A simple test for the difference of means in meta-analysis when study-specific variances are unreported. Issue 14 (21st September 2020)

• Record Type: Journal Article
• Authors: Sangnawakij, Patarawan; Böhning, Dankmar
• Is Part Of: Journal of statistical computation and simulation. Volume 90:Issue 14(2020)
• Page Start: 2524
• Page End: 2536
• Publication Date: 2020-09-21
• Subjects: Continuous outcome -- likelihood ratio -- missing variance -- simulation study -- t-distribution; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2020.1780235
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : Standard meta-analysis requires the quantity of interest and its estimated variance to be reported for each study. Datasets that lack such variance information pose important challenges to meta-analytic inference. In a study with continuous outcomes, only sample means and sample sizes may be reported in the treatment arm. Classical meta-analytical technique is unable to apply statistical inference to such datasets. In this paper, we propose a statistical tool for testing equal means between two groups in meta-analysis when the variances of the constituent studies are unreported, using pivot 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 errors and power probabilities of the proposed tests are investigated as metrics of their performance. The t-test statistic provides type I errors very close to the nominal significance level in all cases and has large power. The generalized likelihood ratio test statistic performs well when the number of studies is moderate-to-large. The performance of our tests surpasses that of the conventional test, which is based on the normal distribution. The difference is especially pronounced when the number of studies is small. The distribution given by our tests is also shown to closely follow the theoretical distribution.