Implications
An implication of this is that where multiple random intercepts exist, the heterogeneity within certain combinations will be minimized. CMA can thus be used as a data mining method to identify the number of intercepts that may be present in the dataset by looking at which studies are included in the local minima that may be obtained through recombination.
A further implication of this is that arguments over inclusion or exclusion of studies may be moot when the distribution of all possible results is taken into account. A useful tool developed by Dr. Gee (reference to come when published) is the "PPES" plot (standing for "Probability of Positive Effect Size," assuming differences are scaled such that larger in a positive direction is desired). For each subset of combinations, where studies are taken j = 1, 2, ... k − 1, k at a time, the proportion of results that show a positive effect size (either WMD or SMD will work) is taken, and this is plotted against j. This can be adapted to a "PMES" plot (standing for "Probability of Minimal Effect Size"), where the proportion of studies exceeding some minimal effect size (e.g., SMD = 0.10) is taken for each value of j = 1, 2, ... k − 1, k. Where a clear effect is present, this plot should asymptote to near 1.0 fairly rapidly. With this, it is possible then that, for instance, disputes over the inclusion or exclusion of two or three studies out of a dozen or more may be framed in the context of a plot that shows a clear effect for any combination of 7 or more studies.
It is also possible through CMA to examine the relationship of covariates with effect sizes. For example, if industry funding is suspected as a source of bias, then the proportion of studies in a given subset that were industry funded can be computed and plotted directly against the effect size estimate. If average age in the various studies was itself fairly variable, then the mean of these means across studies in a given combination can be obtained, and similarly plotted.
Read more about this topic: Combinatorial Meta-analysis
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