Goodness-of-fit test for meta-analysis

Meta-analysis is a very useful tool to combine information from different sources. Fixed effect and random effect models are widely used in meta-analysis. Despite their popularity, they may give us misleading results if the models don't fit the data but are blindly used. Therefore, like any statistical analysis, checking the model fitting is an important step. However, in practice, the goodness-of-fit in meta-analysis is rarely discussed. In this paper, we propose some tests to check the goodness-of-fit for the fixed and random effect models with assumption of normal distributions in meta-analysis. Through simulation study, we show that the proposed tests control type I error rate very well. To demonstrate the usefulness of the proposed tests, we also apply them to some real data sets. Our study shows that the proposed tests are useful tools in checking the goodness-of-fit of the normal models used in meta-analysis.