The contemplated average success probability for normally distributed models with an application to optimal sample...

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Clinical trials require robust statistical methods for evaluating treatment efficacy.
• Optimizing sample size allocation between early and confirmatory trials is crucial for efficiency.
• Existing methods may not fully address the complexities of sequential trial designs.

Purpose of the Study:

• To analytically derive the average success probability (ASP) and contemplated average success probability (CASP).
• To determine the optimal sample size allocation for maximizing CASP under a fixed subtotal sample size.
• To provide a theoretical framework for sample size optimization in two-stage clinical trials.

Main Methods:

• Analytical derivation of ASP and CASP assuming normally distributed observed differences.
• Uniform noninformative prior for population treatment effect and common known variance.
• Optimization of sample sizes for CASP using a theorem for a fixed subtotal sample size.

Main Results:

• An optimal plan for sample size allocation in early and confirmatory trials was derived.
• The optimal CASP was found to be an increasing function of the subtotal sample size.
• Numerical comparisons of ASP values were made with existing literature (Chuang-Stein, 2006).

Conclusions:

• The study provides analytical solutions for ASP and CASP in a two-stage trial setting.
• An optimal sample size allocation strategy is presented for maximizing CASP.
• The findings offer valuable insights for designing efficient clinical trials with sequential sample size adjustments.