  To investigate whether treating cancer patients with
erythropoiesis-stimulating agents (ESAs) would increase the mortality risk,
Bennett et al. [Journal of the American Medical Association 299 (2008)
914--924] conducted a meta-analysis with the data from 52 phase III trials
comparing ESAs with placebo or standard of care. With a standard parametric
random effects modeling approach, the study concluded that ESA administration
was significantly associated with increased average mortality risk. In this
article we present a simple nonparametric inference procedure for the
distribution 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.
