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We propose simple formulas of confidence intervals for the Wald statistic,likelihood ratio statistic, and score statistic for a network meta-analysis. Inaddition, we consider resolutions for concerns that network meta-analyses witha small number of studies cannot hold a nominal confidence level. For a biasadjustment in analyses with a small number of studies, a Bartlett-typeadjustment is a well-known method. Many Bartlett-type adjustment-type methodsare based on maximum likelihood estimators. However, the network meta-analysisoften uses the restricted maximum likelihood estimators that have not beenextensively discussed in Bartlett-type adjustment. In this paper, we propose aBartlett-type adjustment method for the Wald statistic, likelihood ratiostatistic, and score statistic when nuisance parameters are estimated by notonly the maximum likelihood method but also the restricted maximum likelihoodmethod. In addition, we propose a higher-order adjustment by applying thebootstrap method to the Bartlett-type adjusted statistics. Using a computersimulation, we confirmed that the adjusted confidence intervals maintained anominal confidence level. In addition, we confirmed that the confidenceinterval of the likelihood ratio test based on the restricted maximumlikelihood method performs well without further bootstrap adjustment. Finally,we demonstrated that confidence intervals were adjusted for actual networkmeta-analysis.

Easy confidence interval formulas for network meta-analysis and adjustment of confidence intervals for a small number of studies