Methods to assess evidence consistency in dose-response model based network meta-analysis

Network meta-analysis (NMA) simultaneously estimates multiple relative treatment effects based on evidence that forms a network of treatment comparisons. Heterogeneity in treatment definitions, such as dose, can lead to a violation of the consistency assumption that underpins NMA. Model-based NMA (MBNMA) methods have been proposed that allow functional dose-response relationships to be estimated within an NMA, which avoids lumping different doses together and thereby reduces the likelihood of inconsistency. Dose-response MBNMA relies on appropriate specification of the dose-response relationship as well as consistency of relative effects. In this article we describe methods to check for inconsistency in dose-response MBNMA models. Global and local (node-splitting) tests for inconsistency are described that account for studies with ≥3 arms that are typical in dose-finding trials. We show that consistency needs to be assessed with respect to the choice of dose-response function. We illustrate the methods using a network comparing biologics for moderate-to-severe psoriasis. By comparing results from an Emax and an exponential dose-response function we show that failure to correctly characterise the dose-response can introduce apparent inconsistency. The number of comparisons for which node-splitting is possible is also shown to be dependent on the complexity of the selected dose-response function. We highlight that the nature of dose-finding studies, which typically compare multiple doses of the same agent, provide limited scope to assess inconsistency, but these study designs help guard against inconsistency in the first place. We demonstrate the importance of assessing consistency to obtain robust relative effects to inform drug-development and policy decisions.