Noninferiority trial designs for odds ratios and risk differences

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Noninferiority trials are crucial for evaluating new treatments when demonstrating superiority is not feasible or ethical.
• Defining trial margins on the odds ratio (ψ) or risk-difference (δ) scale impacts design parameter calculations.
• Accurate sample size and allocation ratio determination are essential for trial efficiency and reliable results.

Purpose of the Study:

• To derive constrained maximum likelihood methods for determining noninferiority trial design parameters for binary outcomes.
• To provide algorithms for calculating the common response rate (π(N)), minimum sample size (N), and optimal allocation ratio (γ).
• To investigate the impact of margin scale (odds ratio vs. risk-difference) on power and allocation.

Main Methods:

• Constrained maximum likelihood derivations were used to establish relationships between design parameters.
• An algorithm was developed to compute π(N), N, and γ given control response rates, margin type, and error rates.
• The study analyzed how optimal allocation ratios vary with increasing odds ratio (ψ) and risk-difference (δ) margins.

Main Results:

• Under specific conditions, the common response rate π(N) is a fixed parameter between control and experimental rates.
• Setting π(N) equal to the null hypothesis control rate underestimates required sample size.
• Optimal allocations become imbalanced as ψ increases (γ(ψ)<1), while γ(δ) approaches 1/γ(ψ); ranges of allocation ratios exist for minimum sample size.

Conclusions:

• The derived methods enable precise calculation of design parameters for noninferiority trials.
• Trialists can leverage the relationship between allocation ratios and sample size to balance efficiency and practical considerations.
• Discrepancies in power exist when reporting results on different scales for large margins (ψ>2.5), particularly when designing on the risk-difference scale.