Nonparametric inference procedure for percentiles of the random effects distribution in meta-analysis

TL;DR

This paper introduces a nonparametric inference method for estimating the distribution of random effects in meta-analysis, providing more detailed insights than average effects and applicable with study-level summaries.

Contribution

The paper presents a novel nonparametric approach for estimating the entire distribution of random effects in meta-analysis, unlike traditional parametric methods.

Findings

Re-analysis of ESA data shows different results about the distribution center.

The method suggests ESA may benefit mortality in about 25% of populations.

The procedure performs well with moderate sample sizes.

Abstract

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.