Statistics and Its Interface

Volume 13 (2020)

Number 4

Model selection between the fixed-effects model and the random-effects model in meta-analysis

Pages: 501 – 510

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n4.a7

Authors

Ke Yang (Department of Mathematics, Hong Kong Baptist University, Hong Kong)

Hiu-Yee Kwan (School of Chinese Medicine, Hong Kong Baptist University, Hong Kong)

Zhiling Yu (School of Chinese Medicine, Hong Kong Baptist University, Hong Kong)

Tiejun Tong (Department of Mathematics, Hong Kong Baptist University, Hong Kong)

Abstract

The common-effect model and the random-effects model are the two most popular models for meta-analysis in the literature. To choose a proper model between them, the $Q$ statistic and the $I^2$ statistic are commonly used as the criteria. Recently, it is recognized that the fixed-effects model is also essential for meta-analysis, especially when the number of studies is small. With this new model, the existing methods are no longer sufficient for model selection in metaanalysis. In view of the demand, we propose a novel method for model selection between the fixed-effects model and the random-effects model. Specifically, we apply the Akaike information criterion (AIC) to both models and then select the model with a smaller AIC value. A real data example is also presented to illustrate how the new method can be applied. We further propose the generalized AIC (GAIC) to reduce the large variation in the AIC value, and demonstrate its superiority through real data analysis and simulation studies. To the best of our knowledge, this is the first work in meta-analysis for model selection between the fixed-effects model and the random-effects model, and we expect that our new criterion has the potential to be widely applied in meta-analysis and evidence-based medicine.

Keywords

Akaike information criterion (AIC), Common-effect model, Fixed-effects model, Meta-analysis, Model selection, Random-effects model

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Hiu-Yee Kwan’s research was supported by Research Grant Council (No. HKBU-22103017-ECS) and Natural Science Foundation of Guangdong Province (No. 2018A0303130122). Tiejun Tong’s research was supported by the Initiation Grant for Faculty Niche Research Areas (No. RC-IG-FNRA/17- 18/13) and the Century Club Sponsorship Scheme of Hong Kong Baptist University, General Research Fund (No. HKBU12303918) and National Natural Science Foundation of China (No. 11671338).

Received 11 February 2020

Accepted 5 May 2020

Published 31 July 2020