### 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.

Original language | English (US) |
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Journal | Statistical Methods in Medical Research |

DOIs | |

State | Accepted/In press - Jan 1 2017 |

Externally published | Yes |

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### Keywords

- Dirichlet prior
- Fisher’s exact test
- missing at random
- missing completely at random
- quasi-Monte Carlo integration

### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability
- Health Information Management

### Cite this

*Statistical Methods in Medical Research*. https://doi.org/10.1177/0962280217702538