CoChat
Sign Up
Cited by 513Statistical Methods and Bayesian InferenceMeta-analysis and systematic reviewsMarkov Chains and Monte Carlo Methods

How vague is vague?: a simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS

Lambert, Paul C., Sutton, Alex J., Burton, Paul R., Abrams, Keith R., Jones, David R.·2005·Statistics in Medicine
DOI 10.1002/sim.2112
Open this paper in CoChat — free account

Abstract

There has been a recent growth in the use of Bayesian methods in medical research. The main reasons for this are the development of computer intensive simulation based methods such as Markov chain Monte Carlo (MCMC), increases in computing power and the introduction of powerful software such as WinBUGS. This has enabled increasingly complex models to be fitted. The ability to fit these complex models has led to MCMC methods being used as a convenient tool by frequentists, who may have no desire to be fully Bayesian. Often researchers want 'the data to dominate' when there is no prior information and thus attempt to use vague prior distributions. However, with small amounts of data the use of vague priors can be problematic. The results are potentially sensitive to the choice of prior distribution. In general there are fewer problems with location parameters. The main problem is with scale parameters. With scale parameters, not only does one have to decide the distributional form of the prior distribution, but also whether to put the prior distribution on the variance, standard deviation or precision. We have conducted a simulation study comparing the effects of 13 different prior distributions for the scale parameter on simulated random effects meta-analysis data. We varied the number of studies (5, 10 and 30) and compared three different between-study variances to give nine different simulation scenarios. One thousand data sets were generated for each scenario and each data set was analysed using the 13 different prior distributions. The frequentist properties of bias and coverage were investigated for the between-study variance and the effect size. The choice of prior distribution was crucial when there were just five studies. There was a large variation in the estimates of the between-study variance for the 13 different prior distributions. With a large number of studies the choice of prior distribution was less important. The effect size estimated was not biased, but the precision with which it was estimated varied with the choice of prior distribution leading to varying coverage intervals and, potentially, to different statistical inferences. Again there was less of a problem with a larger number of studies. There is a particular problem if the between-study variance is close to the boundary at zero, as MCMC results tend to produce upwardly biased estimates of the between-study variance, particularly if inferences are based on the posterior mean. The choice of 'vague' prior distribution can lead to a marked variation in results, particularly in small studies. Sensitivity to the choice of prior distribution should always be assessed.

Integrity signals

Registry

Crossref · 10.1002/sim.2112

Cites

35 of 35 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The choice of prior distribution can have substantial effects on the results of a Bayesian meta-analysis.

    “The choice of prior distribution, even among those that are intended to be non-informative, can have substantial effects on the results of the analysis (Lambert et al., 2005).”

    From A Re-Evaluation of Random-Effects Meta-Analysis (2009) · cites this paper as Lambert et al., 2005

Cites

Flagged first, then by citations

4 of the 39 references couldn’t be matched to a known paper.

Cited by

Sorted by citations

Related

Authors
Lambert, P. C., Sutton, A. J., Burton, P. R., Abrams, K. R., & Jones, D. R.
Affiliations
University of Leicester (GB)
Corresponding author
Lambert, Paul C.
ORCID
Venue
Statistics in Medicine
Publisher
Wiley
Published
2005
Volume
24
Issue
15
Pages
2401-2428
ISSN
  • 0277-6715 (ISSN-L)
  • 1097-0258
DOI
10.1002/sim.2112
OpenAlex
W2168331993
Cited by
511
References
39
Citations by year
2026: 14 · 2025: 12 · 2024: 13 · 2023: 13 · 2022: 19 · 2021: 29 · 2020: 39 · 2019: 23 · 2018: 45 · 2017: 30 · 2016: 37 · 2015: 39 · 2014: 28 · 2013: 31 · 2012: 35
FWCI
16.23
Type
journal article
Language
en
Open access
closed
Licence
doi.wiley.com/10.1002/tdm_license_1.1 (tdm, 3895 d)
Locations
  • Statistics in Medicine (publishedVersion)
  • PubMed (publishedVersion)
  • Explore Bristol Research (publishedVersion)
  • Leicester Research Archive (University of Leicester) (submittedVersion)
  • Bristol Research (University of Bristol) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
  • Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
Keywords
prior sensitivity, scale parameter, random-effects meta-analysis, between-study variance, effect size estimation, small sample size, WinBUGS, Markov chain Monte Carlo
MeSH terms
Anti-Bacterial Agents, Bayes Theorem, Computer Simulation, Humans, Markov Chains, Monte Carlo Method, Otitis Media, Software

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review