Using systematic review and meta-analysis in order to obtain different empirical-informative prior for bayesian binomial proportion

Year 2021, Volume: 39 Issue: 2, 195 - 202, 02.06.2021

Esin Avcı

Abstract

The Bayesian approach provides a direct and useful inference about parameters better so than the frequentist (likelihood-only based) approach. This is because Bayesian approach uses both sources of information: prior information and likelihood. The eliciting of prior information is important because of a visible impact on the posterior inference. The motivation of this study is to avoid the subjectivity in obtaining informative prior. In order to elicit informative priors, this study proposed using systematic reviews, and the meta-analysis which is a statistical synthesis of the results from a series of empirical studies. Even though the systematic review and meta-analysis may include publication bias, may give more objective information from expert opinion due to the publishing process. This study also aimed to present the impact of domestic information obtained from domestic systematic reviews and meta-analysis on estimation proportion. Systematic reviews and meta-analysis of proportion used in order to obtain discrete, histogram, and conjugate (Beta) informative priors. The effectiveness of the Bayesian inference of proposed different informative prior distributions compared within and between (all-domestic) prior distribution. The results revealed that the discrete and histogram priors were more effective than the conjugate and non-informative priors. On the other hand, the importance of using systematic reviews and meta-analysis for domestic studies was observed.

Keywords

Bayes, informative prior, discrete, Beta, histogram, proportion, energy drink

References

• [1] Ntzoufras I. (2009). Bayesian Modeling Using WinBUGS, Hoboken-New Jersey-USA, Wily&Sons.
• [2] Bolstad, W. M. (2007). Introduction to Bayesian Statistics, 2nd Edition, Wiley-Interscience, A John Wiley&Sons, Inc., Publication.
• [3] Gelman A. (2002). Prior Distribution, Encyclopedia of Environmetrics, 3, Chichester, 1634-1637.
• [4] Borenstein M., Hedges L.V., Higgins J. P.T., Rothstein H.R. (2009). Introduction to Meta-Analysis, West Sussex-UK Wily&Sons.
• [5] Cowles M. K. (2013). Applied Bayesian Statistics: With R and OpenBUGS Examples, Springer-Verlag New York.
• [6] Kramer A. (2016). Introduction to Bayesian Inference, Oracle + DataScience.com, https://www.datascience.com/learn-data-science/fundamentals/introduction-to-bayesian-inference-data-science.
• [7] Albert J. (2009). Discrete Bayes With R. Technology Innovations in Statistics Education. 3(2).
• [8] Albert J. (2007). Bayesian Computation With R, Springer.
• [9] Spiegelhalter D. J., Abrams K. R., Myles J. P. (2004). Bayesian Approaches to Clinical Trails and Health-Care Evaluation, John Wiley&Sons, Inc., Publication.
• [10] DerSimonian R., Larid N. (1986). Meta-analysis in Clinical Trails, Control Clin Trails, 7(3), 177-188.
• [11] Barendregt J. J., Doi S. A., Lee Y. Y., Norman R. E., Vos T. (2013). Meta-analysis of Prevalence. J Epidemiol Community Health, 67(11), 974-978.
• [12] Berry S. M., Carlin B. P., Lee J. J., Muller P. (2010). Bayesian Adaptive Methods for Clinical Trials, CRC Press.
• [13] Whitehead A. (2002). Meta-Analysis of Controlled Clinical Trails, John Wiley&Sons, Inc., Publication.
• [14] Brache K., Thomas G., Stockwell T. (2012). Caffeinated alcoholic beverages in Canada: Prevalence of use, risks and recommended policy responses, Canadian Centre on Substance Abuse, 1-32.