Extending Integrated Nested Laplace Approximation to a Class of Near‐Gaussian Latent Models

Martins, Thiago G.; Rue, Håvard

doi:10.1111/sjos.12073

Cited by 21 publications

(29 citation statements)

References 18 publications

(41 reference statements)

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“…Even if

β_{x}

and x are assumed to be normally distributed, their product is not. As a consequence the latent field v would not be Gaussian if

{italicβ}_{x} x

is included directly as part of v , and the approximations that are used throughout the INLA methodology would not be accurate; see Martins and Rue (). To incorporate product structures, one of the factors, say

β_{x}

, must be treated as a hyperparameter, i.e.…”

Section: Analysis Of Measurement Error Models By Using the Integratedmentioning

confidence: 99%

Bayesian Analysis of Measurement Error Models Using Integrated Nested Laplace Approximations

Muff

Riebler

Held

et al. 2014

Journal of the Royal Statistical Society Series C: Applied Statistics

Self Cite

103

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Summary To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge can be incorporated in the prior distributions. Recently, integrated nested Laplace approximations have been proven to be a computationally convenient alternative to sampling approaches for Bayesian inference in latent Gaussian models. We show how the most common approaches to adjust for ME, the classical and the Berkson ME, fit into this framework. This is achieved through a reformulation with augmented pseudo‐observations and a suitable extension of the latent Gaussian field. Two specific classes are described, which allow for a particularly simple implementation using integrated nested Laplace approximations. We present three applications within the framework of generalized linear (mixed) models with ME. To illustrate the practical feasibility, R code is provided in on‐line supplementary material.

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“…Even if

β_{x}

and x are assumed to be normally distributed, their product is not. As a consequence the latent field v would not be Gaussian if

{italicβ}_{x} x

β_{x}

, must be treated as a hyperparameter, i.e.…”

Section: Analysis Of Measurement Error Models By Using the Integratedmentioning

confidence: 99%

Bayesian Analysis of Measurement Error Models Using Integrated Nested Laplace Approximations

Muff

Riebler

Held

et al. 2014

Journal of the Royal Statistical Society Series C: Applied Statistics

Self Cite

103

View full text Add to dashboard Cite

show abstract

“…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 . 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%

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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“…The main challenge in applying INLA to latent models is that the approach depends heavily on the latent Gaussian prior assumption to work properly. For further details on this issue see [75]. Recently, Martins & Rue [75] proposed an extension that allows INLA to be applied to models where some independent components of the latent field have a so-called “near-Gaussian” prior distribution.…”

Section: Discussionmentioning

confidence: 99%

“…For further details on this issue see [75]. Recently, Martins & Rue [75] proposed an extension that allows INLA to be applied to models where some independent components of the latent field have a so-called “near-Gaussian” prior distribution. All in all, the assumption of Gaussian distributed random effects that is usually taken for granted may be subject to criticism, and there are a number of situations in which this might not be a realistic assumption.…”

Section: Discussionmentioning

confidence: 99%

“…However, the Bayesian toolbox used is all-purpose and can be applied to detect other more complex forms of misspecification as well, such as non-Gaussian distributed random effects [75], alternative functional relationships in the population-mean structure, random effects precisions depending on a binary covariate (e.g. treatment group), alternative prior distributions or different hyperprior parameter values.…”

Section: Discussionmentioning

confidence: 99%

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Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: An example from a vertigo phase III study with longitudinal count data as primary endpoint

Adrion

Mansmann

2012

BMC Med Res Methodol

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BackgroundA statistical analysis plan (SAP) is a critical link between how a clinical trial is conducted and the clinical study report. To secure objective study results, regulatory bodies expect that the SAP will meet requirements in pre-specifying inferential analyses and other important statistical techniques. To write a good SAP for model-based sensitivity and ancillary analyses involves non-trivial decisions on and justification of many aspects of the chosen setting. In particular, trials with longitudinal count data as primary endpoints pose challenges for model choice and model validation. In the random effects setting, frequentist strategies for model assessment and model diagnosis are complex and not easily implemented and have several limitations. Therefore, it is of interest to explore Bayesian alternatives which provide the needed decision support to finalize a SAP.MethodsWe focus on generalized linear mixed models (GLMMs) for the analysis of longitudinal count data. A series of distributions with over- and under-dispersion is considered. Additionally, the structure of the variance components is modified. We perform a simulation study to investigate the discriminatory power of Bayesian tools for model criticism in different scenarios derived from the model setting. We apply the findings to the data from an open clinical trial on vertigo attacks. These data are seen as pilot data for an ongoing phase III trial. To fit GLMMs we use a novel Bayesian computational approach based on integrated nested Laplace approximations (INLAs). The INLA methodology enables the direct computation of leave-one-out predictive distributions. These distributions are crucial for Bayesian model assessment. We evaluate competing GLMMs for longitudinal count data according to the deviance information criterion (DIC) or probability integral transform (PIT), and by using proper scoring rules (e.g. the logarithmic score).ResultsThe instruments under study provide excellent tools for preparing decisions within the SAP in a transparent way when structuring the primary analysis, sensitivity or ancillary analyses, and specific analyses for secondary endpoints. The mean logarithmic score and DIC discriminate well between different model scenarios. It becomes obvious that the naive choice of a conventional random effects Poisson model is often inappropriate for real-life count data. The findings are used to specify an appropriate mixed model employed in the sensitivity analyses of an ongoing phase III trial.ConclusionsThe proposed Bayesian methods are not only appealing for inference but notably provide a sophisticated insight into different aspects of model performance, such as forecast verification or calibration checks, and can be applied within the model selection process. The mean of the logarithmic score is a robust tool for model ranking and is not sensitive to sample size. Therefore, these Bayesian model selection techniques offer helpful decision support for shaping sensitivity and ancillary analyses in a statistical analysis p...

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Extending Integrated Nested Laplace Approximation to a Class of Near‐Gaussian Latent Models

Cited by 21 publications

References 18 publications

Bayesian Analysis of Measurement Error Models Using Integrated Nested Laplace Approximations

Bayesian Analysis of Measurement Error Models Using Integrated Nested Laplace Approximations

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

Bayesian model selection techniques as decision support for shaping a statistical analysis plan of a clinical trial: An example from a vertigo phase III study with longitudinal count data as primary endpoint

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