Causal Inference for Meta-Analysis and Multi-Level Data Structures, with Application to Randomized Studies of Vioxx

We construct a framework for meta-analysis and other multi-level data structures that codifies the sources of heterogeneity between studies or settings in treatment effects and examines their implications for analyses. The key idea is to consider, for each of the treatments under investigation, the subject's potential outcome in each study or setting were he to receive that treatment. We consider four sources of heterogeneity: (1) response inconsistency, whereby a subject's response to a given treatment would vary across different studies or settings, (2) the grouping of nonequivalent treatments, where two or more treatments are grouped and treated as a single treatment under the incorrect assumption that a subject's responses to the different treatments would be identical, (3) nonignorable treatment assignment, and (4) response-related variability in the composition of subjects in different studies or settings. We then examine how these sources affect heterogeneity/homogeneity of conditional and unconditional treatment effects. To illustrate the utility of our approach, we re-analyze individual participant data from 29 randomized placebo-controlled studies on the cardiovascular risk of Vioxx, a Cox-2 selective nonsteroidal anti-inflammatory drug approved by the FDA in 1999 for the management of pain and withdrawn from the market in 2004.