Modifying the false discovery rate procedure based on the information theory under arbitrary correlation structure and its performance in high-dimensional genomic data

Abstract

Abstract Background Controlling the False Discovery Rate (FDR) in Multiple Comparison Procedures (MCPs) has widespread applications in many scientific fields. Previous studies show that the correlation structure between test statistics increases the variance and bias of FDR. The objective of this study is to modify the effect of correlation in MCPs based on the information theory. We proposed three modified procedures (M1, M2, and M3) under strong, moderate, and mild assumptions based on the conditional Fisher Information of the consecutive sorted test statistics for controlling the false discovery rate under arbitrary correlation structure. The performance of the proposed procedures was compared with the Benjamini–Hochberg (BH) and Benjamini–Yekutieli (BY) procedures in simulation study and real high-dimensional data of colorectal cancer gene expressions. In the simulation study, we generated 1000 differential multivariate Gaussian features with different levels of the correlation structure and screened the significance features by the FDR controlling procedures, with strong control on the Family Wise Error Rates. Results When there was no correlation between 1000 simulated features, the performance of the BH procedure was similar to the three proposed procedures. In low to medium correlation structures the BY procedure is too conservative. The BH procedure is too liberal, and the mean number of screened features was constant at the different levels of the correlation between features. The mean number of screened features by proposed procedures was between BY and BH procedures and reduced when the correlations increased. Where the features are highly correlated the number of screened features by proposed procedures reached the Bonferroni (BF) procedure, as expected. In real data analysis the BY, BH, M1, M2, and M3 procedures were done to screen gene expressions of colorectal cancer. To fit a predictive model based on the screened features the Efficient Bayesian Logistic Regression (EBLR) model was used. The fitted EBLR models based on the screened features by M1 and M2 procedures have minimum entropies and are more efficient than BY and BH procedures. Conclusion The modified proposed procedures based on information theory, are much more flexible than BH and BY procedures for the amount of correlation between test statistics. The modified procedures avoided screening the non-informative features and so the number of screened features reduced with the increase in the level of correlation.