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I am working on the last part of my meta-analysis. I am using a random-effects model. I am looking at uncontrolled effect sizes (difference between pre-test and post-test scores using Cohen's d).

I need to conduct a test for publication bias.

1) Given the type of meta-analysis I am running, what test should I use? I feel like based on what I read, this may be the Deeks' test.

2) I seem unable to find the formula for the any form of the tests. Could someone provide a reference that has (hopefully, easy to understand) the formula needed?

Thanks again

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    $\begingroup$ The Deeks' test is described in Deeks, J. J., Macaskill, P., & Irwig, L. (2005). The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed. Journal of Clinical Epidemiology, 58, 9, 882-893. $\endgroup$
    – User33
    Commented Jul 26, 2016 at 6:47
  • $\begingroup$ You can find plenty of useful commands in the mada R package, including that providing you the results of the Deeks test. $\endgroup$
    – Giuseppe Biondi-Zoccai
    Commented Jul 26, 2016 at 7:36
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    $\begingroup$ Note that what the tests reveal, if anything, is small study bias. Calling it publication bias implies you know what caused it. $\endgroup$
    – mdewey
    Commented Jul 26, 2016 at 8:34

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There is an extended comparison of methods to assess small study effects available here in an open source article by Moreno and colleagues entitled "Assessment of regression--based methods to adjust for publication bias through a comprehensive simulation study". Since they compare a dozen different methods under six scenarios it is hard to summarise their conclusions succinctly. Broadly speaking Egger's method using the variance as the measure of study precision and Peters' method using sample size performed well.

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