Control of the mean number of false discoveries, Bonferroni and stability of multiple testing TeX Export

@misc{gordon:glazko:qiu:yakovlev:2007, abstract = {The Bonferroni multiple testing procedure is commonly perceived as being overly conservative in large-scale simultaneous testing situations such as those that arise in microarray data analysis. The objective of the present study is to show that this popular belief is due to overly stringent requirements that are typically imposed on the procedure rather than to its conservative nature. To get over its notorious conservatism, we advocate using the Bonferroni selection rule as a procedure that controls the per family error rate (PFER). The present paper reports the first study of stability properties of the Bonferroni and Benjamini--Hochberg procedures. The Bonferroni procedure shows a superior stability in terms of the variance of both the number of true discoveries and the total number of discoveries, a property that is especially important in the presence of correlations between individual \$p\$-values. Its stability and the ability to provide strong control of the PFER make the Bonferroni procedure an attractive choice in microarray studies.}, archivePrefix = {arXiv}, author = {Gordon, Alexander and Glazko, Galina and Qiu, Xing and Yakovlev, Andrei}, citeulike-article-id = {2219578}, citeulike-linkout-0 = {http://arxiv.org/abs/0709.0366}, citeulike-linkout-1 = {http://arxiv.org/pdf/0709.0366}, citeulike-linkout-2 = {http://dx.doi.org/10.1214/07-AOAS102}, comment = {The authors propose to view Bonferroni adjustments as a method to control per family error rate (expected \# of false rejections), rather than family wise error rate (probability of one or more false rejections; FWER <= PFER). This interpretation allows raising the overall nominal level \$\gamma\$ of the procedure to values closer or greater than 1, thus increasing the ultimate p-values \$\gamma/m\$ where \$m\$ is the number of hyptotheses to be tested, and this in turn helps increasing the power. In comparisons with FDR (which is not a fair comparison, as FDR controls the expected proportion of false discoveries in all rejections), the Bonferroni procedure was found to be somewhat more stable, and an "optimum" rejection rate seems to have been discovered for the particular test setting under study.}, day = {4}, doi = {10.1214/07-AOAS102}, eprint = {0709.0366}, journal = {The Annals of Applied Statistics}, keywords = {bonferroni, fdr, multiple\_testing}, month = {Sep}, number = {1}, pages = {179--190}, posted-at = {2008-01-11 15:58:43}, priority = {0}, title = {Control of the mean number of false discoveries, Bonferroni and stability of multiple testing}, url = {http://dx.doi.org/10.1214/07-AOAS102}, volume = {1}, year = {2007} }

TY - ELEC ID - gordon:glazko:qiu:yakovlev:2007 L3 - citeulike-article-id:2219578 N2 - The Bonferroni multiple testing procedure is commonly perceived as being overly conservative in large-scale simultaneous testing situations such as those that arise in microarray data analysis. The objective of the present study is to show that this popular belief is due to overly stringent requirements that are typically imposed on the procedure rather than to its conservative nature. To get over its notorious conservatism, we advocate using the Bonferroni selection rule as a procedure that controls the per family error rate (PFER). The present paper reports the first study of stability properties of the Bonferroni and Benjamini--Hochberg procedures. The Bonferroni procedure shows a superior stability in terms of the variance of both the number of true discoveries and the total number of discoveries, a property that is especially important in the presence of correlations between individual $p$-values. Its stability and the ability to provide strong control of the PFER make the Bonferroni procedure an attractive choice in microarray studies. IS - 1 JF - The Annals of Applied Statistics EP - 190 TI - Control of the mean number of false discoveries, Bonferroni and stability of multiple testing VL - 1 SP - 179 KW - bonferroni KW - fdr KW - multiple_testing N1 - The authors propose to view Bonferroni adjustments as a method to control per family error rate (expected # of false rejections), rather than family wise error rate (probability of one or more false rejections; FWER <= PFER). This interpretation allows raising the overall nominal level $\gamma$ of the procedure to values closer or greater than 1, thus increasing the ultimate p-values $\gamma/m$ where $m$ is the number of hyptotheses to be tested, and this in turn helps increasing the power. In comparisons with FDR (which is not a fair comparison, as FDR controls the expected proportion of false discoveries in all rejections), the Bonferroni procedure was found to be somewhat more stable, and an "optimum" rejection rate seems to have been discovered for the particular test setting under study. AU - Gordon, Alexander AU - Glazko, Galina AU - Qiu, Xing AU - Yakovlev, Andrei PY - 2007/Sep/04/ UR - http://dx.doi.org/10.1214/07-AOAS102 ER -