of the random effects. We re-analyzed the ESA mortality data with the new method. Our results about the center of the random effects distribution were markedly different from those reported by Bennett et al. Moreover, our procedure, which estimates the distribution of the random effects, as opposed to just a simple population average, suggests that the ESA may be beneficial to mortality for approximately a quarter of the study populations. This new meta-analysis technique can be implemented with study-level summary statistics. In contrast to existing methods for parametric random effects models, the validity of our proposal does not require the number of studies involved to be large. From the results of an extensive numerical study, we find that the new procedure performs well even with moderate individual study sample sizes.