A robust P-value for treatment effect in meta-analysis with publication bias.

Publication bias is a major and intractable problem in meta-analysis. There have been several attempts in the literature to adapt methods to allow for such bias, but these are only possible if we are prepared to make strong assumptions about the underlying selection mechanism. We discuss the assumption that the probability that a paper is published may depend in some unspecified way on the P-value being claimed by that study. We suggest a new robust P-value for the overall treatment effect, which turns out to be closely related to the correlation of the associated radial plot. Properties of the method are discussed and illustrated in two examples.