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Funnels for publication bias – have we lost the plot?

With an average of 75 trials published in peer-review journals every day [1], it can get pretty complicated even for a full-time, professional data analyst to keep up with the flood of information [2]. Metaanalysis, using a set of statistical methods to integrate data from independent studies, is a god-send, as much of the groundwork of searching for relevant studies, assessing their reliability, risk of bias, and summarising the results, has already been done and results are presented in bite-size chunks in the form of ‘forest-plots’ [3]. But before we rub our hands in glee at the thought of all the time we have saved trawling through data, let us give some thought to an often used method to detect reporting bias in meta-analyses, the funnel plot. A funnel plot is a scatter diagram used to visually depict the relationship between the effect of an intervention/treatment (x axis) and study precision (y axis), of the study (Fig. 1) [4]. From a statistical point of view, the precision of the estimated intervention effect will increase with increase in study size (presuming the event rate was the same across all studies) [5], and the dots representing such larger studies will appear at the top of the funnel (a in Fig. 1), while in contrast, effect estimates from smaller studies may be expected to scatter near the bottom of the funnel (b in Fig. 1). ‘Small-study effects’ is a term used to describe a trend for smaller studies in a meta-analysis to show larger treatment effects [6]; one reason for this may be publication bias, where the chances of a small study being published is higher if the study shows a ‘statistically significant’ effect [7]. Although it should be noted that the term ‘small-study effect’ for this phenomenon is somewhat misleading, since large studies can be imprecise, just as small studies can be precise. We propose that ‘imprecise-study effects’ may be a better description. In the absence of publication bias, if both large and smaller (and both precise and imprecise) studies are published, the scatter plot should resemble a funnel. In the presence of publication bias, there will be asymmetry, as though a bite has been taken out of the funnel (Fig. 2) [8]. In standard texts about publication bias, the missing chunks always appear at the bottom, on the supposition that it is easier to filedrawer smaller studies, rather than large studies involving multi-centres, though this has recently been shown to be untrue [9]. And though putting studies in the file drawer may contribute to funnel