samples by outcome and cannot compute a true risk, but it must not be read as a relative risk for a common outcome. [5] [6]

I would avoid contradicting my colleague harshly in front of the family, but I would correct the overclaim by explaining that the figure of four is an odds ratio, which for a common outcome overstates the relative risk, and that the true increase in likelihood is smaller. Where the data allow, I would reach for the relative risk, computed from a prospective design, or better still an absolute measure such as the absolute risk reduction, so the family understands the real magnitude rather than an inflated ratio. I would align the team afterwards so the family hears one defensible message. [5] [8]

A hazard ratio of 0.7 means the treated group experienced the outcome at 70 percent of the rate of the control group across the follow-up period, because the hazard ratio compares the instantaneous event rates of the two survival curves and respects censoring. Because it is an average over time, it can hide curves that separate late, converge, or cross, so before acting on it I would inspect the Kaplan-Meier plot to confirm the benefit is spread evenly and that the proportional-hazards assumption holds. I would also read the confidence interval against the null value of 1. [7]