We evaluated the robustness of our results to possible publication bias by using funnel plots to guide a series of sensitivity analyses. Funnel plots involve plotting the outcome effect sizes against its imprecision (standard error). Estimates with larger standard errors (e.g. those derived from small sample studies) are expected to have greater spread from the meta-analytic expectation, whereas estimates with small standard errors (e.g. those derived from large sample studies) are expected to have relatively small deviations from the meta-analytic expectation. Thus, a funnel shape is expected for this type of plot, with the amount of spread of scatter continuously related to the larger standard error studies. Importantly, regardless of spread, the scatter should be symmetrical around the meta-analytic expectation. Where effect sizes are conspicuously absent from the funnel, such that the spread is asymmetrical, publication bias is possible.
