On confidence intervals for the hazard ratio in randomized clinical trials

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Survival Analysis

Background:

• Log-rank test and Cox proportional hazards model are standard for survival data analysis.
• Existing confidence intervals (Wald, Peto) for hazard ratios have limitations, including incorrect coverage or inconsistency.

Purpose of the Study:

• To develop a novel confidence interval for the hazard ratio that addresses limitations of existing methods.
• To ensure the confidence interval aligns with the significance of the log-rank test.

Main Methods:

• Inverting the score test under the Cox proportional hazards model.
• Modifying the variance estimator to align the score test with the log-rank test, even with ties.
• Evaluating performance through simulation studies and a colon cancer dataset.

Main Results:

• The proposed confidence interval excludes the null value (hazard ratio = 1) if and only if the log-rank test is significant.
• The new interval demonstrates correct coverage probability, unlike Peto's method.
• The proposed confidence interval is often more accurate and narrower than the Wald confidence interval.

Conclusions:

• The developed score-test-based confidence interval offers a reliable alternative for hazard ratio inference in clinical trials.
• This method provides accurate coverage and better precision compared to Wald and Peto intervals.
• The approach is robust in the presence of ties and aligns with log-rank test outcomes.