How trace plots help interpret meta-analysis results

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; implementation in R is facilitated in a Bayesian or frequentist framework using the bayesmeta and metafor packages, respectively.