Sensitivity Analysis of Publication Bias in Meta-analysis : A Bayesian Approach

Due to the selection process in academic publication, all meta-analysis of published literature is more or less affected by the so-called publication bias and tends to overestimate the effect of interest. Statistically, publication bias in meta-analysis is a selection bias which results from a non-random sampling from the population of unpublished studies. Several authors proposed methods of modelling publication bias using a selection model approach, which considers a joint modelling of the weight function representing the publication probability of each study and a regression of the outcome of interest. Copas (1999) showed that in this approach some of the model parameters are not estimable and a sensitivity analysis should be conducted. In implementing the Copas’s sensitivity analysis of publication bias, a practical difficulty arises in determining the range of sensitivity parameters appropriately. We propose in this article a Bayesian hierarchical model which extends Copas’s selectivity model and incorporates the experts’ opinions as a prior distribution of sensitivity parameters. We illustrate this approach with an example of the passive smoking and lung cancer meta-analysis.