What is the meaning and interpretation of terms like Confidence Interval (CI), Hazard Ratio (HR), p-value, Odds Ratio (OR), and Relative Risk (RR) in medical research papers?

Understanding Statistical Terms in Medical Research

Statistical measures like confidence intervals, hazard ratios, p-values, odds ratios, and relative risk are essential tools that tell you whether a treatment actually works, how strong the effect is, and how confident you can be in the results.

P-Value: Probability of Results Occurring by Chance

• A p-value represents the probability of obtaining results at least as extreme as those observed if there were truly no difference between groups (null hypothesis) 1
• P < 0.05 means there is less than a 5% probability (5 out of 100 times) that the observed difference occurred by chance alone 1
• 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 1
• Common mistake: P < 0.05 does NOT mean the treatment definitely works; it means if there were no real effect, you'd only see results this extreme 5% of the time 2
• P-values should be reported precisely to two decimal places when >0.01, three decimal places when <0.01, or as "p<0.001" for very small values 1

Confidence Interval (CI): Range of Plausible Values

• A 95% confidence interval shows the range of values within which the true effect in the population likely resides 3
• The confidence interval provides both the magnitude of effect AND the precision of that estimate—narrow intervals mean more precision, wide intervals mean more uncertainty 1
• Point estimates (like a hazard ratio of 0.44) must always be accompanied by 95% confidence intervals to assess both statistical plausibility and clinical relevance 1
• If a confidence interval for relative risk or hazard ratio crosses 1.0, the result is NOT statistically significant because 1.0 means "no effect" 4
• Example: A 95% CI of 0.8 to 3.0 indicates substantial uncertainty—the lower limit suggests a potential 20% protective effect while the upper limit suggests up to a 3-fold increased risk 4

Relative Risk (RR): Probability Comparison Between Groups

• Relative risk is the probability of an outcome occurring in one group (e.g., treatment) versus the probability in a comparison group (e.g., placebo) 5
• RR = 1.0 means no difference between groups; RR < 1.0 means reduced risk (protective); RR > 1.0 means increased risk (harmful) 5
• Example from research: RR 0.71 (95% CI 0.53 to 0.95) means the treatment group had 29% lower risk of intubation compared to control, and this is statistically significant because the CI doesn't cross 1.0 5
• In meta-analyses, pooled relative risk with 95% CI and p-value are presented together, and when RR remains significant across sensitivity analyses, this supports a robust effect 1

Odds Ratio (OR): Odds Comparison Between Groups

• An odds ratio represents the odds (probability of disease divided by 1 minus the probability) of an outcome according to an explanatory variable 5
• OR interpretation is similar to RR: OR = 1.0 means no difference; OR < 1.0 means reduced odds; OR > 1.0 means increased odds 5
• Example: OR = 1.29 (95% CI = 1.01,1.64, p = 0.041) means 29% higher odds of the outcome in the intervention group, statistically significant 5
• ORs are commonly used in case-control studies and logistic regression analyses 5

Hazard Ratio (HR): Rate of Events Over Time

• A hazard ratio measures the ratio of hazard rates (the rate at which an event occurs) for a given outcome between two groups over time 5
• HR = 1.0 means equal rates; HR < 1.0 means lower rate (protective); HR > 1.0 means higher rate (harmful) 5
• Example: HR 7.94 (95% CI 1.03,62.5, p = 0.05) means incomplete surgical resection had nearly 8 times the rate of death compared to complete resection 5
• HRs are used in survival analysis and time-to-event outcomes like mortality or disease progression 5
• Adjusted hazard ratios account for confounding variables, making them more reliable than unadjusted ratios 6

Reading Forest Plots and Tables

• Forest plots display effect sizes (RR, OR, HR) as points with horizontal lines representing confidence intervals 5
• If the confidence interval line crosses the vertical line at 1.0, the result is not statistically significant 5
• The size of the square or point often represents the weight or sample size of that study 5
• Tables typically show: number of events, total participants, effect measure with 95% CI, and p-value 5

Statistical vs. Clinical Significance

• Statistical significance (p < 0.05) does NOT automatically mean clinical importance—a tiny effect can be statistically significant with large sample sizes but meaningless to patients 7
• Clinical significance requires the magnitude of results to be larger than the minimal clinically important difference 7
• Always examine both the p-value AND the confidence interval to determine if results are both statistically significant and clinically meaningful 1
• Example: A treatment might reduce hospital stay by 0.5 days (p = 0.03), which is statistically significant but clinically trivial 5

Common Abbreviations on Graphs

• RR = Relative Risk; OR = Odds Ratio; HR = Hazard Ratio; CI = Confidence Interval 5
• k = number of studies (in meta-analyses) 5
• n = number of participants 5
• M = Mean; Mdn = Median; SD = Standard Deviation 5
• IQR = Interquartile Range (25th to 75th percentile) 5
• MD = Mean Difference; SMD = Standardized Mean Difference 5
• H vs. L = High versus Low (comparison groups) 5
• DR = Dose-Response 5

Critical Pitfalls to Avoid

• Never interpret p ≥ 0.05 as "proof of no effect"—it only means insufficient evidence to reject the null hypothesis 2
• Do not confuse statistical significance with clinical relevance—always assess whether the effect size matters to patient outcomes 7
• Wide confidence intervals indicate high uncertainty, even if p < 0.05, suggesting results should be interpreted cautiously 4
• Evaluate study quality and design, not just the p-value—a statistically significant result from a poorly designed study is unreliable 1
• P-values and confidence intervals provide complementary information and should always be reported together 1