  Network meta-analysis (NMA) is a statistical technique for the comparison of
treatment options. The nodes of the network are the competing treatments and
edges represent comparisons of treatments in trials. Outcomes of Bayesian NMA
include estimates of treatment effects, and the probabilities that each
treatment is ranked best, second best and so on. How exactly network geometry
affects the accuracy and precision of these outcomes is not fully understood.
Here we carry out a simulation study and find that disparity in the number of
trials involving different treatments leads to a systematic bias in estimated
rank probabilities. This bias is associated with an increased variation in the
precision of treatment effect estimates. Using ideas from the theory of complex
networks, we define a measure of `degree irregularity' to quantify asymmetry in
the number of studies involving each treatment. Our simulations indicate that
more regular networks have more precise treatment effect estimates and smaller
bias of rank probabilities. We also find that degree regularity is a better
indicator of NMA quality than both the total number of studies in a network and
the disparity in the number of trials per comparison. These results have
implications for planning future trials. We demonstrate that choosing trials
which reduce the network's irregularity can improve the precision and accuracy
of NMA outcomes.
