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

If the number of treatments in a network meta-analysis is large, it may be possible and useful to model the main effect of treatment as random, that is to say as random realizations from a normal distribution of possible treatment effects. This then constitutes a third sort of random effect that may be considered in connection with such analyses. The first and most common models treatment-by-trial interaction as being random and the second, rather rarer, models the main effects of trial as being random and thus permits the recovery of intertrial information. Taking the example of a network meta-analysis of 44 similar treatments in 10 trials, we illustrate how a hierarchical approach to modeling a random main effect of treatment can be used to produce shrunk (toward the overall mean) estimates of effects for individual treatments. As a related problem, we also consider the issue of using a random-effect model for the within-trial variances from trial to trial. We provide a number of possible graphical representations of the results and discuss the advantages and disadvantages of such an approach.