Predictively consistent prior effective sample sizes.

Area of Science:

• Statistics
• Biostatistics
• Clinical Trial Design

Background:

• Incorporating prior information via prior distributions is crucial for efficient randomized clinical trials, particularly for reducing control group sizes.
• Quantifying prior information using effective sample size (ESS) aids in trial design, but current methods yield inconsistent results for non-conjugate priors.

Purpose of the Study:

• To introduce a predictive consistency criterion for evaluating methods of calculating prior ESS.
• To propose a new, predictively consistent method for calculating prior ESS, termed the local-information-ratio ESS.
• To demonstrate the application of the new method in scenarios with non-conjugate priors and in clinical trial design.

Main Methods:

• Evaluation of existing ESS calculation methods against a proposed predictive consistency criterion.
• Development and theoretical justification of the local-information-ratio ESS.
• Application of the local-information-ratio ESS to specific statistical models (e.g., normal data with Student-t prior, exponential data with generalized Gamma prior).

Main Results:

• Current methods for calculating prior ESS do not satisfy the predictive consistency criterion.
• The proposed local-information-ratio ESS method is shown to be predictively consistent.
• The new method provides corrected ESS values for non-conjugate settings, illustrated with examples.

Conclusions:

• A fundamental flaw in existing prior ESS calculation methods is identified through the predictive consistency criterion.
• The local-information-ratio ESS offers a reliable approach for quantifying prior information in complex statistical models.
• This advancement has direct implications for designing randomized clinical trials using historical data and for subgroup analyses.