Title: Meta-Regression Trees

Authors: Elise Dusseldorp, Xinru Li, Xiaogang Su, Juan C. Gonzalez,
         Jacqueline Meulman

Abstract:
In meta-analysis, the aim is to estimate an overall effect size across
studies. But is this overall effect size a good representative of the “true”
underlying effect? When the study effect sizes included in the meta-analysis
are considered to be homogeneous, the answer to this question is yes. But
often, the answer is no, because there is too much heterogeneity in the data.
To explain this heterogeneity, meta-regression is performed and study
characteristics are used as predictors. However a disadvantage of
meta-regression is that interactions are often ignored. In the current study,
we propose meta-regression trees, estimated by the R-package metacart, to
detect homogeneous subgroups of studies with regard to their effect sizes. The
resulting meta-regression tree represents interaction effects between the
characteristics and the leaves of the tree are the homogeneous subgroups.
However, due to the algorithmic nature of the method, confidence intervals of
the effects in the subgroups are too optimistic, the test of the moderator
effect(s) is too liberal, and the search strategy may result in local optima.
We propose three new extensions to overcome these problems, involving the
smooth sigmoid surrogate strategy for splitting, a special bootstrap procedure
and a permutation test. By means of a simulation study the performance of
these three extensions was investigated. In addition, the new method was
applied to a real meta-analytic data set.