A modified test for small‐study effects in meta‐analyses of controlled trials with binary endpoints

TLDR

Publication bias in meta‑analyses is often assessed by funnel‑plot asymmetry, but formal tests can produce inflated false‑positive rates for binary outcomes, especially with large effects, few events, or uniformly sized trials. The authors propose a modified linear‑regression test for funnel‑plot asymmetry that uses the efficient score and its variance (Fisher information). They evaluate this test against existing methods through simulation studies reflecting the characteristics of published controlled trials. When between‑trial heterogeneity is low, the modified test achieves nominal false‑positive rates while retaining power comparable to the original Egger test; with high heterogeneity, no test consistently performs well.

Abstract

Publication bias and related bias in meta-analysis is often examined by visually checking for asymmetry in funnel plots of treatment effect against its standard error. Formal statistical tests of funnel plot asymmetry have been proposed, but when applied to binary outcome data these can give false-positive rates that are higher than the nominal level in some situations (large treatment effects, or few events per trial, or all trials of similar sizes). We develop a modified linear regression test for funnel plot asymmetry based on the efficient score and its variance, Fisher's information. The performance of this test is compared to the other proposed tests in simulation analyses based on the characteristics of published controlled trials. When there is little or no between-trial heterogeneity, this modified test has a false-positive rate close to the nominal level while maintaining similar power to the original linear regression test ('Egger' test). When the degree of between-trial heterogeneity is large, none of the tests that have been proposed has uniformly good properties.