How trace plots help interpret meta-analysis results

TL;DR

This paper highlights the usefulness of trace plots in meta-analysis, especially for visualizing sensitivity to between-study heterogeneity parameter tau, enhancing interpretation of Bayesian and frequentist results.

Contribution

It introduces and illustrates the application of trace plots in meta-analysis, emphasizing their role in understanding the impact of tau on study effect estimates.

Findings

Trace plots reveal sensitivity to tau in meta-analysis.

Bayesian and frequentist methods produce similar trace plot insights.

Implementation is facilitated by R packages bayesmeta and metafor.

Abstract

The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of tau, the between-study standard deviation, and the shrunken estimates of the study effects as a function of tau. With a small or moderate number of studies, tau is not estimated with much precision, and parameter estimates and shrunken study effect estimates can vary widely depending on the correct value of tau. The trace plot allows visualization of the sensitivity to tau along with a plot that shows which values of tau are plausible and which are implausible. A comparable frequentist or empirical Bayes version provides similar results. The concepts are illustrated using examples in meta-analysis and meta-regression; implementaton in R is facilitated in a Bayesian or frequentist framework using the bayesmeta and metafor packages, respectively.