`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...

When combining results from separate investigations in a meta-analysis, random effects methods enable the modeling of differences between studies by incorporating a heterogeneity parameter ø 2 that accounts explicitly for across-study variation. We develop a simple form for the variance of Cochran's homogeneity statistic Q, leading to interval estimation of ø 2 utilizing an approximating distribution for Q; this enables us to extend the point estimation of DerSimonian and Laird. We also develop asymptotic likelihood methods and compared them with this method. We then use these approximating distributions to give a new method of calculating the weight given to the individual studies' results when estimating the overall mean which takes into account variation in these point estimates of ø 2 . Two examples illustrate the methods presented, where we show that the new weighting scheme is between the standard fixed and random effects models in down-weighting the results of large studie...

We introduce a Bayesian approach which estimates and adjusts for selection bias in a set of studies used in a meta-analysis. We use a hierarchical model for study outcome, and propose an additional model component to account for publication bias, which is the possibility that studies of interest are not equally likely to be published and hence observed studies are not a random sample. Estimation is based on the data augmentation principle and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. After examining simulation performance, we apply our techniques to a meta-analysis of 35 studies of the relationship between lung cancer and spousal exposure to environmental tobacco smoke. We find that the 95% posterior probability interval for relative risk is shifted downward after allowing for this. These results are consistent with earlier, ad hoc, approaches to this problem. Keywords and phrases: Meta-analysis, publication bias, missing studies, Markov...

It is human nature for “the affirmative or active to effect more than the negative or privative. So that a few times hitting, or presence, countervails oft-times failing or absence.”