Nonparametric classes of weight functions to model publication bias

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Abstract
This paper addresses the use of weight functions to model publication bias in meta-analysis. Since publication bias is hard to gauge, a nonparametric ε-contamination class of weight functions is introduced. Sensitivity of conclusions to the specification of the weight function is explored by examining the range of results for the entire ε-contamination class. First, lower bounds are found on the coverage of confidence intervals. If little publication bias is suspected, results are robust even when considered over the entire ε-contamination class. However, if more substantial publication bias is suspected, then the coverage provided by the usual interval estimator is not robust. In this case, an alternative interval estimator is suggested. Secondly, for the case in which prior information is available, upper and lower bounds are found on posterior quantities of interest.

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