Publication Bias in Meta-Analysis: A Bayesian Data-Augmentation Approach to Account for Issues Exemplified in the Passive Smoking Debate

`Publication bias' is a relatively new statistical phenomenon that only arises when one attempts through a meta-analysis to review all studies, significant or insignificant, in order to provide a total perspective on a particular issue. This has recently received some notoriety as an issue in the evaluation of the relative risk of lung cancer associated with passive smoking, following legal challenges to a 1992 EPA analysis which concluded that such exposure is associated with significant excess risk of lung cancer. We introduce a Bayesian approach which estimates and adjusts for publication bias. Estimation is based on a data augmentation principle within a hierarchical model, and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. This technique yields a quantitative adjustment for the passive smoking meta-analysis. We estimate that there may be both negative and positive but insignificant studies omitted, and that failing to allow for these woul..