Interpreting meta-regression: application to recent controversies in antidepressants' efficacy - Petkova, Eva; Tarpey, Thaddeus; Huang, Lei; Deng, Liping (Statistics in medicine, 2013)
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.