This paper addresses the use of weight functions to model publication bias in meta-analysis. Since this bias is hard to gauge, we introduce a non-parametric \(\varepsilon\)-contamination class of weight functions. We then illustrate how to explore sensitivity of conclusions to the specification of the weight function by examining the range of results for the entire class.
We find lower bounds on the coverage of confidence intervals. If no publication bias is present, results are robust even when considered over the entire \(\varepsilon\)-contamination class. However, if publication bias is present, then the coverage provided by the usual interval estimator is not robust. In this case, an alternative interval estimator is suggested. We also illustrate how both upper and lower bounds on posterior quantities of interest may be found for the case in which prior information is available.