A recent meta-regression of antidepressant efficacy on baseline depression severity has caused considerable controversy in the popular media. A central source of the controversy is a lack of clarity about the relation of meta-regression parameters to corresponding parameters in models for subject-level data. This paper focuses on a linear regression with continuous outcome and predictor, a case that is often considered less problematic. We frame meta-regression in a general mixture setting that encompasses both finite and infinite mixture models. In many applications of meta-analysis, the goal is to evaluate the efficacy of a treatment from several studies, and authors use meta-regression on grouped data to explain variations in the treatment efficacy by study features. When the study feature is a characteristic that has been averaged over subjects, it is difficult not to interpret the meta-regression results on a subject level, a practice that is still widespread in medical research. Although much of the attention in the literature is on methods of estimating meta-regression model parameters, our results illustrate that estimation methods cannot protect against erroneous interpretations of meta-regression on grouped data. We derive relations between meta-regression parameters and within-study model parameters and show that the conditions under which slopes from these models are equal cannot be verified on the basis of group-level information only. The effects of these model violations cannot be known without subject-level data. We conclude that interpretations of meta-regression results are highly problematic when the predictor is a subject-level characteristic that has been averaged over study subjects. Copyright © 2013 John Wiley & Sons, Ltd.
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