The Endogenous Kink (EK) method for publication bias correction

Dear meta-analysts: Heiko Rachinger and I have prepared a Stata code for implementing our endogenous kink (EK) method for correcting for publication bias, which we develop in a paper that has been recently published in Research Synthesis Methods. The code is available for downloading here. The code is very simple to use and requires only supplying an Excel file with the estimates and their standard errors (see instructions in the code file).

For those of you who are unfamiliar with the EK method, it fits a piecewise linear meta-regression of the estimates on the standard errors. Denoting the estimates by Ei and the standard errors by SEi, EK’s meta-regression specification is:

Ei = α1 + δ*(SEi-a)*I(SEi>=a) + ui

where a is an endogenously determined cutoff value (the kink), I(SE>=a) is a dummy variable (1 if SE>=a, 0 otherwise), and u is the error term. The code returns the EK’s estimate and standard error of the mean true effect size (α1) and the EK’s estimate and standard error of the intensity of publication bias (δ).

The intuition behind the EK method is straightforward: Estimates for which SE<a tend to be sufficiently precise to reach statistical significance, given a first-step estimate of the true effect, and are thus unlikely to be publication-selected; for these, the model just fits a constant. Estimates for which SE>a, on the other hand, are more likely to be statistically insignificant and thus selected out; for these, the model fits a line with slope δ. The model thus assumes a nonlinear relation between estimates and standard errors (like PEESE, for example) and includes FAT-PET as a special case (for a<=0).

Feel free to use and share the code. Any comments or suggestions are most welcome at Pedro Bom

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