Background: Publication bias (PB) is known to be a threat to the validity of meta-analysis (MA) that may consequently lead to incorrect decisions in health policy. A new Bayesian approach that adjusts for PB is proposed and results compared with existing methods.

Objectives: The purpose of this work is to be able to estimate PB and adjust for it so that bias in the treatment effect is reduced.

Methods: A Bayesian approach to MA is implemented in WinBUGS software (Bayesian inference Using Gibbs Sampling). The PB/small study effect is estimated by measuring the extent to which smaller studies are giving results which are different from larger ones. The treatment effect is split into a true/unbiased effect and a bias term using a semi-parametric regression model. Data from several well-known MAs in the literature are analysed and the results contrasted with those derived from existing PB adjustment meta-analysis methods. Additionally, a simulation study has been conducted to assess the performance of the method under controlled conditions.

Results: The bias associated with each study depends on any systematic association between effect size and study precision. Thus, if all studies have approximately the same effect, the bias term is negligible. However, if smaller studies have larger effect sizes then inclusion of the bias term will mean these smaller studies will be further down-weighted with respect to the weights they would be given in a standard MA model and their influence on the pooled effect size diminished. Results of the simulation study will also be presented.

Conclusions: This approach to adjusting for PB seems promising and further work on validating using simulation studies are under way to understand further the properties of the method.