The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference

Böhning, D. and Kuhnert, R. (2005) The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference. Statistical Papers, 46 (4). pp. 541-554. ISSN 0932-5026 doi: 10.1007/BF02763004

Abstract/Summary

We consider the case of a multicenter trial in which the center specific sample sizes are potentially small. Under homogeneity, the conventional procedure is to pool information using a weighted estimator where the weights used are inverse estimated center-specific variances. Whereas this procedure is efficient for conventional asymptotics (e. g. center-specific sample sizes become large, number of center fixed), it is commonly believed that the efficiency of this estimator holds true also for meta-analytic asymptotics (e.g. center-specific sample size bounded, potentially small, and number of centers large). In this contribution we demonstrate that this estimator fails to be efficient. In fact, it shows a persistent bias with increasing number of centers showing that it isnot meta-consistent. In addition, we show that the Cochran and Mantel-Haenszel weighted estimators are meta-consistent and, in more generality, provide conditions on the weights such that the associated weighted estimator is meta-consistent.