Network Meta-Analysis for Decision-Making

4Generalised Linear Models

4.1 A Unified Framework for Evidence Synthesis

Chapter 2 describes fixed and random effects models that can be used for pairwise and network meta-analysis based on aggregate data from randomised controlled trials (RCTs) reporting a binary outcome. The models are formulated within the familiar framework of generalised linear models (GLM) (McCullagh and Nelder, 1989) and applied to data with a specific likelihood (binomial) that are pooled on the log odds ratio scale using a logit link function. Chapter 3 describes methods for model critique and comparison for the same type of data.

In order to cover the variety of outcomes reported in trials and the range of data transformations required to achieve approximate linearity, we now extend this framework to allow synthesis of data with normal, binomial, Poisson and multinomial likelihoods, with identity, logit, log, complementary log–log, and probit link functions, based on the common core fixed or random effects models for the linear predictor.

We describe a general modular approach where different likelihoods and link functions may be employed, but the synthesis (or network meta-analysis model), which occurs at the level of the linear predictor, takes the exact same form in every case. Thus we present a single model for pairwise meta-analysis, indirect comparisons and network meta-analysis (mixed treatment comparisons) with or without multi-arm trials for any combination of likelihood and (appropriate) ...