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Nonparametric inference procedure for percentiles of the random effects distribution in meta-analysis. (English) Zbl 1189.62177

Summary: To investigate whether treating cancer patients with erythropoiesis-stimulating agents (ESAs) would increase the mortality risk, C. L. Bennett et al. [J. Am. Med. Assoc. 299, 914–924 (2008)] conducted a meta-analysis with the data from 52 phase III trials comparing ESAs with placebos 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.
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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62G10 Nonparametric hypothesis testing
65C60 Computational problems in statistics (MSC2010)
62N02 Estimation in survival analysis and censored data
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References:

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