Bayesian credible intervals for binomial proportions in a single patient trial

Area of Science:

• Biostatistics
• Clinical Trial Analysis
• Statistical Modeling

Background:

• Assessing individual treatment efficacy is crucial for clinical practice.
• Existing methods may not adequately capture performance changes in single subjects.
• Performance is often measured by percent correct scores in pre- and post-treatment tests.

Purpose of the Study:

• To develop and present a Bayesian statistical framework for evaluating individual treatment improvement.
• To model changes in percent correct scores from pre- to post-treatment.
• To provide clinicians with a method for assessing single-subject treatment outcomes.

Main Methods:

• Utilized a Bayesian approach with binomial and beta distributions to model test performance.
• Developed three models: equal pre- and post-test proportions, independent proportions, and correlated proportions.
• Employed posterior predictive distributions and calculated 95% credible intervals for performance changes.

Main Results:

• The study provides methods to calculate credible intervals for post-treatment scores based on pre-treatment performance.
• Demonstrated the application of these methods using data from a cochlear implant trial.
• The Bayesian framework allows for nuanced assessment of individual performance gains.

Conclusions:

• The proposed Bayesian methods offer a statistically sound approach to evaluating individual treatment effects.
• These methods are applicable to various clinical scenarios involving pre- and post-test performance data.
• The study enhances the ability to precisely measure and interpret individual patient progress.