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Volume 10, Issue 1 2011 Article 55 Statistical Applications in Genetics and Molecular Biology False Discovery Rate Estimation for Stability Selection: Application to Genome-Wide Association Studies Ismaïl Ahmed, Inserm Anna-Liisa Hartikainen, University of Oulu Marjo-Riitta Järvelin, Imperial College London Sylvia Richardson, Imperial College London Recommended Citation: Ahmed, Ismaïl; Hartikainen, Anna-Liisa; Järvelin, Marjo-Riitta; and Richardson, Sylvia (2011) "False Discovery Rate Estimation for Stability Selection: Application to Genome-Wide Association

Volume 6, Issue 1 2007 Article 32 Statistical Applications in Genetics and Molecular Biology Estimating the Arm-Wise False Discovery Rate in Array Comparative Genomic Hybridization Experiments Daniel P. Gaile, State University of New York at Buffalo Elizabeth D. Schifano, Cornell University Jeffrey C. Miecznikowski, State University of New York at Buffalo James J. Java, State University of New York at Buffalo Jeffrey M. Conroy, Roswell Park Cancer Institute Norma J. Nowak, New York State Center of Excellence in Bioinformatics and Life Sciences Recommended

Volume 6, Issue 1 2007 Article 27 Statistical Applications in Genetics and Molecular Biology On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure Gerwyn H. Green, Department of Medicine, Lancaster University Peter J. Diggle, Department of Medicine, Lancaster University & Johns Hopkins Bloomberg School of Public Health Recommended Citation: Green, Gerwyn H. and Diggle, Peter J. (2007) "On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure," Statistical Applications in Genetics and

the estimated power exceeds a certain threshold (Posch et al., 2009). These designs, however, can require a large number of interim analyses which may not be practical and computationally expensive. In this paper we propose a sample size reassessment procedure for studies where a large number of hypotheses is tested controlling the false discovery rate (FDR). In an interim analysis the distribution of the effect sizes under the alternative is estimated with an empirical Bayes mixture model (Muralidharan, 2010) or a kernel deconvolution density estimator (van Iterson

Volume 11, Issue 5 2012 Article 4 Statistical Applications in Genetics and Molecular Biology Estimators of the local false discovery rate designed for small numbers of tests Marta Padilla, Ottawa Institute of Systems Biology, Department of Biochemistry, Microbiology, and Immunology, University of Ottawa David R. Bickel, Ottawa Institute of Systems Biology, Department of Biochemistry, Microbiology, and Immunology, University of Ottawa Recommended Citation: Padilla, Marta and Bickel, David R. (2012) "Estimators of the local false discovery rate designed for small

1 Introduction 1.1 Background and problem statement Since the successful application of the false discovery rate (FDR) to high-dimensional biological data (Efron et al., 2001), methodological research has taken two main directions in addition to the hierarchical Bayesian direction in which a joint prior distribution of all unknown quantities is given. The purely frequentist line of research has continued to generalize the theorem of Benjamini and Hochberg (1995) for strictly controlling the FDR and has resulted in methods of similarly controlling related

Volume 6, Issue 1 2007 Article 14 Statistical Applications in Genetics and Molecular Biology Inference on the Limiting False Discovery Rate and the P-value Threshold Parameter Assuming Weak Dependence between Gene Expression Levels within Subject Glenn Heller, Memorial Sloan-Kettering Cancer Center Jing Qin, National Institute of Allergy and Infectious Diseases Recommended Citation: Heller, Glenn and Qin, Jing (2007) "Inference on the Limiting False Discovery Rate and the P- value Threshold Parameter Assuming Weak Dependence between Gene Expression Levels within

} \quad \matrix{ {{\rm{if }}{r_i} \le {\textstyle{N \over 2}};} \cr {{\rm{if }}{r_i} > {\textstyle{N \over 2}}.} \cr } }.$ Similarly, p. 537 should have Ψ ( p i ; Ψ † )= q in place of Q ( p i ; Ψ † )= q . Using different notation, correct expressions for ψ ( r i ; Ψ * ) were reported in Bickel (2011) and Yang et al. (2013). References Bickel, D. R. (2011): Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions. Technical Report, Ottawa Institute of Systems Biology, arXiv:1106.4490. Bickel, D

hand, there are cases where each p-value is marginally incorrect, yet the joint distribution of the set of p-values is satisfactory. Here, we propose a criterion defining a well behaved set of simultaneously calculated p-values that provides precise control of common error rates and we introduce diagnostic procedures for assessing whether the criterion is satisfied with simulations. Multiple testing p-values that satisfy our new criterion avoid potentially large study specific errors, but also satisfy the usual assumptions for strong control of false discovery rates

asymptotic control of the false discovery rate. The methodology is illustrated with application to two high-throughput datasets as well as to simulated data. KEYWORDS: false discovery rate, familywise error, mixture model, multiple comparisons, simultaneous inference Author Notes: The author would like to thank Tom Nichols for helpful discussions and the Editor and two referees, whose comments substantially improved the manuscript. This research is supported by grant GM72007 from the Joint DMS/DBS/NIGMS Biological Mathematics Program. 1 Introduction Because of advancements