Using pseudo-data to correct for publication bias in meta-analysis.

In many ways, adjustment for publication bias in meta-analysis parallels adjustment for ascertainment bias in genetic studies. We investigate a previously published simulation-based method for dealing with complex ascertainment bias and show that it can be modified for use in meta-analysis when publication bias is suspected. The method involves simulating sets of pseudo-data under the assumed model using guesses for the unknown parameters. The pseudo-data are subjected to the same selection criteria as are believed to have operated on the original data. A conditional likelihood is then used to estimate the adjusted values of the unknown parameters. This method is used to re-analyse a published meta-analysis of the effect of the MTHFR gene on homocysteine levels. Simulation studies show that the pseudo-data method is unbiased; they give an indication of the number of pseudo-data values required and suggest that a two-stage adjustment produces less variable estimates. This method can be thought of as an example of the selection model approach to publication bias correction. As the selection mechanism must be assumed, it is important to investigate the sensitivity of any conclusions to this assumption.