Approximations for trimmed Fisher procedures in research synthesis

When combining the results of independent studies it often happens that some studies are potentially aberrant either in quality or in actual values. Because aberrant studies are often at the extremes, we may wish to trim some of the largest and smallest effects. In such a case the use of p-values may well serve as a diagnostic method. However, the use of ordered effects changes the distribution of the underlying statistics. We provide a discussion of the exact distribution of the trimmed version of the Fisher procedure. Because of the complexity of the exact distribution, several approximations are presented. These alternatives are applied to a meta-analysis on the effect of the dose of a drug on the risk of mortality.