Random main effects of treatment: A case study with a network meta-analysis

Two-stage or not two-stage? That is the question for IPD meta-analysis projects

Individual participant data meta-analysis (IPDMA) projects obtain, check, harmonise and synthesise raw data from multiple studies. When undertaking the meta-analysis, researchers must decide between a two-stage or a one-stage approach. In a two-stage approach, the IPD are first analysed separately within each study to obtain aggregate data (e.g., treatment effect estimates and standard errors); then, in the second stage, these aggregate data are combined in a standard meta-analysis model (e.g., common-effect or random-effects). In a one-stage approach, the IPD from all studies are analysed in a single step using an appropriate model that accounts for clustering of participants within studies and, potentially, between-study heterogeneity (e.g., a general or generalised linear mixed model). The best approach to take is debated in the literature, and so here we provide clearer guidance for a broad audience. Both approaches are important tools for IPDMA researchers and neither are a panacea. If most studies in the IPDMA are small (few participants or events), a one-stage approach is recommended due to using a more exact likelihood. However, in other situations, researchers can choose either approach, carefully following best practice. Some previous claims recommending to always use a one-stage approach are misleading, and the two-stage approach will often suffice for most researchers. When differences do arise between the two approaches, often it is caused by researchers using different modelling assumptions or estimation methods, rather than using one or two stages per se.

The dark side of the force: Multiplicity issues in network meta-analysis and how to address them

Standard models for network meta-analysis simultaneously estimate multiple relative treatment effects. In practice, after estimation, these multiple estimates usually pass through a formal or informal selection procedure, eg, when researchers draw conclusions about the effects of the best performing treatment in the network. In this paper, we present theoretical arguments as well as results from simulations to illustrate how such practices might lead to exaggerated and overconfident statements regarding relative treatment effects. We discuss how the issue can be addressed via multilevel Bayesian modelling, where treatment effects are modelled exchangeably, and hence estimates are shrunk away from large values. We present a set of alternative models for network meta-analysis, and we show in simulations that in several scenarios, such models perform better than the usual network meta-analysis model.