A bias correction method for hazard ratio estimation and its inference in a multiple-arm clinical trial

Area of Science:

• Clinical Trials Methodology
• Biostatistics
• Pharmaceutical Research

Background:

• Multi-arm clinical trials with a shared control group accelerate drug development by testing multiple experimental regimens simultaneously.
• When a single experimental treatment is compared against a common control group multiple times, adjustments for multiple testing are crucial to maintain statistical integrity.
• Existing methods like stepwise over-correction (SOC) are effective for response rate endpoints but require adaptation for time-to-event data.

Purpose of the Study:

• To extend the stepwise over-correction (SOC) method to multi-arm clinical trials with time-to-event as the primary endpoint.
• To develop a statistical approach that utilizes confidence intervals of the hazard ratio for significance testing.
• To introduce a bias-corrected estimation method for treatment effects in multi-arm trials, enabling inference at the full alpha level.

Main Methods:

• Extension of the stepwise over-correction (SOC) method for time-to-event endpoints in multi-arm trials.
• Development of a bias formula for the maximum treatment effect estimate compared to the true effect.
• Introduction of a novel reject region for statistical inference, avoiding alpha-splitting and pre-specified test order.

Main Results:

• The proposed method successfully extends SOC to time-to-event endpoints, using hazard ratio confidence intervals for significance.
• A formula for bias correction in maximum treatment effect estimation is provided.
• The new approach maintains type I error control while enhancing statistical power compared to traditional methods.

Conclusions:

• The extended SOC method offers a robust framework for analyzing multi-arm trials with time-to-event data.
• Bias-corrected estimates allow for full alpha-level inference without compromising statistical validity.
• This approach improves efficiency and success rates in clinical trials by optimizing statistical power and error control.