Assessment of vague and noninformative priors for Bayesian estimation of the realized random effects in random-effects meta-analysis
Random-effects meta-analysis has become a well-established tool applied in many areas, for example, when combining the results of several clinical studies on a treatment effect. Typically, the inference aims at the common mean and the amount of heterogeneity. In some applications, the laboratory effects are of interest, for example, when assessing uncertainties quoted by laboratories participating in an interlaboratory comparison in metrology. We consider the Bayesian estimation of the realized random effects in random-effects meta-analysis. Several vague and noninformative priors are examined as well as a proposed novel one. Conditions are established that ensure propriety of the posteriors for the realized random effects. We present extensive simulation results that assess the inference in dependence on the choice of prior as well as mis-specifications in the statistical model. Overall good performance is observed for all priors with the novel prior showing the most promising results. Finally, the uncertainties reported by eleven national metrology institutes and universities for their measurements on the Newtonian constant of gravitation are assessed.
KeywordsRandom-effects model Bayesian estimation Reference prior Newtonian constant of gravitation
Mathematics Subject Classification62F15 62P35
The authors are thankful to Professor Göran Kauermann and two anonymous Reviewers for careful reading of the paper and for their suggestions which have improved an earlier version of this paper. They also thank Alfred Link for the validation of the numerical results and for helpful discussions.
- Berger, J., Bernardo, J.M.: On the development of reference priors. In: Bernardo, J.M., Berger, J., Dawid, A.P., Smith, A.F.M. (eds.) Bayesian statistics, vol. 4, pp. 35–60. University Press, Oxford (1992)Google Scholar
- Berger, J., Bernardo, J.M.: Reference priors in a variance components problem. In: Goel, P. (ed.) Proceedings of the Indo-USA Workshop on Bayesian Analysis in Statistics and Econometrics, pp. 323–340. Springer, New-York (1992)Google Scholar
- Cochran, W.G.: The combination of estimates from different experiments. Biometrics 10, 109–129 (1954)Google Scholar
- Higgins, J., Thompson, S.G., Spiegelhalter, D.J.: A re-evaluation of random-effects meta-analysis. J. R. Stat. Soc. Ser. A (Stat. Soc.) 172, 137–159 (2009)Google Scholar
- Hurtado Rúa, S.M., Mazumdar, M., Strawderman, R.L.: The choice of prior distribution for a covariance matrix in multivariate meta-analysis: a simulation study. Stat. Med. 34, 4083–4104 (2015)Google Scholar
- McCulloch, C.E., Neuhaus, J.M.: Generalized linear mixed models. Wiley Online Library, New York (2001)Google Scholar
- Müller, I., Brade, V., Hagedorn, H.-J., Straube, E., Schörner, C., Frosch, M., Hlobil, H., Stanek, G., Hunfeld, K.-P.: Is serological testing a reliable tool in laboratory diagnosis of syphilis? Meta-analysis of eight external quality control surveys performed by the german infection serology proficiency testing program. J. Clin. Microbiol. 44, 1335–1341 (2006)CrossRefGoogle Scholar
- Sahai, H., Ojeda, M.: Analysis of variance for random models. Unbalanced data, vol. 2. Birkhauser, Boston, Basel, Berlin (2004)Google Scholar
- Simpson, D.P., Rue, H., Martins, T.G., Riebler, A., Sørbye, S.H.: Penalising model component complexity: a principled, practical approach to constructing priors Stat. Sci. (2016, to appear)Google Scholar
- Stone, M., Springer, B.G.F.: A paradox involving quasi-prior distributions. Biometrika 52, 623–627 (1965)Google Scholar