Dr Malchanceux is conducting a study on a binary outcome. She randomly assigns participants to either a treatment group or a control group, and then compares the risk of the outcome in the two groups. She calculates a risk ratio of 1.00 with a 95% confidence interval of [0.87, 1.15]. What can she conclude?

Question

BlackTom AI · Accepted Answer

A risk ratio (relative risk) of 1.00 indicates that the point estimate of the effect shows no difference in risk between treatment and control. Key concepts: the null value for a risk ratio is 1 (no effect); a 95% confidence interval (CI) gives a range of values compatible with the data at the 5% significance level; if the CI includes the null value, the result is not statistically significant at alpha = 0.05.

Step-by-step reasoning:
1. Identify the point estimate: RR = 1.00. That alone suggests no observed difference.
2. Examine the 95% CI: [0.87, 1.15]. This interval contains 1.00 (the null).
3. Statistical decision rule: for a two-sided 95% CI, if the interval includes the null value, you cannot reject the null hypothesis at the 5% level. Therefore the observed difference is not statistically significant.
4. Interpret the interval: the true risk ratio is compatible with anywhere between a 13% reduction in risk (0.87) and a 15% increase in risk (1.15). Because the CI spans both potential benefit and potential harm and includes no effect, the data are inconclusive regarding a true effect.

Why the correct answer is correct:
- The CI crossing 1 means the evidence is insufficient to declare a statistically significant difference; this is precisely what answer D states.

Why other common interpretations are incorrect:
- Saying “there is definitely no difference” is wrong because the CI shows uncertainty; the true effect could be less than or greater than 1 within the interval.
- Claiming “statistically significant increase” or “decrease” is incorrect because the CI does not exclude 1.
- Claiming “equivalence” is incorrect because equivalence requires a predefined equivalence margin and appropriate testing; a CI that merely includes 1 does not prove equivalence.

Conclusion: The correct conclusion is D — the risk ratio is not statistically significant because the 95% confidence interval crosses the null value of 1.

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