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Meta-Analysis With Fixed, Unknown, Study-Specific Parameters

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  • Brian Claggett
  • Minge Xie
  • Lu Tian

Abstract

Meta-analysis is a valuable tool for combining information from independent studies. However, most common meta-analysis techniques rely on distributional assumptions that are difficult, if not impossible, to verify. For instance, in the commonly used fixed-effects and random-effects models, we take for granted that the underlying study-level parameters are either exactly the same across individual studies or that they are realizations of a random sample from a population, often under a parametric distributional assumption. In this article, we present a new framework for summarizing information obtained from multiple studies and make inference that is not dependent on any distributional assumption for the study-level parameters. Specifically, we assume the study-level parameters are unknown, fixed parameters and draw inferences about, for example, the quantiles of this set of parameters using study-specific summary statistics. This type of problem is known to be quite challenging (see Hall and Miller). We use a novel resampling method via the confidence distributions of the study-level parameters to construct confidence intervals for the above quantiles. We justify the validity of the interval estimation procedure asymptotically and compare the new procedure with the standard bootstrapping method. We also illustrate our proposal with the data from a recent meta-analysis of the treatment effect from an antioxidant on the prevention of contrast-induced nephropathy.

Suggested Citation

  • Brian Claggett & Minge Xie & Lu Tian, 2014. "Meta-Analysis With Fixed, Unknown, Study-Specific Parameters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1660-1671, December.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:508:p:1660-1671
    DOI: 10.1080/01621459.2014.957288
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    Cited by:

    1. Wei, Waverly & Zhou, Yuqing & Zheng, Zeyu & Wang, Jingshen, 2024. "Inference on the best policies with many covariates," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Guang Yang & Dungang Liu & Junyuan Wang & Min‐ge Xie, 2016. "Meta‐analysis framework for exact inferences with application to the analysis of rare events," Biometrics, The International Biometric Society, vol. 72(4), pages 1378-1386, December.
    3. Ruoyu Wang & Qihua Wang & Wang Miao, 2023. "A robust fusion-extraction procedure with summary statistics in the presence of biased sources," Biometrika, Biometrika Trust, vol. 110(4), pages 1023-1040.
    4. Li, Haoqi & Lin, Huazhen & Yip, Paul S.F. & Li, Yuan, 2019. "Estimating population size of heterogeneous populations with large data sets and a large number of parameters," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 34-44.

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