Assessing the implications of publication bias for two popular estimates of between-study variance in meta-analysis

Perhaps the greatest threat to the validity of a meta-analysis is the possibility of publication bias, where studies with interesting or statistically significant results are more likely to be published. This obviously impacts on inference concerning the treatment effect but also has implications for estimates of between-study variance. Two popular and established estimation methods are considered and formulae for assessing the implications of the bias are provided in terms of a general process for selecting studies. Meta-analysts, concerned that publication bias may be present, can use these as part of a sensitivity analysis to assess the robustness of their estimates of between-study variance using any selection process that is likely to be used in practice. The procedure is illustrated using a meta-analysis of clinical trials concerning the effectiveness of endoscopic sclerotherapy for preventing death in patients with cirrhosis and oesophagogastric varices.