The Testing of Normality in Meta-Analysis Method under Mixed Effect Model

One of the procedure of meta-analysis method is pooled estimators from different studies. We always assume the statistics from different studies are from normal distribution. The normality has nice propensities (ex: symmetry distribution) for sampling distribution. We could be easy to construct the confidence interval of parameters and the Wald statistics to use to perform tests of hypotheses on parameters. In practice, we never discuss and test for normality about the statistics in meta-analysis. We only care about the homogeneity test, the summary estimator and testing overall effect in meta-analysis. The normality is very import, because the meta-analysis results of estimation and testing the overall effect are based on normality assumption, regardless of fixed and random effect model. Chen(2015) discussed the type I error rate and power of goodness-of-fit testing for meta-analysis, including Anderson-Darling test(AD), Cramer-von Mises test(CvM), Shapiro-Wilk test(SW). They simulated the statistics of each study form distribution. This was unreasonable and not realistic. The statistics of each study should be estimated from samples of each study in practice. In this study, we focus on category variables, just 2x2 table, for example, case-control study, cohort study, from clinical trial data or specific phenotype study et al. The samples of each study would simulate from mixed effect logistic regression model. We would discuss type I error rate and power of the normality for statistics from each study under different goodness-of-fit test and also compare with the results in Chen(2015). Finally, we also apply our method to analyze a real data sets of meta-analysis.