Publication bias and meta-analysis for 2x2 tables: an average Markov chain Monte Carlo EM algorithm

A major difficulty in meta-analysis is publication bias. Studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results. Correcting for this bias is not possible without making untestable assumptions. In this paper, a sensitivity analysis is discussed for the meta-analysis of 2x2 tables using exact conditional distributions. A Markov chain Monte Carlo EM algorithm is used to calculate maximum likelihood estimates. A rule for increasing the accuracy of estimation and automating the choice of the number of iterations is suggested.