Abstract:
This paper develops and illustrates the use of hierarchical Bayes linear models for meta-analyses. The methodology can be thought of as a compromise between the fixed-effect meta-analytic methods that are most often used in the literature (properly criticized for ignoring sources of among-study variation) and the more extreme critics of meta-analysis who argue that it is almost never appropriate to combine results from disparate studies. After reviewing the recommendations of a recent NAS report on combining information, the paper explains the data requirements, the statistical models and the prior distributions used in the hierarchical Bayes approach. Much of the focus is on the estimation and interpretation of the standard deviation, tau, of interstudy differences in effects. To this end, a special plot, called a trace plot, is introduced that shows the role of tau in the meta-analysis. Another useful graph summarizes the "shrinkage" property of the Bayesian posterior distributions of the study-specific effect estimates. The methodology is illustrated with a meta-analysis of 9 studies of the effect of indoor air pollution on childhood respiratory illness. Two analyses of these data (originally collected and analyzed by Hasselblad et al., 1992) are presented. The first ignores differences in study designs, while the second uses characteristics of the studies (namely, the list of potential confounders each study considered) to build a model to explain differences in effects among studies, and to estimate the average effect that would be found in studies that adjust for all three of the potential confounders being considered.
tr27.pdf