10.4.2  Different reasons for funnel plot asymmetry

Although funnel plot asymmetry has long been equated with publication bias (Light 1984, Begg 1988), the funnel plot should be seen as a generic means of displaying small-study effects – a tendency for the intervention effects estimated in smaller studies to differ from those estimated in larger studies (Sterne 2000). Small-study effects may be due to reasons other than publication bias (Egger 1997a, Sterne 2000) . Some of these are shown in Table 10.4.a.

 

Differences in methodological quality are an important potential source of funnel plot asymmetry. Smaller studies tend to be conducted and analysed with less methodological rigour than larger studies (Egger 2003). Trials of lower quality also tend to show larger intervention effects (Schulz 1995). Therefore trials that would have been ‘negative’, if conducted and analysed properly, may become ‘positive’ (Figure 10.4.a, Panel C).

 

True heterogeneity in intervention effects may also lead to funnel plot asymmetry. For example, substantial benefit may be seen only in patients at high risk for the outcome which is affected by the intervention and these high risk patients are usually more likely to be included in early, small studies (Davey Smith 1994, Glasziou 1995). In addition, small trials are generally conducted before larger trials are established and in the intervening years standard treatment may have improved (resulting in smaller intervention effects in the larger trials). Furthermore, some interventions may have been implemented less thoroughly in larger trials and may, therefore, have resulted in smaller estimates of the intervention effect (Stuck 1998). Finally, it is of course possible that an asymmetrical funnel plot arises merely by the play of chance. Terrin et al. have suggested that the funnel plot is inappropriate for heterogeneous meta-analyses, drawing attention to the premise that the studies come from a single underlying population given by the originators of the funnel plot (Light 1984, Terrin 2003).

 

A proposed enhancement (Peters 2008) to the funnel plot is to include contour lines corresponding to perceived ‘milestones’ of statistical significance (P = 0.01, 0.05, 0.1 etc). This allows the statistical significance of study estimates, and areas in which studies are perceived to be missing, to be considered. Such ‘contour-enhanced’ funnel plots may help review authors to differentiate asymmetry due to publication bias from that due to other factors. For example if studies appear to be missing in areas of statistical non-significance (see Figure 10.4.b, Panel A for an example) then this adds credence to the possibility that the asymmetry is due to publication bias. Conversely, if the supposed missing studies are in areas of higher statistical significance (see Figure 10.4.b, Panel B for an example), this would suggest the cause of the asymmetry may be more likely to be due to factors other than publication bias (see Table 10.4.a). If there are no statistically significant studies then publication bias may not be a plausible explanation for funnel plot asymmetry (Ioannidis 2007b).

 

In interpreting funnel plots, systematic review authors thus need to distinguish the different possible reasons for funnel plot asymmetry listed in Table 10.4.a. Knowledge of the particular intervention, and the circumstances in which it was implemented in different studies, can help identify true heterogeneity as a cause of funnel plot asymmetry. There remains a concern that visual interpretation of funnel plots is inherently subjective. Therefore, we now discuss statistical tests for funnel plot asymmetry, and the extent to which they may assist in the objective interpretation of funnel plots. When review authors are concerned that small study effects are influencing the results of a meta-analysis, they may want to conduct sensitivity analyses in order to explore the robustness of the meta-analysis’ conclusions to different assumptions about the causes of funnel plot asymmetry: these are discussed in Section 10.4.4.