Accuracy evaluation of the unified P-value from combining correlated P-values

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