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Meta-analyses are widely used to synthesize research findings from multiple sources of evidence. Publication bias arises when statistically significant or positive findings are more likely to be reported and included in meta-analysis. Various methods have been proposed to test and adjust for publication bias. However, there is less investigation in the impact of publication bias in meta-regression models where the between-study heterogeneity can be partially explained by covariates. We conduct an extensive Monte Carlo simulation to compare available methods for assessing publication bias in meta-regression models with covariates. We examine the performance of each method under different model specifications in terms of Type I error rates and power of the test for publication bias.