Comparison of a two-stage and three-stage interim-analysis procedure

Area of Science:

• Statistical modeling
• Hypothesis testing
• Experimental design

Background:

• Traditional significance testing often requires large sample sizes.
• Sequential analysis methods can improve efficiency but require careful design.
• Combining p-values offers a flexible approach for multi-stage testing.

Purpose of the Study:

• To develop and evaluate two-stage and three-stage sampling plans using a statistical model for combining p-values.
• To compare the performance of these multi-stage plans against conventional single end-of-study tests.
• To assess Type I error rates, statistical power, and expected sample sizes.

Main Methods:

• A statistical model for combining p-values was employed.
• Rejection and acceptance regions were defined for two-stage and three-stage sampling plans.
• Performance metrics including Type I error rates, power, early termination frequencies, and expected sample sizes were compared.

Main Results:

• Both two-stage and three-stage sampling plans effectively controlled Type I error rates.
• The two-stage plan offered a minimal loss in statistical power with significant sample size reduction compared to single-stage tests.
• The three-stage plan achieved greater sample size reduction at the cost of a slightly larger power decrease.

Conclusions:

• Multi-stage sampling plans, utilizing interim analyses, are more efficient than single end-of-study analyses in terms of power per unit of sample size.
• Two-stage and three-stage designs provide appropriate Type I error protection.
• These sequential strategies offer a favorable balance between statistical power and sample size efficiency.