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Difficulty: EasyStatistical Inference and Hypothesis Testing

A team of public health researchers conducts a randomized controlled trial to investigate the efficacy of a novel dietary intervention in preventing the onset of type 2 diabetes mellitus in high-risk patients. After completing the five-year study, the researchers analyze the data and report that the relative risk of developing diabetes in the intervention group compared to the control group is 0.700.70. The 95%95\% confidence interval for this relative risk is reported as 0.550.55 to 0.880.88, and the associated p-value is 0.020.02. Based on these statistical parameters, which of the following is the most accurate conclusion regarding the study results?

  1. The dietary intervention is associated with a statistically significant decrease in the risk of developing diabetes.Answer
  2. B
    The positive predictive value of the dietary intervention for preventing diabetes is 70%.
  3. C
    The p-value of 0.02 indicates that 2% of the participants in the intervention group developed diabetes.
  4. D
    The results are invalid because a retrospective cohort design must be used to calculate relative risk.
  5. E
    The findings demonstrate that the dietary intervention is an effect modifier rather than an independent protective factor.

Answer

The dietary intervention is associated with a statistically significant decrease in the risk of developing diabetes.
The correct answer accurately synthesizes the provided statistical parameters. A relative risk (RR) of 0.70 implies a 30% reduction in the risk of developing diabetes in the intervention group. To establish that this finding is not due to random chance, the 95% confidence interval (CI) and p-value must be evaluated. For ratio measures like RR, the null hypothesis value is 1.0 (indicating equal risk in both groups). Because the 95% CI is 0.55 to 0.88, it does not include 1.0, meaning the protective effect is statistically significant at the 0.05 alpha level. This is independently confirmed by the p-value of 0.02, which is less than 0.05.

Step-by-Step Solution

1
Evaluate the reported relative risk (RR).
The relative risk is 0.70.
An RR less than 1.0 indicates that the exposure (dietary intervention) is protective against the outcome (diabetes).
2
Determine if the findings are statistically significant using the confidence interval.
The 95% confidence interval is 0.55 to 0.88.
For relative risk and odds ratios, the null value (indicating no difference) is 1.0. Because the entire confidence interval lies below 1.0, the result is statistically significant.
3
Confirm statistical significance using the p-value.
The p-value is 0.02.
A p-value less than the standard alpha level of 0.05 indicates statistical significance, confirming the conclusion drawn from the confidence interval.

Key Concept

In hypothesis testing, a relative risk is considered statistically significant if its 95% confidence interval does not cross the null value of 1.0, which corresponds to a p-value of less than 0.05.
Estimated Time:1m 0s
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Topics

Statistical Inference and Hypothesis Testing

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