Bayesian confidence interval for difference of the proportions in a 2×2 table with structural zero

Abstract

This article studies the construction of a Bayesian confidence interval for risk difference in a 2×2 table with structural zero. The exact posterior distribution of the risk difference is derived under the Dirichlet prior distribution, and a tail-based interval is used to construct the Bayesian confidence interval. The frequentist performance of the tail-based interval is investigated and compared with the score-based interval by simulation. Our results show that the tail-based interval at Jeffreys prior performs as well as or better than the score-based confidence interval.

Keywords:

• 2×2 table with structural zero
• risk difference
• Bayesian analysis
• Dirichlet prior
• confidence interval

Acknowledgement

We are very grateful to the anonymous referee for many helpful comments and suggestions. This research was supported by National Natural Science Foundation of China (10761010), National Social Science Foundation of China (08XTJ001).