Bayesian Extension of Fisher's Exact Test in the Presence of Missing Data

• Activity Number: 536
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Heather Yan Lin*+ and Stuart R. Lipsitz and Debajyoti Sinha and Garrett Fitzmaurice and Stephen Lipshutlz and J. Jack Lee
• Companies: MD Anderson Cancer Center and Brigham and Women's Hospital and Florida State University and Harvard Medical School and University of Miami Miller School of Medicine and MD Anderson Cancer Center
• Keywords: Dirichlet prior ; Gibbs sampler ; Ignorable missing data

Abstract

Altham (1969) showed that a one-sided p-value from Fisher's exact test of independence in 2 x 2 contingency tables is equal to the posterior probability of negative association in a 2 x 2 contingency table under a Bayesian analysis using an improper prior. Using the same Bayesian perspective, we derive an extension of the Fisher's exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable. We use a simulation study to explore the power and Type I error rate of our proposed test. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.