Combining data from experiments that may be similar

Given data from L experiments or observational studies initially believed to be similar, it is desired to estimate the mean corresponding to an experiment or observational study, EJ, of particular interest. It is often profitable to use the data from related studies to sharpen the estimate corresponding to experiment EJ. However, it is essential that all of the data that are combined be concordant with the data from EJ. We improve the methodology first proposed by Malec & Sedransk (1992) which uses the observed data to determine the nature and amount of the pooling of the data. We do this by eliminating the need to specify a scale parameter, and by showing how the technique can accommodate unknown variance components. We show the efficacy of the method by presenting an asymptotic result about the posterior probability function associated with all partitions of the experiment means, /il5..., /<L, into subsets, and by carrying out a numerical investigation. The latter study shows that our method provides sensible estimates, in contrast to some alternatives in common use, and exhibits the large gains in precision that are possible. We also analyse a dataset from six clinical trials that studied the effect of using aspirin following a myocardial infarction. Our analysis is useful because it has a perspective that is different from other published analyses of these data.