Confidence intervals for a random-effects meta-analysis based on Bartlett-type corrections

In medical meta-analysis, the DerSimonian-Laird confidence interval for the average treatment effect has been widely adopted in practice. However, it is well known that its coverage probability (the probability that the interval actually includes the true value) can be substantially below the target level. One particular reason is that the validity of the confidence interval depends on the assumption that the number of synthesized studies is sufficiently large. In typical medical meta-analyses, the number of studies is fewer than 20. In this article, we developed three confidence intervals for improving coverage properties, based on (i) the Bartlett corrected likelihood ratio statistic, (ii) the efficient score statistic, and (iii) the Bartlett-type adjusted efficient score statistic. The Bartlett and Bartlett-type corrections improve the large sample approximations for the likelihood ratio and efficient score statistics. Through numerical evaluations by simulations, these confidence intervals demonstrated better coverage properties than the existing methods. In particular, with a moderate number of synthesized studies, the Bartlett and Bartlett-type corrected confidence intervals performed well. An application to a meta-analysis of the treatment for myocardial infarction with intravenous magnesium is presented.