Degree irregularity and rank probability bias in network meta-analysis

Network meta-analysis (NMA) is a statistical technique for the comparison of treatment options. 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 topology 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. Conversely, these topological effects are not observed for the accuracy of treatment effect estimates. This reinforces the importance of taking into account multiple measures, rather than making decisions based on a single metric. We also find that degree regularity is a better indicator for the accuracy and precision of parameter estimates in NMA 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 parameter estimates from NMA.