Asymptotic properties of maximum likelihood estimators with sample size recalculation

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Determining treatment effect significance requires precise statistical power and type I error control.
• Interim analyses allow for sample size re-estimation (SSR) to maintain desired statistical properties.
• Estimating treatment effects accurately is a secondary, yet crucial, experimental objective.

Purpose of the Study:

• To investigate the impact of sample size re-estimation (SSR) on the asymptotic distributions of statistical estimators.
• To determine how SSR affects the accuracy of treatment effect significance and estimation.
• To identify conditions under which SSR-adjusted distributions deviate from standard non-adjusted distributions.

Main Methods:

• Utilized theoretical analysis to derive asymptotic distributions of standardized statistics under SSR.
• Employed Monte-Carlo simulation studies to empirically assess the behavior of estimators with and without SSR.
• Applied an illustrative example to demonstrate practical implications of SSR on statistical inference.

Main Results:

• Asymptotic distributions of standardized statistics under SSR are generally random mixtures of distributions.
• These distributions are non-normal, except in specific scenarios related to the SSR model choice.
• Simulations and examples confirm that estimators with SSR can exhibit different asymptotic behaviors compared to those without SSR.

Conclusions:

• Sample size re-estimation introduces complexities in statistical distributions, potentially affecting standard inferential procedures.
• The choice of SSR model is critical in determining the nature of the resulting asymptotic distributions.
• Researchers must consider the influence of SSR on statistical properties to ensure valid interpretation of treatment effects.