Dataset for: Bartlett-type corrections and bootstrap adjustments of likelihood-based inference methods for network meta-analysis

In network meta-analyses that synthesize direct and indirect comparison evidence concerning multiple treatments, multivariate random effects models have been routinely used for addressing between-studies heterogeneities. Although their standard inference methods depend on large sample approximations (e.g., restricted maximum likelihood [REML] estimation) for the number of trials synthesized, the numbers of trials are often moderate or small. In these situations, standard estimators cannot be expected to behave in accordance with asymptotic theory; in particular, confidence intervals cannot be assumed to exhibit their nominal coverage probabilities (also, the type-I error probabilities of the corresponding tests cannot be retained). The invalidity issue may seriously influence the overall conclusions of network meta-analyses. In this article, we develop several improved inference methods for network meta-analyses to resolve these problems. We first introduce two efficient likelihood-based inference methods, the likelihood-ratio test–based and efficient score test–based methods, in a general framework of network meta-analysis. Then, to improve the small sample inferences, we developed improved higher-order asymptotic methods using Bartlett-type corrections and bootstrap adjustment methods. The proposed methods adopt Monte Carlo approaches using parametric bootstraps to effectively circumvent complicated analytical calculations of case-by-case analyses and to permit flexible application to various statistical models network meta-analyses. These methods can also be straightforwardly applied to multivariate meta-regression analyses and to tests for the evaluation of inconsistency. In numerical evaluations via simulations, the proposed methods generally performed well compared with the ordinary REML-based inference method. Applications to two network meta-analysis datasets are provided.