Bayesian confidence interval for the risk ratio in a correlated 2 × 2 table with structural zero

Abstract

This paper studies the construction of a Bayesian confidence interval for the risk ratio (RR) in a 2 × 2 table with structural zero. Under a Dirichlet prior distribution, the exact posterior distribution of the RR is derived, and tail-based interval is suggested for constructing Bayesian confidence interval. The frequentist performance of this confidence interval is investigated by simulation and compared with the score-based interval in terms of the mean coverage probability and mean expected width of the interval. An advantage of the Bayesian confidence interval is that it is well defined for all data structure and has shorter expected width. Our simulation shows that the Bayesian tail-based interval under Jeffreys’ prior performs as well as or better than the score-based confidence interval.

Keywords:

• Bayesian analysis
• confidence interval
• Dirichlet prior
• matched-pair design
• risk ratio

Acknowledgements

This research was supported by National Natural Science Foundation of China (10761010, 11061037).