Exact Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• Fisher's exact test provides exact p-values for 2x2 contingency tables.
• A one-sided p-value is equivalent to a posterior probability of negative association under specific Bayesian conditions.
• Missing data can complicate standard statistical analyses, including exact tests.

Purpose of the Study:

• To extend Fisher's exact test p-value to scenarios with missing data.
• To propose Bayesian p-values for testing independence in 2x2 tables with missing data.
• To evaluate the performance of these new methods via simulation.

Main Methods:

• Derivation of an extended Fisher's exact test p-value under the missing at random or completely at random assumption.
• Development of Bayesian p-values using alternative priors for 2x2 contingency tables with missing data.
• Simulation study to assess Type I error rates and statistical power.

Main Results:

• The study successfully extends Fisher's exact test p-value to handle missing data.
• Proposed Bayesian p-values offer a robust alternative for analyzing 2x2 tables with missing data.
• Simulation results provide insights into the performance characteristics of the novel methods.

Conclusions:

• The extended Fisher's exact test and proposed Bayesian p-values are valuable tools for analyzing 2x2 contingency tables with missing data.
• These methods enhance statistical inference in the presence of incomplete observations.
• The study demonstrates the utility of Bayesian approaches in addressing missing data challenges in categorical data analysis.