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SAMPLE SIZE AND POSITIVE FALSE DISCOVERY RATE CONTROL FOR MULTIPLE TESTING
, 2007
"... Positive false discovery rate (pFDR) is a useful overall measure of errors for multiple hypothesis testing, especially when the underlying goal is to attain one or more discoveries. Control of pFDR critically depends on how much evidence is available from data to distinguish between false and true n ..."
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Positive false discovery rate (pFDR) is a useful overall measure of errors for multiple hypothesis testing, especially when the underlying goal is to attain one or more discoveries. Control of pFDR critically depends on how much evidence is available from data to distinguish between false and true nulls. Oftentimes, as many aspects of the data distributions are unknown, one may not be able to obtain strong enough evidence from the data for pFDR control. This raises the question as to how much data is needed in order to attain a target pFDR level. We study the asymptotics of the minimum number of observations per null for the pFDR control associated with multiple Studentized tests and F tests, especially when the differences between false nulls and true nulls are small. For Studentized tests, we consider tests on shifts or other parameters associated with normal and general distributions. For F tests, we also take into account the effect of the number of covariates in linear regression. The results show that in determining the minimum sample size per null for pFDR control, higher order statistical properties of data are important, and the number of covariates is important in tests to detect regression effects. 1. Introduction. A
CHOOSING THE LESSER EVIL: TRADEOFF BETWEEN FALSE DISCOVERY RATE AND NONDISCOVERY RATE
"... Abstract: The problem of multiple comparisons has become increasingly important in light of the significant surge in volume of data available to statisticians. The seminal work of Benjamini and Hochberg (1995) on the control of the false discovery rate (FDR) has brought forth an alternative way of m ..."
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Abstract: The problem of multiple comparisons has become increasingly important in light of the significant surge in volume of data available to statisticians. The seminal work of Benjamini and Hochberg (1995) on the control of the false discovery rate (FDR) has brought forth an alternative way of measuring type I error rate that is often more relevant than the one based on the familywise error rate. In this paper, we emphasize the importance of considering type II error rates in the context of multiple hypothesis testing. We propose a suitable quantity, the expected proportion of false negatives among the true alternative hypotheses, which we call nondiscovery rate (NDR). We argue that NDR is a natural extension of the type II error rate of single hypothesis to multiple comparisons. The utility of NDR is emphasized through the tradeoff between FDR and NDR, which is demonstrated using a few real and simulated examples. We also show analytically the equivalence between the FDRadjusted pvalue approach of Yekutieli and Benjamini (1999) and the qvalue method of Storey (2002). This equivalence dissolves the dilemma encountered by many practitioners of choosing the “right ” FDR controlling procedure. Key words and phrases: False discovery rate, genomescans, microarray data, multiple comparisons, multiple hypothesis testing, nondiscovery rate, power, type I error, type II error. 1.
False discovery control in largescale spatial multiple testing. Manuscript submitted for publication
, 2012
"... Summary. This article develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both pointwise and clusterwise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false di ..."
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Summary. This article develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both pointwise and clusterwise spatial analyses, and derive oracle procedures which optimally control the false discovery rate, false discovery exceedance and false cluster rate, respectively. A datadriven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain. Our multiple testing procedures are asymptotically valid and can be effectively implemented using Bayesian computational algorithms for analysis of large spatial data sets. Numerical results show that the proposed procedures lead to more accurate error control and better power performance than conventional methods. We demonstrate our methods for analyzing the time trends in tropospheric ozone in eastern US.
A review of microarray experimental design strategies for genetical genomics studies. Physiol. Genomics 28:15–23
, 2006
"... studies ..."
Incorporating biological pathways via a Markov random field model in genomewide association studies
 PLoS Genetics
"... Genomewide association studies (GWAS) examine a large number of markers across the genome to identify associations between genetic variants and disease. Most published studies examine only single markers, which may be less informative than considering multiple markers and multiple genes jointly bec ..."
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Genomewide association studies (GWAS) examine a large number of markers across the genome to identify associations between genetic variants and disease. Most published studies examine only single markers, which may be less informative than considering multiple markers and multiple genes jointly because genes may interact with each other to affect disease risk. Much knowledge has been accumulated in the literature on biological pathways and interactions. It is conceivable that appropriate incorporation of such prior knowledge may improve the likelihood of making genuine discoveries. Although a number of methods have been developed recently to prioritize genes using prior biological knowledge, such as pathways, most methods treat genes in a specific pathway as an exchangeable set without considering the topological structure of a pathway. However, how genes are related with each other in a pathway may be very informative to identify association signals. To make use of the connectivity information among genes in a pathway in GWAS analysis, we propose a Markov Random Field (MRF) model to incorporate pathway topology for association analysis. We show that the conditional distribution of our MRF model takes on a simple logistic regression form, and we propose an iterated conditional modes algorithm as well as a decision theoretic approach for statistical inference of each gene’s association with disease. Simulation studies show that our proposed framework is more effective to identify genes associated with disease than a single gene–based method. We also illustrate the usefulness of our approach through its applications to a real data
2 Hierarchical Mixture Models for Expression Profiles
, 2006
"... A class of probability models for inference about alterations in gene expression is reviewed. The class entails discrete mixing over patterns of equivalent and differential expression among different mRNA populations, continuous mixing over latent mean expression values conditional on each pattern, ..."
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A class of probability models for inference about alterations in gene expression is reviewed. The class entails discrete mixing over patterns of equivalent and differential expression among different mRNA populations, continuous mixing over latent mean expression values conditional on each pattern, and variation of data conditional on latent means. An R package EBarrays implements inference calculations derived within this model class. The role of genespecific probabilities of differential expression in the formation of calibrated gene lists is emphasized. In the context of the model class, differential expression is shown to be not just a shift in expected expression levels, but also an assertion about statistical independence of measurements from different mRNA populations. From this latter perspective, EBarrays is shown to be conservative in its assessment of differential expression. Technological advances and resources created by genome sequencing projects
2003) Cancer
 In Africa? Lancet Oncol 4: 5
"... Multiple myeloma (MM) is a cancer of plasma cells, which is the second most common hematological malignancy in the United States.1 It is characterized by malignant, neoplastic transformation of terminally di!erentiated B cells ..."
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Multiple myeloma (MM) is a cancer of plasma cells, which is the second most common hematological malignancy in the United States.1 It is characterized by malignant, neoplastic transformation of terminally di!erentiated B cells
Recent developments towards optimality in multiple hypothesis testing
, 2006
"... There are many different notions of optimality even in testing a single hypothesis. In the multiple testing area, the number of possibilities is very much greater. The paper first will describe multiplicity issues that arise in tests involving a single parameter, and will describe a new optimality r ..."
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There are many different notions of optimality even in testing a single hypothesis. In the multiple testing area, the number of possibilities is very much greater. The paper first will describe multiplicity issues that arise in tests involving a single parameter, and will describe a new optimality result in that context. Although the example given is of minimal practical importance, it illustrates the crucial dependence of optimality on the precise specification of the testing problem. The paper then will discuss the types of expanded optimality criteria that are being considered when hypotheses involve multiple parameters, will note a few new optimality results, and will give selected theoretical references relevant to optimality considerations under these expanded criteria.