Based Winbugs Software In The 2 ¡Á 2 Contingency Tables With Structural Zero Risk Difference And Risk Ratio Calculation Of The Bayesian Confidence Interval And Sample Volume Determined

Recently with correlated 2×2 table with structural zero getting more and more widly used in some infectious disease studies and two-step procedure studies, researches on risk difference(RD) and risk ratio(RR) in a correlated 2×2 talbe with structural zero are quite active by frequentist. Such as, Agresti(1990), Lui(2000) and Tang et al.(2003). Meanwhile,Bayesian approach also has been widly applied in contingency tables. For example, Pham-Gia et al.(1993), Hashemi et al.(1998) and so on. However all above mentioned works are studied under independent binomial sampling. It is worth to mention a series researches by Shi and Bai. They studied the Bayesian confidence interval of RD and RR in matched pair design,and first pay attention to RD and RR in a correlated 2×2 table with structural zero. The exact posterior density and distribution functions for RD and RR under Dirichlet prior have been derived and the frequentist performance of the Bayesian tail interval based on mean coverage probability and related measures has been investigated by simulation in Shi et al.(2009) and Bai et al.(2011), respectively. Their conclusions on RD and RR in a correlated 2×2 table with structural zero filled the theory gap in the field of Bayesian analysis.This thesis based on related studies on RD and RR in a correlated 2×2 talbe with structural zero by Shi et al.(2009) and Bai et al.(2011). By using Winbugs, a popular software for Bayesian analysis using Markov Chain Monte Carlo(MCMC) techniques, we calculated the Bayesian tail interval of RD and RR, then compared to results by Shi et al.(2009) and Bai et al.(2011). We found that conclusions reached by Winbugs are quite similar to Shi et al.(2009) and Bai et al.(2011), especially for large sample size. Therefore it is feasible, convenient and effective to perform calculations by Winbugs. Moreover, based on Shi et al.(2009) and Bai et al.(2011)'s conclusions, that, if the interval width is of more interest, the Bayesian tail-based interval under Jeffreys'prior performs better than the score-based confidence interval, we calculated required sample size using ALC(Average length criterion) criteria based on the tail-based intervals of RD, and do the same thing using maximum posterior variance and average posterior variance criteria based on the posterior variance of RD.