探討以真實虛無假設個數估計量修正控制 FDR 之多重比較法

In the multiple comparisons problem, using the same significant level for each hypothesis is a common practice but in turn, it will inflate the overall type I error rate. Bonferroni (1936) suggested using the probability of rejecting at least one true null hypothesis as the Type I error rate, which is so called FWER (Family-Wise Error Rate). However, the power of the testing procedures based on FWER is very low. Benjamini and Hochberg (1995) thus proposed using the expected proportion of errors among the rejected hypotheses (FDR, False Discovery Rate). Nevertheless, most of the testing procedures proposed in the literatures assume under the weak-control. As a result, as the number of the true alternative hypotheses increases, the power of these testing methods will be decreasing dramatically. Benjamini and Hochberg (2000) used the number of the true null hypotheses (m0) to establish the testing criterion which can preserve the Type I error and in turn improve power. However, the value of m0 in experiment is often unknown; many estimators m0 have been proposed. This thesis will use Monte Carlo simulations to evaluate of the performance of the estimators under various settings. In addition, these estimators are used to form the adaptive testing procedures. We further investigate how the performance of the adaptive testing procedures based on five criteria, specificity, sensitivity, FDR, FNDR, FWER, is.