For a recent workshop on meta-analysis in ecology, given by Julia Koricheva , I put together a brief 'how to' in R using the metafor package, which can be found here. One of the most valuable parts of this workshop was the matter of independence of observations in data sets. While 'meta-regression' techniques mostly resolve this issue by allowing for the specification of random effects (e.g. nesting multiple observations within a study), the calculation of within-study observations often makes use of a common control. This issue could arise when a study has multiple levels of a co-variate of interest. For example, if you are interested in the response of plant growth to CO2 enrichment, and a study uses multiple levels of CO2. By excluding data from your analysis, one could unintentionally introduce bias to your analysis, but the same could be true by not properly accounting for the non-independence among observations. Marc Lajeunesse recently illustrated how failing to account for common controls can affect the precision of study-level effect sizes and he also proposes a methodology for overcoming this issue.
Unfortunately, the implementation of his solution is somewhat complex and , as yet , has not been implemented in R or 'OpenMEE', an open-source and user-friendly program for meta-analysis. In the meantime, the next best solution would be a sensitivity analysis where one uses only one observation from a study using a common control and then comparing results with separate models that use each level of the co-variate. I would only recommend this solution when a small number of studies in the data have this issue. If multiple number of studies have similarly structured data, one could also add an explanatory (or 'moderator' ) variable to your meta-regression model (see next paragraph). The most common solution to this problem that I have seen is to classify such observations as independent in mutually exclusive categories, which reduces bias (Lajeunesse 2011). For example, one could include multiple observations from the same study by including angiosperm/gymnosperm (or species) as an additional explanatory variable in your meta-regression model. I hope that the solution to the 'common control' problem is implemented in upcoming versions of 'metafor', 'meta', and OpenMEE, as it would enable more data to be used in meta-analyses. Please let me know if anybody has any code that they would be willing to share! |