Dudoit / Laan Multiple Testing Procedures with Applications to Genomics

1. Auflage 2007
ISBN: 978-0-387-49317-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 590 Seiten

Reihe: Springer Series in Statistics

This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. These are applied to a range of problems in biomedical and genomic research, including identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments; tests of association between gene expression measures and biological annotation metadata; sequence analysis; and genetic mapping of complex traits using single nucleotide polymorphisms. The procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions, null hypotheses, and test statistics.

Autoren/Hrsg.

Dudoit, Sandrine

Laan, Mark J. Van Der

Inhaltsverzeichnis

1;Preface;7
1.1;Intended readership;8
1.2;Overview;8
1.3;Supplements;14
1.4;Acknowledgments;14
2;Contents;16
3;List of Figures;26
4;List of Tables;30
5;1 Multiple Hypothesis Testing;33
5.1;1.1 Introduction;33
5.2;1.2 Multiple hypothesis testing framework;41
6;2 Test Statistics Null Distribution;80
6.1;2.1 Introduction;80
6.2;2.2 Type I error control and choice of a test statistics null distribution;83
6.3;2.3 Null shift and scale-transformed test statistics null distribution;91
6.4;2.4 Null quantile-transformed test statistics null distribution;100
6.5;2.5 Null distribution for transformations of the test statistics;106
6.6;2.6 Testing single-parameter null hypotheses based on t- statistics;110
6.7;2.7 Testing multiple-parameter null hypotheses based on F- statistics;118
6.8;2.8 Weak and strong Type I error control and subset pivotality;125
6.9;2.9 Test statistics null distributions based on bootstrap and permutation data generating distributions;129
7;3 Overview of Multiple Testing Procedures;140
7.1;3.1 Introduction;140
7.2;3.2 Multiple testing procedures for controlling the number of Type I errors: FWER;143
7.3;3.3 Multiple testing procedures for controlling the number of Type I errors: gFWER;165
7.4;3.4 Multiple testing procedures for controlling the proportion of Type I errors among the rejected hypotheses: FDR;176
7.5;3.5 Multiple testing procedures for controlling the proportion of Type I errors among the rejected hypotheses: TPPFP;180
8;4 Single-Step Multiple Testing Procedures for Controlling General Type I Error Rates, T( FVn );192
8.1;4.1 Introduction;192
8.2;4.2 T( FVn )- controlling single- step procedures;194
8.3;4.3 Adjusted p-values for T( FVn )- controlling single- step procedures;200
8.4;4.4 T( FVn )- controlling bootstrap- based single- step procedures;205
8.5;4.5 T( FVn )- controlling two- sided single- step procedures;218
8.6;4.6 Multiple hypothesis testing and confidence regions;222
8.7;4.7 Optimal multiple testing procedures;228
9;5 Step-Down Multiple Testing Procedures for Controlling the Family- Wise Error Rate;230
9.1;5.1 Introduction;230
9.2;5.2 FWER-controlling step-down common-cut-off procedure based on maxima of test statistics;233
9.3;5.3 FWER-controlling step-down common-quantile procedure based on minima of unadjusted p- values;243
9.4;5.4 FWER-controlling step-up common-cut-off and common- quantile procedures;255
9.5;5.5 FWER-controlling bootstrap-based step-down procedures;258
10;6 Augmentation Multiple Testing Procedures for Controlling Generalized Tail Probability Error Rates;265
10.1;6.1 Introduction;265
10.2;6.2 Augmentation multiple testing procedures for controlling the generalized family- wise error rate, gFWER( k) = Pr( Vn > k);272
10.3;6.3 Augmentation multiple testing procedures for controlling the tail probability for the proportion of false positives, TPPFP( q) = Pr( Vn/ Rn > q);275
10.4;6.4 TPPFP-based multiple testing procedures for controlling the false discovery rate, FDR = E[ Vn/Rn];281
10.5;6.5 General results on augmentation multiple testing procedures;286
10.6;6.6 gTP-based multiple testing procedures for controlling the generalized expected value, gEV ( g) = E[ g( Vn, Rn)];299
10.7;6.7 Initial FWER- and gFWER-controlling multiple testing procedures;302
10.8;6.8 Discussion;303
11;7 Resampling-Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability Error Rates;318
11.1;7.1 Introduction;318
11.2;7.2 gTP-controlling resampling-based empirical Bayes procedures;320
11.3;7.3 Adjusted p-values for gTP-controlling resampling- based empirical Bayes procedures;329
11.4;7.4 Finite sample rationale for gTP control by resampling- based empirical Bayes procedures;332
11.5;7.5 Formal asymptotic gTP control results for resampling- based empirical Bayes procedures;335
11.6;7.6 gTP-controlling resampling-based weighted empirical Bayes procedures;341
11.7;7.7 FDR-controlling empirical Bayes procedures;342
11.8;7.8 Discussion;347
12;Color Plates;349
13;8 Simulation Studies: Assessment of Test Statistics Null Distributions;373
13.1;8.1 Introduction;373
13.2;8.2 Bootstrap-based multiple testing procedures;376
13.3;8.3 Simulation Study 1: Tests for regression coefficients in linear models with dependent covariates and error terms;379
13.4;8.4 Simulation Study 2: Tests for correlation coefficients;388
14;9 Identification of Differentially Expressed and Co- Expressed Genes in High- Throughput Gene Expression Experiments;395
14.1;9.1 Introduction;395
14.2;9.2 Apolipoprotein AI experiment of Callow et al. (2000);396
14.3;9.3 Cancer microRNA study of Lu et al. (2005);430
15;10 Multiple Tests of Association with Biological Annotation Metadata;441
15.1;10.1 Introduction;441
15.2;10.2 Statistical framework for multiple tests of association with biological annotation metadata;445
15.3;10.3 The Gene Ontology;453
15.4;10.4 Tests of association between GO annotation and differential gene expression in ALL;467
15.5;10.5 Discussion;481
16;11 HIV-1 Sequence Variation and Viral Replication Capacity;505
16.1;11.1 Introduction;505
16.2;11.2 HIV-1 dataset of Segal et al. (2004);505
16.3;11.3 Multiple testing procedures;507
16.4;11.4 Software implementation in SAS;509
16.5;11.5 Results;510
16.6;11.6 Discussion;512
17;12 Genetic Mapping of Complex Human Traits Using Single Nucleotide Polymorphisms: The ObeLinks Project;516
17.1;12.1 Introduction;516
17.2;12.2 The ObeLinks Project;518
17.3;12.3 Multiple testing procedures;522
17.4;12.4 Results;524
17.5;12.5 Discussion;528
18;13 Software Implementation;545
18.1;13.1 R package multtest;545
18.2;13.2 SAS macros;555
19;A Summary of Multiple Testing Procedures;558
20;B Miscellaneous Mathematical and Statistical Results;575
20.1;B.1 Probability inequalities;575
20.2;B.2 Convergence results;576
20.3;B.3 Properties of floor and ceiling functions;577
21;C SAS Code;579
22;References;584
23;Author Index;598
24;Subject Index;601