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.
For the meta-analysis of controlled clinical trials with binary outcome a test statistic for testing an overall treatment effect is proposed, which is based on a refined estimator for the variance of the treatment effect estimator usually used in the random-effects model of meta-analysis. In simulation studies it is shown that the proposed test keeps the prescribed significance level much better than the commonly used tests in the fixed-effects and random-effects model, respectively. Moreover, when using the test it is not necessary to choose between fixed effects and random effects approaches in advance. The proposed method applies in the same way to the analysis of a controlled multi-centre study with binary outcome, including a possible interaction between drugs and centres.
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