A modified random-effect procedure for combining risk difference in sets of \(2\times 2\) tables from clinical trials.

*(English)*Zbl 1446.62272Summary: Meta-analyses of sets of clinical trials often combine risk differences from several \(2\times 2\) tables according to a random-effects model. The DerSimonian-Laird random-effects procedure, widely used for estimating the populaton mean risk difference, weights the risk difference from each primary study inversely proportional to an estimate of its variance (the sum of the between-study variance and the conditional within-study variance). Because those weights are not independent of the risk differences, however, the procedure sometimes exhibits bias and unnatural behavior. The present paper proposes a modified weighting scheme that uses the unconditional within-study variance to avoid this source of bias. The modified procedure has variance closer to that available from weighting by ideal weights when such weights are known. We studied the modified procedure in extensive simulation experiments using situations whose parameters resemble those of actual studies in medical research. For comparison we also included two unbiased procedures, the unweighted mean and a sample-size-weighted mean; their relative variability depends on the extent of heterogeneity among the primary studies. An example illustrates the application of the procedures to actual data and the differences among the results.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

##### Keywords:

clinical trials; Dersimonian-Laird method; meta-analysis; random effects; risk difference; semiweighted mean; \(2\times 2\) tables; weighted mean##### Software:

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\textit{J. D. Emerson} et al., J. Ital. Stat. Soc. 2, No. 3, 269--290 (1993; Zbl 1446.62272)

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##### References:

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