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Author: Zijiang Yang Publisher: ISBN: Category : Languages : en Pages : 91
Book Description
The main research topic in this dissertation is the development of the closure method of multiple testing procedures. Considering a general procedure that allows the underlying test statistics as well as the associated parameters to be dependent, we first propose a step-down procedure controlling the FWER, which is defined as the probability of committing at least one false discovery. Holm (1979) first proposed a step-down procedure for multiple hypothesis testing with a control of the familywise error rate (FWER) under any kind of dependence. Under the normal distributional setup, Seneta and Chen (2005) sharpened the Holm procedure by taking into account the correlations between the test statistics. In this dissertation, the Seneta-Chen procedure is further modified yielding a more powerful FWER controlling procedure. We then advance our research and propose another step-down procedure to control the generalized FWER (k-FWER), which is defined as the probability of making at least k false discoveries. We compare our proposed k-FWER procedure with the Lehmann and Romano (2005) procedure. The proposed k-FWER procedure is more powerful, particularly when there is a strong dependence in the tests. When the proportion of true null hypotheses is expected to be small, the traditional tests are usually conservative by a factor associated with pi0, which is the proportion of true null hypotheses among all null hypotheses. Under independence, two procedures controlling the FWER and the k-FWER are proposed in this dissertation. Simulations are carried out to show that our procedures often provide much better FWER or k-FWER control and power than the traditional procedures.
Author: Zijiang Yang Publisher: ISBN: Category : Languages : en Pages : 91
Book Description
The main research topic in this dissertation is the development of the closure method of multiple testing procedures. Considering a general procedure that allows the underlying test statistics as well as the associated parameters to be dependent, we first propose a step-down procedure controlling the FWER, which is defined as the probability of committing at least one false discovery. Holm (1979) first proposed a step-down procedure for multiple hypothesis testing with a control of the familywise error rate (FWER) under any kind of dependence. Under the normal distributional setup, Seneta and Chen (2005) sharpened the Holm procedure by taking into account the correlations between the test statistics. In this dissertation, the Seneta-Chen procedure is further modified yielding a more powerful FWER controlling procedure. We then advance our research and propose another step-down procedure to control the generalized FWER (k-FWER), which is defined as the probability of making at least k false discoveries. We compare our proposed k-FWER procedure with the Lehmann and Romano (2005) procedure. The proposed k-FWER procedure is more powerful, particularly when there is a strong dependence in the tests. When the proportion of true null hypotheses is expected to be small, the traditional tests are usually conservative by a factor associated with pi0, which is the proportion of true null hypotheses among all null hypotheses. Under independence, two procedures controlling the FWER and the k-FWER are proposed in this dissertation. Simulations are carried out to show that our procedures often provide much better FWER or k-FWER control and power than the traditional procedures.
Author: Charles W. Miller Publisher: ISBN: Category : Languages : en Pages : 101
Book Description
As the availability of large datasets becomes more prevalent, so does the need to discover significant findings among a large collection of hypotheses. Multiple testing procedures (MTP) are used to control the familywise error rate (FWER) or the chance to commit at least one type I error when performing multiple hypotheses testing. When controlling the FWER, the power of a MTP to detect significant differences decreases as the number of hypotheses increases. It would be ideal to discover the same false null hypotheses despite the family of hypotheses chosen to be tested. Holland and Cheung (2002) developed measures called familywise robustness criteria (FWR) to study the effect of family size on the acceptance and rejection of a hypothesis. Their analysis focused on procedures that controlled FWER and false discovery rate (FDR). Newer MTPs have since been developed which control the generalized FWER (gFWER (k) or k-FWER) and false discovery proportion (FDP) or tail probabilities for the proportion of false positives (TPPFP). This dissertation reviews these newer procedures and then discusses the effect of family size using the FWRs of Holland and Cheung. In the case where the test statistics are independent and the null hypotheses are all true, the Type R enlargement familywise robustness measure can be expressed as a ratio of the expected number of Type I errors. In simulations, positive dependence among the test statistics was introduced, the expected number of Type I errors and the Type R enlargement FWR increased for step-up procedures with higher levels of correlation, but not for step-down or single-step procedures.
Author: Alex Dmitrienko Publisher: CRC Press ISBN: 1584889853 Category : Mathematics Languages : en Pages : 323
Book Description
Useful Statistical Approaches for Addressing Multiplicity IssuesIncludes practical examples from recent trials Bringing together leading statisticians, scientists, and clinicians from the pharmaceutical industry, academia, and regulatory agencies, Multiple Testing Problems in Pharmaceutical Statistics explores the rapidly growing area of multiple c
Author: Sandrine Dudoit Publisher: Springer Science & Business Media ISBN: 0387493174 Category : Science Languages : en Pages : 611
Book Description
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.
Author: Yiyong Fu Publisher: ISBN: Category : Languages : en Pages : 122
Book Description
The importance of multiplicity adjustment has gained wide recognition in modern scientific research. Without it, there will be too many spurious results and reproducibility becomes an issue; with it, if overtly conservative, discoveries will be made more difficult. In the current literature on repeated testing of multiple hypotheses, Bonferroni-based methods are still the main vehicle carrying the bulk of multiplicity adjustment. There is room for power improvement by suitably utilizing both hypothesis-wise and analysis- wise dependencies. This research will contribute to the development of a natural group-sequential extension of the classical stepwise multiple testing procedures, such as Dunnett's stepdown and Hochberg's step-up procedures. It is shown that the proposed group-sequential procedures strongly control the familywise error rate while being more powerful than the recently developed class of group-sequential Bonferroni-Holm's procedures. Particularly in this research, a convexity property is discovered for the distribution of the maxima of pairwise null P-values with the underlying test statistics having distributions such as bivariate normal, t, Gamma, F, or Archimedean copulas. Such property renders itself for an immediate use in improving Holm's procedure by incorporating pairwise dependencies of P-values. The improved Holm's procedure, as all stepdown multiple testing procedures, can also be naturally extended to group-sequential setting.
Author: Peter H. Westfall Publisher: John Wiley & Sons ISBN: 9780471557616 Category : Mathematics Languages : en Pages : 382
Book Description
Combines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.
Author: Mourad Elloumi Publisher: John Wiley & Sons ISBN: 1118853725 Category : Computers Languages : en Pages : 1126
Book Description
The first comprehensive overview of preprocessing, mining, and postprocessing of biological data Molecular biology is undergoing exponential growth in both the volume and complexity of biological data and knowledge discovery offers the capacity to automate complex search and data analysis tasks. This book presents a vast overview of the most recent developments on techniques and approaches in the field of biological knowledge discovery and data mining (KDD) providing in-depth fundamental and technical field information on the most important topics encountered. Written by top experts, Biological Knowledge Discovery Handbook: Preprocessing, Mining, and Postprocessing of Biological Data covers the three main phases of knowledge discovery (data preprocessing, data processing also known as data mining and data postprocessing) and analyzes both verification systems and discovery systems. BIOLOGICAL DATA PREPROCESSING Part A: Biological Data Management Part B: Biological Data Modeling Part C: Biological Feature Extraction Part D Biological Feature Selection BIOLOGICAL DATA MINING Part E: Regression Analysis of Biological Data Part F Biological Data Clustering Part G: Biological Data Classification Part H: Association Rules Learning from Biological Data Part I: Text Mining and Application to Biological Data Part J: High-Performance Computing for Biological Data Mining Combining sound theory with practical applications in molecular biology, Biological Knowledge Discovery Handbook is ideal for courses in bioinformatics and biological KDD as well as for practitioners and professional researchers in computer science, life science, and mathematics.
Author: Ranajit Chakraborty Publisher: Newnes ISBN: 0444518754 Category : Computers Languages : en Pages : 614
Book Description
The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. A series of handbooks is the only way of presenting the various aspects of statistical methodology, applications and developments. This volume deals with bioinformatics.
Author: Zijiang Yang
Author: Zijiang Yang
Author: 
Author: Charles W. Miller
Author: Alex Dmitrienko
Author: Sandrine Dudoit
Author: Yiyong Fu
Author: Peter H. Westfall
Author: Joseph P. Romano
Author: Mourad Elloumi
Author: Ranajit Chakraborty