Accuracy Evaluation of the Unified P-Value from Combining Correlated P-Values

Meta-analysis methods that combine -values into a single unified -value are frequently employed to improve confidence in hypothesis testing. An assumption made by most meta-analysis methods is that the -values to be combined are independent, which may not always be true. To investigate the accuracy of the unified -value from combining correlated -values, we have evaluated a family of statistical methods that combine: independent, weighted independent, correlated, and weighted correlated -values. Statistical accuracy evaluation by combining simulated correlated -values showed that correlation among -values can have a significant effect on the accuracy of the combined -value obtained. Among the statistical methods evaluated those that weight -values compute more accurate combined -values than those that do not. Also, statistical methods that utilize the correlation information have the best performance, producing significantly more accurate combined -values. In our study we have demonstrated that statistical methods that combine -values based on the assumption of independence can produce inaccurate -values when combining correlated -values, even when the -values are only weakly correlated. Therefore, to prevent from drawing false conclusions during hypothesis testing, our study advises caution be used when interpreting the -value obtained from combining -values of unknown correlation. However, when the correlation information is available, the weighting-capable statistical method, first introduced by Brown and recently modified by Hou, seems to perform the best amongst the methods investigated.