You can conduct a meta-analysis on the results from controlled studies or from observational studies. The Borenstein et al. book I previously mentioned discusses this in detail (see pages 359-361, for example). There are important things to watch out for with observational studies (read those pages and other parts of the book related to the subject), but it is certainly common to do this type of analysis. The meta-analysis is done in the same way. An important thing to keep in mind: whether the original studies are controlled (randomized, replicated, etc.) or are observational, the actual meta-analysis is of the observational type. One simply starts with "observations" of estimated effect sizes and their standard errors for each study, which is a set of observations. The precautions about the interpretation of individual observational studies always apply to the results from a meta-analysis.
... View more