Rethinking Probability of Success as Bayes Utility.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Decision Theory

Background:

• Existing hybrid frequentist-Bayesian approaches define probability of success (PoS) using traditional power functions.
• These definitions are not univocal and present potential drawbacks.
• Current methods focus on rejecting the null hypothesis, not on choosing the correct hypothesis.

Purpose of the Study:

• To propose a unifying, decision-theoretic approach for defining PoS.
• To introduce a new definition of PoS based on expected utility (u-PoS).
• To evaluate the conceptual advantages and impact on sample size compared to existing methods.

Main Methods:

• Developed a decision-theoretic framework for hybrid frequentist-Bayesian trials.
• Defined a new PoS metric as the expected utility of the trial (u-PoS).
• Analyzed the properties of u-PoS, including its relationship with sample size.

Main Results:

• The proposed u-PoS is defined as the expected probability of making the correct choice between null and alternative hypotheses.
• This approach offers a conceptual improvement over existing PoS definitions.
• Optimal sample sizes are reduced when the design prior assigns positive probability to the null hypothesis.

Conclusions:

• The decision-theoretic approach provides a more robust definition of PoS in hybrid trials.
• The u-PoS metric aligns better with the goal of choosing the correct hypothesis.
• This framework can lead to more efficient clinical trial designs with smaller sample sizes.