Multiple Testing With an Empirical Alternative Hypothesis

An optimal multiple testing procedure is identified for linear hypotheses under the general linear model, maximizing the expected number of false null hypotheses rejected at any significance level. The optimal procedure depends on the unknown data-generating distribution, but can be consistently estimated. Drawing information together across many hypotheses, the estimated optimal procedure provides an empirical alternative hypothesis by adapting to underlying patterns of departure from the null. Proposed multiple testing procedures based on the empirical alternative are evaluated through simulations and an application to gene expression microarray data. Compared to a standard multiple testing procedure, it is not unusual for use of an empirical alternative hypothesis to increase by 50% or more the number of true positives identified at a given significance level.

Differential Expression with the Bioconductor Project

A basic, yet challenging task in the analysis of microarray gene expression data is the identification of changes in gene expression that are associated with particular biological conditions. We discuss different approaches to this task and illustrate how they can be applied using software from the Bioconductor Project. A central problem is the high dimensionality of gene expression space, which prohibits a comprehensive statistical analysis without focusing on particular aspects of the joint distribution of the genes expression levels. Possible strategies are to do univariate gene-by-gene analysis, and to perform data-driven nonspecific filtering of genes before the actual statistical analysis. However, more focused strategies that make use of biologically relevant knowledge are more likely to increase our understanding of the data.

A graph theoretic approach to testing associations between disparate sources of functional genomic data

The last few years have seen the advent of high-throughput technologies to analyze various properties of the transcriptome and proteome of several organisms. The congruency of these different data sources, or lack thereof, can shed light on the mechanisms that govern cellular function. A central challenge for bioinformatics research is to develop a unified framework for combining the multiple sources of functional genomics information and testing associations between them, thus obtaining a robust and integrated view of the underlying biology. We present a graph theoretic approach to test the significance of the association between multiple disparate sources of functional genomics data by proposing two statistical tests, namely edge permutation and node label permutation tests. We demonstrate the use of the proposed tests by finding significant association between a Gene Ontology-derived "predictome" and data obtained from mRNA expression and phenotypic experiments for Saccharomyces cerevisiae. Moreover, we employ the graph theoretic framework to recast a surprising discrepancy presented in Giaever et al. (2002) between gene expression and knockout phenotype, using expression data from a different set of experiments.

A NOVEL AND SIMPLE RULE OF THUMB FOR MULTIPLICITY CONTROL IN EQUIVALENCE TESTING USING TWO ONE-SIDED TESTS

Equivalence testing is growing in use in scientific research outside of its traditional role in the drug approval process. Largely due to its ease of use and recommendation from the United States Food and Drug Administration guidance, the most common statistical method for testing (bio)equivalence is the two one-sided tests procedure (TOST). Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. In this manuscript, a condition that bounds the family-wise error rate (FWER) using TOST is given. This condition then leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal Type I error rate down by (k - 1) is sufficient to maintain the family-wise error rate at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non drug-development setting is given.