Distribution Theory Following Blinded and Unblinded Sample Size Re-estimation under Parametric Models

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Statistical Inference

Background:

• Existing literature on maximum likelihood estimators under fixed alternatives shows inconsistent nuisance parameter estimates with sample size re-estimation (SSR) in blinded studies.
• These findings have limited the application of SSR in clinical trial design.
• The use of fixed alternatives leads to unrealistic power convergence and hinders robust statistical analysis.

Purpose of the Study:

• To propose the use of local alternatives instead of fixed alternatives for analyzing blinded experiments.
• To demonstrate the consistency of nuisance parameter estimates and the convergence of sample sizes to optimal values under local alternatives.
• To validate the practical utility of SSR procedures in hypothesis testing with predetermined effect sizes.

Main Methods:

• Treatment assignments in blinded experiments are treated as missing data, imputed using single imputation from marginal distributions.
• The first step of the Expectation-Maximization (EM) algorithm is employed, mimicking imputation under the null hypothesis.
• Monte-Carlo simulation studies are used to confirm theoretical findings, alongside a multiple logistic regression example for practical illustration.

Main Results:

• Under local alternatives, both blinded and unblinded estimates of nuisance parameters are shown to be consistent.
• Re-estimated sample sizes converge to their locally asymptotically optimal values.
• Simulation studies confirm the theoretical findings, demonstrating the robustness of the proposed method.

Conclusions:

• The study advocates for the use of local alternatives in hypothesis testing for blinded experiments.
• Both blinded and unblinded SSR procedures yield similar sample sizes and power when a minimally clinically relevant local effect size is predetermined.
• The findings support the practical application of SSR, enhancing the efficiency and reliability of clinical trial designs.