Hierarchical network meta-analysis models to address sparsity of events and differing treatment classifications with regard to adverse outcomes.

Meta-analysis for adverse events resulting from medical interventions has many challenges, in part due to small numbers of such events within primary studies. Furthermore, variability in drug dose, potential differences between drugs within the same pharmaceutical class and multiple indications for a specific treatment can all add to the complexity of the evidence base. This paper explores the use of synthesis methods, incorporating mixed treatment comparisons, to estimate the risk of adverse events for a medical intervention, while acknowledging and modelling the complexity of the structure of the evidence base. The motivating example was the effect on malignancy of three anti-tumour necrosis factor (anti-TNF) drugs (etanercept, adalimumab and infliximab) indicated to treat rheumatoid arthritis. Using data derived from 13 primary studies, a series of meta-analysis models of increasing complexity were applied. Models ranged from a straightforward comparison of anti-TNF against non-anti-TNF controls, to more complex models in which a treatment was defined by individual drug and its dose. Hierarchical models to allow 'borrowing strength' across treatment classes and dose levels, and models involving constraints on the impact of dose level, are described. These models provide a flexible approach to estimating sparse, often adverse, outcomes associated with interventions. Each model makes its own set of assumptions, and approaches to assessing goodness of fit of the various models will usually be extremely limited in their effectiveness, due to the sparse nature of the data. Both methodological and clinical considerations are required to fit realistically complex models in this area and to evaluate their appropriateness.