Exact inference on meta-analysis with generalized fixed-effects and random-effects models

ABSTRACT

Meta-analysis with fixed-effects and random-effects models provides a general framework for quantitatively summarizing multiple comparative studies. However, a majority of the conventional methods rely on large-sample approximations to justify their inference, which may be invalid and lead to erroneous conclusions, especially when the number of studies is not large, or sample sizes of the individual studies are small. In this article, we propose a set of ‘exact’ confidence intervals for the overall effect, where the coverage probabilities of the intervals can always be achieved. We start with conventional parametric fixed-effects and random-effects models, and then extend the exact methods beyond the commonly postulated Gaussian assumptions. Efficient numerical algorithms for implementing the proposed methods are developed. We also conduct simulation studies to compare the performance of our proposal to existing methods, indicating our proposed procedures are better in terms of coverage level and robustness. The new proposals are then illustrated with the data from meta-analyses for estimating the efficacy of statins and BCG vaccination.

KEYWORDS:

• Meta-analysis
• exact inference
• fixed-effects model
• random-effects model

Acknowledgments

The authors thank Professor L. J. Wei for constructive comments on the paper and kindly providing the data for the statins example. The first and fourth authors gratefully acknowledge support from NSF grant: DMS1513483. The second author acknowledges support from NIH grant: R01 HL089778-05.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

NSF [grant number DMS1513483];NIH [grant number R01 HL089778-05].

Notes on contributors

Sifan Liu

Sifan Liu is postdoctoral associate, Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ 08854.

Lu Tian

Lu Tian is associate professor, Department of Biomedical Data Science, Stanford University, Palo Alto, CA 94305.

Steve Lee

Steve Lee is statistical consultant, South San Francisco, CA 94080.

Min-ge Xie

Min- ge Xie is distinguished professor, Department of Statistics and Biostatistics, Rutgers University.