Allocation of subjects to test null relative risks smaller than one

Area of Science:

• Biostatistics
• Clinical Trial Design
• Epidemiology

Background:

• Determining optimal sample size and allocation is crucial for the statistical power of clinical trials.
• Existing methods may not efficiently maximize power when testing for a reduced relative risk.
• Prophylactic interventions, like vaccines, often require large sample sizes, making efficiency paramount.

Purpose of the Study:

• To identify optimal subject allocation proportions for maximizing statistical power in intervention studies.
• To evaluate the sample size reduction achieved by proposed allocation strategies compared to equal allocation.
• To recommend appropriate statistical tests for analyzing studies with a reduced relative risk hypothesis.

Main Methods:

• Derived an optimal allocation proportion k'=1/(1+sqrt(r(0))) to maximize power for testing relative risk reduction.
• Investigated practical, approximate allocation proportions k'(s) for various null ratios r(0).
• Evaluated likelihood score tests and an arcsine test for their size and power, including a skewness correction.

Main Results:

• The proposed allocation proportions k' and k'(s) achieve near-optimal power and minimize sample size.
• Compared to equal allocation, k' and k'(s) reduced sample sizes by 5.5% to 24% depending on the null ratio.
• The skewness-corrected score test demonstrated accurate size control and slightly improved power.

Conclusions:

• Allocating a specific proportion of subjects to intervention, calculated as k' or k'(s), is effective for power maximization.
• These methods offer significant sample size savings, particularly valuable for large-scale prophylactic intervention trials.
• The score test, especially with skewness correction, is recommended for planning studies to detect a reduced relative risk.