Combining dependent p-values with transformation using empirical distribution of correlated data and its application...

Combining dependent $p$-values is a critical challenge in large-scale hypothesis testing, with applications in genome-wide association studies, transcriptomics, environmental studies, and meta-analyses. Existing methods-such as those based on transforming $p$-values into heavy-tailed distribution or estimating the correlation matrix of test statistics-often fail to control Type I error under complex dependency structures or rely heavily on impractical assumptions of dependency structures. To address these issues, we develop a new method consisting of two procedures: First, we propose an iterative algorithm to estimate the empirical null distribution function of dependent data. The proposed algorithm incorporates imputations of data simulated from the estimated null distribution. Second, we generate modified $p$-values based on the estimated empirical null distribution and show that these modified $p$-values are decorrelated. Combining these modified $p$-values provides more accurate Type I error control compared to existing methods. In addition, it improves statistical power through the strategy of imputation, while maintaining robustness across various dependency structures. Extensive numerical studies and real-world applications demonstrate the effectiveness of the proposed method in improving both Type I error control and testing power.