A semi-parametric method is developed for assessing publication bias prior to performing a meta-analysis. Summary estimates for the individual studies in the meta-analysis are assumed to have known distributional form. Selective publication is modeled using a nonparametric weight function, defined on the two-sided p-value scale. The shape of the estimated weight function provides visual evidence of the presence of bias, if it exists, and observed trends may be tested using rank order statistics or likelihood ratio tests. The method is intended as an exploratory technique prior to embarking on a standard meta-analysis.
"An Approach for Assessing Publication Bias Prior to Performing a Meta-Analysis." Statist. Sci. 7 (2) 237 - 245, May, 1992. https://doi.org/10.1214/ss/1177011363