On correcting the overestimation of the permutation-based false discovery rate estimator

Recent attempts to account for multiple testing in the analysis of microarray data have focused on controlling the false discovery rate (FDR), which is defined as the expected percentage of the number of false positive genes among the claimed significant genes. As a consequence, the accuracy of the FDR estimators will be important for correctly controlling FDR. Xie et al. found that the standard permutation method of estimating FDR is biased and proposed to delete the predicted differentially expressed (DE) genes in the estimation of FDR for one-sample comparison. However, we notice that the formula of the FDR used in their paper is incorrect. This makes the comparison results reported in their paper unconvincing. Other problems with their method include the biased estimation of FDR caused by over- or under-deletion of DE genes in the estimation of FDR and by the implicit use of an unreasonable estimator of the true proportion of equivalently expressed (EE) genes. Due to the great importance of accurate FDR estimation in microarray data analysis, it is necessary to point out such problems and propose improved methods.

Our results confirm that the standard permutation method overestimates the FDR. With the correct FDR formula, we show the method of Xie et al. always gives biased estimation of FDR: it overestimates when the number of claimed significant genes is small, and underestimates when the number of claimed significant genes is large. To overcome these problems, we propose two modifications. The simulation results show that our estimator gives more accurate estimation.