How do p-value and confidence interval correlate with relative risk?

Understanding the Relationship Between P-Values, Confidence Intervals, and Relative Risk

P-values and confidence intervals work together to provide complementary information about relative risk: the p-value indicates whether an observed difference is statistically significant (typically p<0.05), while the confidence interval shows both the magnitude of the effect and the precision of that estimate. 1, 2

Statistical Significance Through P-Values

• A p-value represents the probability of obtaining results at least as extreme as those observed if the null hypothesis (no difference) were true 1, 3
• P-values less than 0.05 indicate statistical significance, meaning there is less than a 5% probability the observed difference occurred by chance alone 3
• The smaller the p-value, the stronger the evidence against the null hypothesis—p-values between 0.05-0.01 represent modest evidence, while p<0.001 represents strong evidence 3
• P-values should be reported precisely (e.g., p=0.03) rather than simply stating "p<0.05" 1

Confidence Intervals and Relative Risk Interpretation

• Confidence intervals provide the range within which the true relative risk lies with a specified degree of probability (typically 95%), along with information about the direction and strength of the effect 1, 2
• When a 95% confidence interval for relative risk crosses 1.0, the result is not statistically significant, regardless of the point estimate 4
• For example, a relative risk with 95% CI of 0.8-3.0 indicates substantial uncertainty—the lower limit suggests a potential 20% protective effect while the upper limit suggests up to 3-fold increased risk 4

Practical Integration in Clinical Research

• Both measures should be reported together because they provide complementary information: p-values indicate statistical significance while confidence intervals demonstrate clinical relevance and precision 1, 2
• The magnitude of difference between groups should always be reported as a point estimate (absolute differences, odds ratios, hazard ratios, or relative risks as appropriate) accompanied by confidence intervals 1
• In meta-analyses examining relative risk, results are typically presented showing both the pooled relative risk with 95% CI and the associated p-value (e.g., relative risk 0.570,95% CI 0.408-0.795, p=0.001) 1

Critical Interpretation Pitfalls

• P-values are heavily influenced by sample size—large studies can produce statistically significant p-values even when clinical differences are minimal 1, 5
• A statistically significant p-value does not automatically indicate clinical significance; the effect size and confidence interval must be evaluated for clinical relevance 5, 2
• When confidence intervals are wide, substantial uncertainty exists about the true effect size, even if the p-value suggests statistical significance 4
• The word "trend" should only be used for statistical tests of trends, not to describe p-values approaching but not reaching the pre-specified significance level 1

Reporting Standards for Relative Risk

• Precise p-values should be reported to two decimal places when >0.01, three decimal places when <0.01, or as "p<0.001" for very small values 1
• Point estimates of relative risk must be accompanied by 95% confidence intervals to allow assessment of both statistical plausibility and clinical relevance 1, 2
• When relative risk remains statistically significant across sensitivity analyses (e.g., after excluding studies with highest/lowest relative risk), this supports a robust effect 1