Network meta‐analysis with integrated nested Laplace approximations

Sauter, Rafael; Held, Leonhard

doi:10.1002/bimj.201400163

Cited by 13 publications

(17 citation statements)

References 29 publications

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“…Although we have not discussed this method and not implemented it in nmaINLA; INLA of course could be used. The explanations and the necessary R‐code are presented in Sauter and Held …”

Section: Discussionmentioning

confidence: 99%

“…The explanations and the necessary R-code are presented in Sauter and Held. 25 One may find it restrictive to assume that heterogeneity and inconsistency random effects are normally distributed, hence explore different distributions for this assumption, for instance, t distribution. 42 Although this modeling approach is not in the scope of latent Gaussian models, INLA still can be used as an inference tool for such models.…”

Section: Discussionmentioning

confidence: 99%

“…The R‐INLA package is available on INLA website (http://www.r‐inla.org/). The use of R‐INLA to fit different NMA models including Lu‐Ades model is explained in Sauter and Held and the accompanying Supporting Information. However, for the practitioner carrying out an NMA, the range of options and the required knowledge of available features in R‐INLA might be overwhelming.…”

Section: Bayesian Inference For Fitting Network Meta‐analysis Models mentioning

confidence: 99%

“…The second application includes 24 trials investigating interventions to aid smoking cessation and has been considered by Jackson et al and Sauter and Held among others. The number of individuals who successfully quits smoking after 6 to 12 months is reported for 4 different interventions (1 , no contact; 2 , self‐help; 3 , individual counseling; and 4 , group counseling).…”

Section: Applicationsmentioning

confidence: 99%

“…Paul et al introduced INLA implementation of bivariate meta‐analyses of diagnostic test studies. Sauter and Held showed that many NMA models that are in the class of LGMs and INLA can be used as an inference technique alternative to MCMC for NMA models. They demonstrated how INLA can be applied to a NMA model with difference‐based likelihood, with arm‐based likelihood and the node‐splitting approach …”

Section: Introductionmentioning

confidence: 99%

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A design‐by‐treatment interaction model for network meta‐analysis and meta‐regression with integrated nested Laplace approximations

Günhan

Friede

Held

2018

Research Synthesis Methods

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Network meta‐analysis (NMA) is gaining popularity for comparing multiple treatments in a single analysis. Generalized linear mixed models provide a unifying framework for NMA, allow us to analyze datasets with dichotomous, continuous or count endpoints, and take into account multiarm trials, potential heterogeneity between trials and network inconsistency. To perform inference within such NMA models, the use of Bayesian methods is often advocated. The standard inference tool is Markov chain Monte Carlo (MCMC), which is computationally expensive and requires convergence diagnostics. A deterministic approach to do fully Bayesian inference for latent Gaussian models can be achieved by integrated nested Laplace approximations (INLA), which is a fast and accurate alternative to MCMC. We show how NMA models fit in the class of latent Gaussian models and how NMA models are implemented using INLA and demonstrate that the estimates obtained by INLA are in close agreement with the ones obtained by MCMC. Specifically, we emphasize the design‐by‐treatment interaction model with random inconsistency parameters (also known as the Jackson model). Also, we have proposed a network meta‐regression model, which is constructed by incorporating trial‐level covariates to the Jackson model to explain possible sources of heterogeneity and/or inconsistency in the network. A publicly available package, , is developed to automate the INLA implementation of NMA models, which are considered in this paper. Three applications illustrate the use of INLA for a NMA.

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“…Although we have not discussed this method and not implemented it in nmaINLA; INLA of course could be used. The explanations and the necessary R‐code are presented in Sauter and Held …”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Bayesian Inference For Fitting Network Meta‐analysis Models mentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A design‐by‐treatment interaction model for network meta‐analysis and meta‐regression with integrated nested Laplace approximations

Günhan

Friede

Held

2018

Research Synthesis Methods

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Contribution to the discussion of “When should meta‐analysis avoid making hidden normality assumptions?” A Bayesian perspective

Röver

Friede

2018

Biometrical J

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We congratulate Drs. Jackson and White on a very interesting paper, providing a comprehensive summary of explicit and implicit normality and independence assumptions commonly being made in randomeffects meta-analysis that are easily overlooked and that may deserve more consideration . Some of the problems discussed, however, are less of an issue when analyses are done in a Bayesian framework. Normality assumptions are made explicit in the model's likelihood specification. Any departure from assumptions 1-4 (as listed in Tab. 3) then may cause problems, just as in the frequentist case. Additional assumptions enter the analysis in the form of the prior specification, expressing the information on parameters before taking the data into consideration. These can usually be made reasonably vague, if desired (e.g., a uniform prior for the effect µ, and a weakly informative prior for the heterogeneity τ ), and these may also be subjected to sensitivity analyses (Röver, 2017). At the inference or prediction stage, computations are usually carried out exactly, following Bayes' theorem, and, unlike in the frequentist framework, no approximations are necessary at this point (Spiegelhalter et al., 2004, Sec. 3). Normal or other approximations could of course also be used in a Bayesian analysis, e.g., when extrapolating around the posterior mode (Gelman et al., 2014, Sec. 13) or when when analysis is based on INLA (Rue et al., 2009). Such methods have been proposed for network meta-analysis (Sauter and Held, 2015;Günhan et al., 2018), however, such cases are usually explicitly indicated.To exemplify the issue, consider the smoking cessation example data (example one). We utilize the bayesmeta R package to derive the posterior distribution for the logarithmic odds ratio (log-OR), using an (improper) uniform prior for the effect µ and a half-normal prior with scale 0.5 for the heterogeneity τ (Röver, 2017). For the frequentist analyses, we use the metafor package with default settings (Viechtbauer, 2010). Figure 1 illustrates the normal approximation utilized in the construction of the confidence interval along with the effect's posterior density. The (marginal) posterior distribution is not normal, but rather a normal mixture (Röver, 2017), as becomes obvious when comparing to a normal approximation (based on matching mean and variance) that is also shown.Differences between (frequentist) normal approximation and posterior tend to be particularly large in case of substantial uncertainty in the heterogeneity parameter. While this happens especially in the common case of few studies (Friede et al., 2017a; see also Fig. 1), differences are still noticeable in the present data set consisting of twelve seemingly homogeneous OR estimates, where, due to an estimated heterogeneity of τ = 0, effectively one ends up performing a common-effect analysis in the frequentist framework. An value of τ = 0 is a "most optimistic" estimate here, in the sense that it will lead to the shortest possible confidence interval for a random-effects analy...

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Fast and accurate Bayesian model criticism and conflict diagnostics using R‐INLA

Ferkingstad

Held

Rue

2017

Stat

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Bayesian hierarchical models are increasingly popular for realistic modelling and analysis of complex data. This trend is accompanied by the need for flexible, general and computationally efficient methods for model criticism and conflict detection. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points, as, for example, with individuals in repeated measurement data. In such cases, the following question arises: Are any of the groups "outliers," or in conflict with the remaining groups? Existing general approaches aiming to answer such questions tend to be extremely computationally demanding when model fitting is based on Markov chain Monte Carlo. We show how group-level model criticism and conflict detection can be carried out quickly and accurately through integrated nested Laplace approximations (INLA). The new method is implemented as a part of the open-source R-INLA package for Bayesian computing (http://r-inla.org).

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Network meta‐analysis with integrated nested Laplace approximations

Cited by 13 publications

References 29 publications

A design‐by‐treatment interaction model for network meta‐analysis and meta‐regression with integrated nested Laplace approximations

A design‐by‐treatment interaction model for network meta‐analysis and meta‐regression with integrated nested Laplace approximations

Contribution to the discussion of “When should meta‐analysis avoid making hidden normality assumptions?” A Bayesian perspective

Fast and accurate Bayesian model criticism and conflict diagnostics using R‐INLA

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