The magnitude of small-study effects in the Cochrane Database of Systematic Reviews: an empirical study of nearly 30 000 meta-analyses

Publication bias, more generally termed as small-study effect, is a major threat to the validity of meta-analyses. Most meta-analysts rely on the p values from statistical tests to make a binary decision about the presence or absence of small-study effects. Measures are available to quantify small-study effects' magnitude, but the current literature lacks clear rules to help evidence users in judging whether such effects are minimal or substantial. This article aims to provide rules of thumb for interpreting the measures. We use six measures to evaluate small-study effects in 29932 meta-analyses from the Cochrane Database of Systematic Reviews. They include Egger's regression intercept and the skewness under both the fixed-effect and random-effects settings, the proportion of suppressed studies, and the relative change of the estimated overall result due to small-study effects. The cut-offs for different extents of small-study effects are determined based on the quantiles in these distributions. We present the empirical distributions of the six measures and propose a rough guide to interpret the measures' magnitude. The proposed rules of thumb may help evidence users grade the certainty in evidence as impacted by small-study effects.