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In meta‐analyses, it sometimes happens that smaller trials show different, often larger, treatment effects. One possible reason for such ‘small study effects’ is publication bias. This is said to occur when the chance of a smaller study being published is increased if it shows a stronger effect. Assuming no other small study effects, under the null hypothesis of no publication bias, there should be no association between effect size and effect precision (e.g. inverse standard error) among the trials in a meta‐analysis.

A number of tests for small study effects/publication bias have been developed. These use either a non‐parametric test or a regression test for association between effect size and precision. However, when the outcome is binary, the effect is summarized by the log‐risk ratio or log‐odds ratio (log OR). Unfortunately, these measures are not independent of their estimated standard error. Consequently …