Sensitivity Analysis for Bayesian Hierarchical Models

Roos, Małgorzata; Martins, Thiago G.; Held, Leonhard; Rue, Håvard

doi:10.1214/14-ba909

Cited by 67 publications

(60 citation statements)

References 48 publications

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“…JH suggests communicating the distance by considering how much a coin would be weighted to achieve that distance from a fair coin. While we agree that some sort of physical analogy would be appealing (see Roos et al, 2015, for work in this direction), we think that there is still some distance to go. For instance, the fairly REJOINDER 45 stringent condition that σ < 1 for a Gaussian random effect would be mapped to a weighted coin with the alarming property that the probability of getting a head was less than 96%.…”

Section: Daniel Simpson Is a Reader In Statistics Department Of Mathmentioning

confidence: 74%

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You Just Keep on Pushing My Love over the Borderline: A Rejoinder

Simpson¹,

Rue²,

Riebler³

et al. 2017

Statist. Sci.

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The entire reason that we wrote this paper was to provide a concrete object around which to focus a broader discussion about prior choice and we are extremely grateful to the editorial team at Statistical Science for this opportunity. David Dunson (DD), Jim Hodges (JH), Christian Robert, Judith Rousseau (RR) and James Scott (JS) have taken this discussion in diverse and challenging directions and over the next few pages, we will try to respond to the main points they have raised. "IF I COULD LOVE, I WOULD LOVE YOU ALL."-KIKI DURANEThe point of departure for our paper is that most modern statistical models are built to be flexible enough to model diverse data generating mechanisms. Good statistical practice requires us to limit this flexibility, which is typically controlled by a small number of parameters, to the amount "needed" to model the data at hand. The Bayesian framework provides a natural method for doing this although, as DD points out, this trend for penalising model complexity casts a broad shadow over all of modern statistics and data science.The PC prior framework argues for setting priors on these flexibility parameters that are specifically built to penalise a certain type of complexity and avoid overfitting. The discussants raised various points about this core idea. First, DD pointed out that while over-fitting a model is a bad thing, under-fitting is not better: we do not want Occam's razor to slit our throat. We saw this behaviour when using a half-Normal prior on the distance, while the exponential prior does not lead to obvious attenuation of the estimates. This is confirmed experimentally by Klein and Kneib (2016).Both DD and RR note our focus on a specific parameterisation and DD (as well as a large number of reviewers) note that our informal definition of overfitting is parameterisation dependent. We did this on purpose: most people who use complex statistical models do not understand prior mass conditions in terms of Kullback-Leibler balls and the theoretical results in the paper do not justify this level of mathematical sophistication. Our choice to sacrifice generality (and annoy reviewers) in the search for a clear exposition has lead us to a revelation: we can replace questions about prior choice with questions about parameterisation. This leads us to re-phrase DD's implied question: How should we parameterise a flexibility parameter so that we can use an exponential prior?The parameterisation we chose waswhere ξ is the original flexibility parameter indexing model f ξ and f 0 is the base model. JH correctly tweaks our nose over our inability to communicate this distance in a meaningful way (a heinous sin for people who abandoned measure theory in a quest for clarity). While we personally find our interpretationd(ξ ) is the amount of information you lose by abandoning the flexible component in favour of the base model-appealing, it is a bit dry and abstract. JH suggests communicating the distance by considering how much a coin would be weighted to achieve that distance from a fair co...

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Section: Daniel Simpson Is a Reader In Statistics Department Of Mathmentioning

confidence: 74%

mentioning

confidence: 74%

You Just Keep on Pushing My Love over the Borderline: A Rejoinder

Simpson¹,

Rue²,

Riebler³

et al. 2017

Statist. Sci.

Self Cite

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“…Moreover, checking sensitivity of heterogeneity and inconsistency parameters to the chosen prior distributions may be particularly useful for NMA models. Although we did not discuss any sensitivity analysis, it can be easily conducted due to the computational speed of INLA . We note that the standard ranking of treatments as discussed in Lu and Ades is not possible using INLA.…”

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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“…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.…”

Section: Discussionmentioning

confidence: 99%

Network meta‐analysis with integrated nested Laplace approximations

Sauter

Held

2015

Biometrical J

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Analyzing the collected evidence of a systematic review in form of a network meta-analysis (NMA) enjoys increasing popularity and provides a valuable instrument for decision making. Bayesian inference of NMA models is often propagated, especially if correlated random effects for multiarm trials are included. The standard choice for Bayesian inference is Markov chain Monte Carlo (MCMC) sampling, which is computationally intensive. An alternative to MCMC sampling is the recently suggested approximate Bayesian method of integrated nested Laplace approximations (INLA) that dramatically saves computation time without any substantial loss in accuracy. We show how INLA apply to NMA models for summary level as well as trial-arm level data. Specifically, we outline the modeling of multiarm trials and inference for functional contrasts with INLA. We demonstrate how INLA facilitate the assessment of network inconsistency with node-splitting. Three applications illustrate the use of INLA for a NMA.

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Sensitivity Analysis for Bayesian Hierarchical Models

Cited by 67 publications

References 48 publications

You Just Keep on Pushing My Love over the Borderline: A Rejoinder

You Just Keep on Pushing My Love over the Borderline: A Rejoinder

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

Network meta‐analysis with integrated nested Laplace approximations

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