Sensitivity of treatment recommendations to bias in network meta-analysis

Network meta-analysis (NMA) pools evidence on multiple treatments to estimate relative treatment effects. Included studies are typically assessed for risk of bias; however, this provides no indication of the impact of potential bias on a decision based on the NMA. We propose methods to derive bias adjustment thresholds which measure the smallest changes to the data that result in a change of treatment decision. The methods use efficient matrix operations and can be applied to explore the consequences of bias in individual studies or aggregate treatment contrasts, in both fixed and random-effects NMA models. Complex models with multiple types of data input are handled by using an approximation to the hypothetical aggregate likelihood. The methods are illustrated with a simple NMA of thrombolytic treatments and a more complex example comparing social anxiety interventions. An accompanying R package is provided.