Wenge Guo

Controlling False Discoveries in Multidimensional Directional Decisions, with Applications to Gene Expression Data on Ordered Categories

Microarray gene expression studies over ordered categories are routinely conducted to gain insights into biological functions of genes and the underlying biological processes. Some common experiments are time-course/dose-response experiments where a tissue or cell line is exposed to different doses and/or durations of time to a chemical. A goal of such studies is to identify gene expression patterns/profiles over the ordered categories. This problem can be formulated as a multiple testing problem where for each gene the null hypothesis of no difference between the successive mean gene expressions is tested and further directional decisions are made if it is rejected. Much of the existing multiple testing procedures are devised for controlling the usual false discovery rate (FDR) rather than the mixed directional FDR (mdFDR), the expected proportion of Type I and directional errors among all rejections. Benjamini and Yekutieli (2005, Journal of the American Statistical Association 100, 71-93) proved that an augmentation of the usual Benjamini-Hochberg (BH) procedure can control the mdFDR while testing simple null hypotheses against two-sided alternatives in terms of one-dimensional parameters. In this article, we consider the problem of controlling the mdFDR involving multidimensional parameters. To deal with this problem, we develop a procedure extending that of Benjamini and Yekutieli based on the Bonferroni test for each gene. A proof is given for its mdFDR control when the underlying test statistics are independent across the genes. The results of a simulation study evaluating its performance under independence as well as under dependence of the underlying test statistics across the genes relative to other relevant procedures are reported. Finally, the proposed methodology is applied to a time-course microarray data obtained by Lobenhofer et al. (2002, Molecular Endocrinology 16, 1215-1229). We identified several important cell-cycle genes, such as DNA replication/repair gene MCM4 and replication factor subunit C2, which were not identified by the previous analyses of the same data by Lobenhofer et al. (2002) and Peddada et al. (2003, Bioinformatics 19, 834-841). Although some of our findings overlap with previous findings, we identify several other genes that complement the results of Lobenhofer et al. (2002).

On a generalized false discovery rate

The concept of k-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections, for some flxed k ‚ 1. A less conservative notion, the k-FDR, has been introduced very recently by Sarkar [19], generalizing the false discovery rate of Banjamini and Hochberg [1]. In this article, we bring newer insight to the k-FDR considering a mixture model involving independent p-values before motivating the developments of some new procedures that control it. We prove the k-FDR control of the proposed methods under a slightly weaker condition than in the mixture model. We provide numerical evidence of the proposed methods’ superior power performance over some kFWER and k-FDR methods. Finally, we apply our methods to a real data set.

Adaptive Choice of the Number of Bootstrap Samples in Large Scale Multiple Testing

It is a common practice to use resampling methods such as the bootstrap for calculating the p-value for each test when performing large scale multiple testing. The precision of the bootstrap p-values and that of the false discovery rate (FDR) relies on the number of bootstraps used for testing each hypothesis. Clearly, the larger the number of bootstraps the better the precision. However, the required number of bootstraps can be computationally burdensome, and it multiplies the number of tests to be performed. Further adding to the computational challenge is that in some applications the calculation of the test statistic itself may require considerable computation time. As technology improves one can expect the dimension of the problem to increase as well. For instance, during the early days of microarray technology, the number of probes on a cDNA chip was less than 10,000. Now the Affymetrix chips come with over 50,000 probes per chip. Motivated by this important need, we developed a simple adaptive bootstrap methodology for large scale multiple testing, which reduces the total number of bootstrap calculations while ensuring the control of the FDR. The proposed algorithm results in a substantial reduction in the number of bootstrap samples. Based on a simulation study we found that, relative to the number of bootstraps required for the Benjamini-Hochberg (BH) procedure, the standard FDR methodology which was the proposed methodology achieved a very substantial reduction in the number of bootstraps. In some cases the new algorithm required as little as 1/6th the number of bootstraps as the conventional BH procedure. Thus, if the conventional BH procedure used 1,000 bootstraps, then the proposed method required only 160 bootstraps. This methodology has been implemented for time-course/dose-response data in our software, ORIOGEN, which is available from the authors upon request.

Further results on controlling the false discovery proportion

The probability of false discovery proportion (FDP) exceeding

Multiple Testing in a Two-Stage Adaptive Design With Combination Tests Controlling FDR

\gamma\in[0,1)

The Hat Problem and Some Variations

, defined as

A multiple testing procedure for multi-dimensional pairwise comparisons with application to gene expression studies

\gamma

Astronomical Transient Detection Controlling the False Discovery Rate

-FDP, has received much attention as a measure of false discoveries in multiple testing. Although this measure has received acceptance due to its relevance under dependency, not much progress has been made yet advancing its theory under such dependency in a nonasymptotic setting, which motivates our research in this article. We provide a larger class of procedures containing the stepup analog of, and hence more powerful than, the stepdown procedure in Lehmann and Romano [Ann. Statist. 33 (2005) 1138-1154] controlling the

On stepwise control of the generalized familywise error rate

\gamma

Analysis of high dimensional data using pre-defined set and subset information, with applications to genomic data

-FDP under similar positive dependence condition assumed in that paper. We offer better alternatives of the stepdown and stepup procedures in Romano and Shaikh [IMS Lecture Notes Monogr. Ser. 49 (2006a) 33-50, Ann. Statist. 34 (2006b) 1850-1873] using pairwise joint distributions of the null