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A simple test for the difference of means in meta-analysis when study-specific variances are unreported

A simple test for the difference of means in meta-analysis when study-specific variances are unreported
A simple test for the difference of means in meta-analysis when study-specific variances are unreported
Standard meta-analysis requires the quantity of interest and its estimated varianceto be reported for each study. Datasets that lack such variance information pose im-portant challenges to meta-analytic inference. In a study with continuous outcomes,only sample means and sample sizes may be reported in the treatment arm. Classicalmeta-analytical technique is unable to apply statistical inference to such datasets. Inthis paper, we propose a statistical tool for testing equal means between two groupsin meta-analysis when the variances of the constituent studies are unreported, usingpivot inference based on the exact t-distribution and the generalized likelihood ratio.These are considered under a fixed effect model. In simulations, the type I errorsand power probabilities of the proposed tests are investigated as metrics of theirperformance. The t-test statistic provides type I errors very close to the nominalsignificance level in all cases, and has large power. The generalized likelihood ratiotest statistic performs well when the number of studies is moderate-to-large. Theperformance of our tests surpasses that of the conventional test, which is based onthe normal distribution. The difference is especially pronounced when the numberof studies is small. The distribution given by our tests is also shown to closely followthe theoretical distribution.
0094-9655
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Sangnawakij, Patarawan
3baba4ef-a7c4-42d4-b9c2-a363ad9981a1
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Sangnawakij, Patarawan
3baba4ef-a7c4-42d4-b9c2-a363ad9981a1

Bohning, Dankmar and Sangnawakij, Patarawan (2020) A simple test for the difference of means in meta-analysis when study-specific variances are unreported. Journal of Statistical Computation and Simulation. (In Press)

Record type: Article

Abstract

Standard meta-analysis requires the quantity of interest and its estimated varianceto be reported for each study. Datasets that lack such variance information pose im-portant challenges to meta-analytic inference. In a study with continuous outcomes,only sample means and sample sizes may be reported in the treatment arm. Classicalmeta-analytical technique is unable to apply statistical inference to such datasets. Inthis paper, we propose a statistical tool for testing equal means between two groupsin meta-analysis when the variances of the constituent studies are unreported, usingpivot inference based on the exact t-distribution and the generalized likelihood ratio.These are considered under a fixed effect model. In simulations, the type I errorsand power probabilities of the proposed tests are investigated as metrics of theirperformance. The t-test statistic provides type I errors very close to the nominalsignificance level in all cases, and has large power. The generalized likelihood ratiotest statistic performs well when the number of studies is moderate-to-large. Theperformance of our tests surpasses that of the conventional test, which is based onthe normal distribution. The difference is especially pronounced when the numberof studies is small. The distribution given by our tests is also shown to closely followthe theoretical distribution.

Text
A simple test for the difference of means in meta-analysis when study-specific variances are unreported - Accepted Manuscript
Restricted to Repository staff only until 10 June 2021.
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Accepted/In Press date: 10 June 2020

Identifiers

Local EPrints ID: 441477
URI: http://eprints.soton.ac.uk/id/eprint/441477
ISSN: 0094-9655
PURE UUID: b62662c1-96c4-4f2f-b04c-49829df41bba
ORCID for Dankmar Bohning: ORCID iD orcid.org/0000-0003-0638-7106

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Date deposited: 15 Jun 2020 16:30
Last modified: 18 Feb 2021 17:17

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