Biometrical Journal 57 (2015) 6 1049
to MCMC sampling. Further, there is no need to examine convergence of the MCMC samples. This is a key advantage, in particular if the network is large. Indeed, for a large network the number of parameters in the model increases dramatically along with the effort required to investigate the convergence assumption for every parameter if MCMC sampling is applied. These two points make INLA more attractive to use for Bayesian inference of a NMA model.
However, there are several peculiarities in many NMA models for which the implementation in r-inla is not straightforward. The use of correlated multivariate random effects for multiarm trials using the Kronecker product for the covariance matrix is one of the specialities which we discussed. Implementation of the node-split approach is another NMA characteristic which we could accomplish in r-inla using two separate likelihoods.
Node-splitting with INLA is also possible in very large networks like the application discussed by Veroniki et al. (2013) who examine inconsistency in 40 different networks with a dichotomous outcome and a total of 303 loops. INLA has a great potential for performing Bayesian inference for NMA models and offers a major alternative to MCMC software. INLA also offers possibilities for routine prior sensitivity examination (Roos and Held, 2011; Roos et al., 2015), which may be particularly useful in a NMA. We note that ranking of treatments as discussed by Lu and Ades (2006, Section 3.5) is not possible with INLA, but this approach has been recently critized by Puhan et al. (2014) as misleading since it does not take the quality of treatment effect estimates into account.
Acknowledgment We thank Martin Schumacher who suggested to investigate the possibility to perform network meta-analyses with INLA, Gerta R ¨ucker and Milo Puhan who contributed valuable remarks and pointed to several important references and Malgorzata Roos for carefully proofreading this manuscript. Furthermore we also like to thank two anonymuous reviewer and the editor who recommended several changes which lead to substantial improvements of this paper.
Conflict of interest
The authors have declared no conflict of interest.
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