Background: Publication bias has been described as the greatest threat to the validity of meta-analysis. Methods that test for the existence of publication bias rely on suppression producing an asymmetrical funnel plot. It is widely acknowledged that heterogeneity is an alternative cause of asymmetry. If funnel plot asymmetry is present it is difficult to determine whether this is a result of heterogeneity and/or publication bias.

Objectives: To review and apply weighted distribution methodology that adjusts combined effect size estimates for publication bias. To extend this methodology to adjust for publication bias and heterogeneity simultaneously, and to extend the selection models of these methods beyond p-values. Data: The corticosteroids review taken from the CDSR, and simulation studies.

Results: Weighted distributions use two models: one for effect size and one for the selection process. The model for selection has been limited to using the p-value only. In data sets in which there is heterogeneity or the true treatment effect is null this can lead to considerable variability between estimates with very wide confidence intervals. Extending the selection model to include precision can reduce this variability and confidence interval width. Using this model it is possible to include other covariates such as study quality or type. The effect size model can be extended in a similar way. The combination of these two models allows the influence of publication bias and heterogeneity to be considered simultaneously.

Conclusions: Weighted distributions offer a flexible approach to modelling publication bias and heterogeneity that allows the impact of unpublished studies on the combined estimate to be examined. Inclusion of precision in the selection model improves results but when the true effect size is null the model can over adjust. No selection model should be used on its own but in conjunction with others to allow a sensitivity analysis.