Meta-analysis is an area of modern biostatistics where statisticians are in some danger of falling behind the galloping onrush of applications and even newly proposed statistical methods (some as yet unevaluated) that appear in medical and epidemiological journals. Normand's tutorial is therefore very welcome as an overview and introduction for statisticians who may not have received formal training on this topic or been able to keep up with the diverse literature. It is di$cult, however, to cover such a complex topic fully in the space of one article and I feel that her treatment could be usefully augmented in a number of ways, both theoretical/conceptual and practical.
A conceptual issue that may trouble some readers of the tutorial is that there is no clear statement of what is meant by &combining' study results together to produce a single summary measure. I prefer to think of this in statistical terms as estimating a parameter in an appropriate statistical model, and I think that especially for statisticians this should encourage greater clarity in the formulation and interpretation of speci"c meta-analyses. For example, I believe it clari"es the thorny issue of &"xed' versus &random' e!ects methods. The former, more appropriately termed a &"xed e+ect' method, proposes that there is a common true e!ect in all studies being meta-analysed, and so &the only source of uncertainty is that resulting from the sampling of people into studies' (Normand, p. 325). The underlying model does not allow that the true e!ects might di!er across the studies being analysed (because, for example, of di!erences in the populations studied or the intervention applied). I do not understand how this model can be justi"ed by the fact that &interest is centred on making inferences for the very populations that have been sampled' (Normand, p. 324). Whatever our ultimate interest, our model should be governed by what we regard as a reasonable a priori representation of uncertainty about the unknown quantities of interest. A more appropriate frame of thinking for this question is described at the beginning of the tutorial's Section 4.2, but I believe the user should be encouraged to think in terms of underlying models and parameters to be estimated from the very "rst stages of formulating the meta-analysis.
There would be other potential advantages of emphasizing the distinction between parameters and estimates/estimators more strongly than is done in Normand's tutorial. First, it might bring into question