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Inference for multiple and correlated treatment effects in bivariate random effects meta-analysis with small number of studies
Journal of the Korean Data & Information Science Society 2018;29:1-12
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

Minsook Kim1 · Chi Kyung Ahn2 · Donguk Kim3

123Department of Statistics, Sunkyunkwan University
Correspondence to: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail:
Received November 1, 2017; Revised November 25, 2017; Accepted November 27, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Meta-analysis is used to synthesize treatment effects from separate studies under the normality. Since the most clinical researches involve small number of studies, the inference for overall treatment effect may not be accurately estimated. Hartung and Knapp (2001) and Sidik and Jonkman (2002) proposed a refined method for univariate case to provide more accurate inference. Jackson and Riley (2014) extended this refined method to the multivariate case. They showed that the refined method for single overall treatment effect significantly improved the coverage probability (CP) over Wald type through simulation studies of 25 scenarios. In this paper we perform simulation study for inferences of a bivariate random effects meta-analysis based on the their 25 scenarios. We show that the refined method improves CP in simultaneous inference for multiple treatment effects and also how it differs from the results of inference for single treatment effect. It is revealed in our study that CP has greatly improved in simultaneous inference for multiple treatment effects than inference of single treatment effect especially in high correlation and heterogeneity.
Keywords : Bivariate random effects meta-analysis, coverage probability, heterogeneity index, multivariate t distribution, multivairate F distribution.