Improved tests for a random effects meta-regression with a single covariate

The explanation of heterogeneity plays an important role in meta-analysis. The random effects meta-regression model allows the inclusion of trial-specific covariates which may explain a part of the heterogeneity. We examine the commonly used tests on the parameters in the random effects meta-regression with one covariate and propose some new test statistics based on an improved estimator of the variance of the parameter estimates. The approximation of the distribution of the newly proposed tests is based on some theoretical considerations. Moreover, the newly proposed tests can easily be extended to the case of more than one covariate. In a simulation study, we compare the tests with regard to their actual significance level and we consider the log relative risk as the parameter of interest. Our simulation study reflects the meta-analysis of the efficacy of a vaccine for the prevention of tuberculosis originally discussed in Berkey et al. The simulation study shows that the newly proposed tests are superior to the commonly used test in holding the nominal significance level.