From p-values to Bayes Factor: A Meta-Analytic Comparison in Colorectal Research

Area of Science:

• Biostatistics
• Medical Research Synthesis

Background:

• Frequentist meta-analysis is standard but has limitations in hypothesis probability interpretation.
• Bayesian meta-analysis integrates prior knowledge and observed data for nuanced interpretation.

Purpose of the Study:

• To compare frequentist and Bayesian meta-analysis outputs and interpretations.
• To reanalyze published colorectal anastomosis trials using both methods.

Main Methods:

• Reanalyzed two published meta-analyses on colorectal anastomosis (trans-anastomotic tubes and indocyanine green fluorescence imaging).
• Employed both frequentist and Bayesian meta-analysis approaches.
• Conducted sequential Bayesian analyses, updating priors with new studies.

Main Results:

• Both methods yielded similar odds ratios for trans-anastomotic tubes.
• Bayesian analysis showed narrower credible intervals and a Bayes factor favoring the null hypothesis, unlike p-values.
• Bayesian analysis for indocyanine green favored the alternative hypothesis (BF10=19), offering more conservative estimates than frequentist methods.
• Sequential Bayesian analysis increased confidence in the alternative hypothesis as more studies were added.

Conclusions:

• Frequentist and Bayesian meta-analyses may agree on point estimates but diverge significantly in hypothesis testing interpretation.
• Bayesian methods provide direct probability of hypotheses and credible intervals, enhancing interpretability.
• Bayesian approaches are more flexible and intuitive, particularly for incorporating prior knowledge and sequential updating.