Publication bias in meta-analysis: a Bayesian data-augmentation approach to account for issues exemplified in the passive smoking debate

A Bayesian approach is introduced which estimates and adjusts for publication bias in the passive smoking meta-analysis, and it is estimated that the estimated excess risk may be overstated by around 30%, both in U.S. studies and in the global collection of studies.

Abstract

"Publication bias" is a relatively new statistical phenomenon that\nonly arises when one attempts through a meta-analysis to review all studies,\nsignificant or insignificant, in order to provide a total perspective on a\nparticular issue. This has recently received some notoriety as an issue in the\nevaluation of the relative risk of lung cancer associated with passive smoking,\nfollowing legal challenges to a 1992 Environmental Protection Agency analysis\nwhich concluded that such exposure is associated with significant excess risk\nof lung cancer.\n¶ We introduce a Bayesian approach which estimates and adjusts for\npublication bias. Estimation is based on a data-augmentation principle within a\nhierarchical model, and the number and outcomes of unobserved studies are\nsimulated using Gibbs sampling methods. This technique yields a quantitative\nadjustment for the passive smoking meta-analysis. We estimate that there may be\nboth negative and positive but insignificant studies omitted, and that failing\nto allow for these would mean that the estimated excess risk may be overstated\nby around 30%, both in U.S. studies and in the global collection of\nstudies.