Assessment of vague and noninformative priors for Bayesian estimation of the realized random effects in random-effects meta-analysis
Tóm tắt
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.
Tài liệu tham khảo
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)
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)
Bodnar, O., Elster, C.: Analytical derivation of the reference prior by sequential maximization of shannon’s mutual information in the multi-group parameter case. J. Stat. Plan. Inference 147, 106–116 (2014)
Bodnar, O., Elster, C., Fischer, J., Possolo, A., Toman, B.: Evaluation of uncertainty in the adjustment of fundamental constants. Metrologia 53, S46–S54 (2016)
Bodnar, O., Link, A., Arendacká, B., Possolo, A., Elster, C.: Improved estimation in random effects meta-analysis. Stat. Med. (2016). doi:10.1002/sim.7156
Bodnar, O., Link, A., Elster, C.: Objective bayesian inference for a generalized marginal random effects model. Bayesian Anal. 11, 25–45 (2016)
Cochran, W.G.: Problems arising in the analysis of a series of similar experiments. J. R. Stat. Soc. Suppl. 4, 102–118 (1937)
Cochran, W.G.: The combination of estimates from different experiments. Biometrics 10, 109–129 (1954)
DerSimonian, R., Laird, N.: Meta-analysis in clinical trials. Control. Clin. Trials 7, 177–188 (1986)
Gelman, A.: Prior distributions for variance parameters in hierarchical models. Bayesian Anal. 1, 515–533 (2006)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian data analysis. Taylor & Francis, UK (2013)
Guolo, A., Varin, C.: Random-effects meta-analysis: the number of studies matters. Stat. Methods Med. Res. (2015). doi:10.1177/0962280215583568
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)
Higgins, J., Whitehead, A.: Borrowing strength from external trials in a meta-analysis. Stat. Med. 15, 2733–2749 (1996)
Hill, B.M.: Inference about variance components in the one-way model. J. Am. Stat. Assoc. 60, 806–825 (1965)
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)
Kacker, R.N.: Combining information from interlaboratory evaluations using a random effects model. Metrologia 41, 132–136 (2004)
Klein, N., Kneib, T.: Scale-dependent priors for variance parameters in structured additive distributional regression. Bayesian Anal. 11(4), 1071–1106 (2016)
Knapp, G., Hartung, J.: Improved tests for a random effects meta-regression with a single covariate. Stat. Med. 22, 2693–2710 (2003)
Lambert, P.C., Sutton, A.J., Burton, P.R., Abrams, K.R., Jones, D.R.: How vague is vague? a simulation study of the impact of the use of vague prior distributions in mcmc using winbugs. Stat. Med. 24, 2401–2428 (2005)
McCulloch, C.E., Neuhaus, J.M.: Generalized linear mixed models. Wiley Online Library, New York (2001)
Mohr, P.J., Taylor, B.N., Newell, D.B.: Codata recommended values of the fundamental physical constants: 2010. J. Phys. Chem. Ref. Data 41, 043109 (2012)
Mohr, P.J., Taylor, B.N., Newell, D.B.: Codata recommended values of the fundamental physical constants: 2010. Rev. Mod. Phys. 84, 1527–1605 (2012)
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)
Ohlssen, D.I., Sharples, L.D., Spiegelhalter, D.J.: Flexible random-effects models using Bayesian semi-parametric models: applications to institutional comparisons. Stat. Med. 26, 2088–2112 (2007)
Paule, R.C., Mandel, J.: Consensus values and weighting factors. J. Res. Natl. Bureau Stand. 87, 377–385 (1982)
Pullenayegum, E.M.: An informed reference prior for between-study heterogeneity in meta-analyses of binary outcomes. Stat. Med. 30, 3082–3094 (2011)
Rao, P.S.R.S.: Variance components estimation: mixed models, methodologies, and applications. Chapman and Hall, London (1997)
Sahai, H., Ojeda, M.: Analysis of variance for random models. Unbalanced data, vol. 2. Birkhauser, Boston, Basel, Berlin (2004)
Searle, S.R., Casella, G., McCulloch, C.E.: Variance components, vol. 391. Wiley, New York (2009)
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)
Smith, T.C., Spiegelhalter, D.J., Thomas, A.: Bayesian approaches to random-effects meta-analysis: a comparative study. Stat. Med. 14, 2685–2699 (1995)
Stone, M., Springer, B.G.F.: A paradox involving quasi-prior distributions. Biometrika 52, 623–627 (1965)
Sun, D., Berger, J.: Reference priors with partial information. Biometrika 85, 55–71 (1998)
Sutton, A.J., Higgins, J.: Recent developments in meta-analysis. Stat. Med. 27, 625–650 (2008)
Tiao, G.C., Tan, W.Y.: Bayesian analysis of random-effect models in the analysis of variance. i: Posterior distribution of variance components. Biometrika 52, 37–53 (1965)
Toman, B.: Bayesian approaches to calculating a reference value in key comparison experiments. Technometrics 49, 81–87 (2007)
Toman, B., Fischer, J., Elster, C.: Alternative analyses of measurements of the planck constant. Metrologia 49, 567–571 (2012)
Toman, B., Possolo, A.: Laboratory effects models for interlaboratory comparisons. Accredit. Qual. Assur. 14, 553–563 (2009)
Turner, R.M., Davey, J., Clarke, M.J., Thompson, S.G., Higgins, J.: Predicting the extent of heterogeneity in meta-analysis, using empirical data from the cochrane database of systematic reviews. Int. J. Epidemiol. 41, 818–827 (2012)
Turner, R.M., Jackson, D., Wei, Y., Thompson, S.G., Higgins, J.: Predictive distributions for between-study heterogeneity and simple methods for their application in bayesian meta-analysis. Stat. Med. 34, 984–998 (2015)
Warn, D.E., Thompson, S.G., Spiegelhalter, D.J.: Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales. Stat. Med. 21, 1601–1623 (2002)
Yates, F., Cochran, W.G.: The analysis of groups of experiments. J. Agric. Sci. 28, 556–580 (1938)