Exact Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data. (November 2018)

• Record Type: Journal Article
• Authors: Lin, Yan; Lipsitz, Stuart R; Sinha, Debajyoti; Fitzmaurice, Garrett; Lipshultz, Steven
• Is Part Of: Statistical methods in medical research. Volume 27:Number 11(2018)
• Page Start: 3411
• Page End: 3419
• Publication Date: 2018-11
• Subjects: Dirichlet prior -- Fisher's exact test -- missing at random -- missing completely at random -- quasi-Monte Carlo integration; Medicine -- Research -- Statistical methods -- Periodicals; Research -- Periodicals; Review Literature -- Periodicals; Statistics -- methods -- Periodicals; Médecine -- Recherche -- Méthodes statistiques -- Périodiques; 610.727
• DOI: 10.1177/0962280217702538
• Languages: English
• ISSNs: 0962-2802

Abstract

Altham (Altham PME. Exact Bayesian analysis of a 2 × 2 contingency table, and Fisher's "exact" significance test. J R Stat Soc B 1969; 31: 261–269) showed that a one-sided p-value from Fisher's exact test of independence in a 2 × 2 contingency table is equal to the posterior probability of negative association in the 2 × 2 contingency table under a Bayesian analysis using an improper prior. We derive an extension of Fisher's exact test p-value in the presence of missing data, assuming the missing data mechanism is ignorable (i.e., missing at random or completely at random). Further, we propose Bayesian p-values for a test of independence in a 2 × 2 contingency table with missing data using alternative priors; we also present results from a simulation study exploring the Type I error rate and power of the proposed exact test p-values. An example, using data on the association between blood pressure and a cardiac enzyme, is presented to illustrate the methods.