Simple robust procedures for combining risk differences in sets of 2 x 2 tables

Meta-analyses often use a random-effects model to incorporate unexplained heterogeneity of study results. Trimmed versions of meta-analytic estimators for the risk difference, adapted from procedures designed for a random-effects analysis, can resist the impact of a few anomalous studies. A simulation study compared untrimmed and trimmed versions of four meta-analytic procedures that give weighted averages of risk differences. An adaptation of Winsorized estimates of components of variance gains some resistance to anomalous studies when estimating variability. The simulations found that a modified version of the DerSimonian-Laird estimator is attractive when risk differences reveal the added variability described by a random-effects model, and that a 20 per cent trimmed, weighted version of this procedure offers resistance against the impact of highly anomalous results. Among four trimmed procedures considered, the trimmed version of the modified DerSimonian-Laird estimator offers the best performance over a wide range of simulation designs and sample sizes. None of the methods, whether trimmed or untrimmed, is uniformly preferable. A published meta-analysis of a vaccination against TB provides data that serve to illustrate differences among the eight procedures.