Author: Joseph P. RomanoPublisher:
ISBN:
Category :
Languages : en
Pages : 50
Book Description
Control of Generalized Error Rates in Multiple Testing
Author: Joseph P. RomanoGeneralized Error Control in Multiple Hypothesis Testing
Author: Wenge GuoPublisher:
ISBN:
Category :
Languages : en
Pages : 143
Book Description
Multiple hypothesis testing is concerned with appropriately controlling the rate of false positives when testing a large number of hypotheses simultaneously, while maintaining the power of each test as much as possible. For testing multiple null hypotheses, the classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. However, quite often, especially when a large number of hypotheses are simultaneously tested, the notion of FWER turns out to be too stringent, allowing little chance to detect many false null hypotheses. Therefore, researchers have focused in the last decade on defining alternative less stringent error rates and developing methods that control them. The false discovery rate (FDR), the expected proportion of falsely rejected null hypotheses, due to Benjamini and Hochberg (1995), is the first of these alternative error rates that has received considerable attention. Recently, the ideas of controlling the probabilities of falsely rejecting at least k null hypotheses, which is the k-FWER, and the false discovery proportion (FDP) exceeding a certain threshold y have been introduced as alternatives to the FWER and methods controlling these new error rates have been suggested. Very recently, following the idea similar to that of the k-FWER, Sarkar (2006) generalized the FDR to the k-FDR, the expected ratio of k or more false rejections to the total number of rejections, which is a less conservative notion of error rate than the FDR and k-FWER. In this work, we develop multiple testing theory and methods for controlling the new type I error rates. Specifically, it consists of four parts: (1) We develop a new stepdown FDR controlling procedure under no assumption on dependency of the underlying p-values, which has much smaller critical constants than that of the existing Benjamini-Yekutieli stepup procedure; (2) We develop new k-FWER and FDP stepdown procedures under the assumption of independence, which are much more powerful than the existing k-FWER and FDP procedures and show that under certain condition, the k-FWER stepdown procedure is unimprovable; (3) We offer a unified approach for construction of k-FWER controlling procedures by generalizing the closure principle in the context of the FWER to the case of the k-FWER; (4) We develop new Benjamini-Hochberg type k-FDR stepup and stepdown procedures in different settings and apply them to one real microarray data analysis.
A Manual of the History of Dogmas
Author: Bernard John OttenPublisher:
ISBN:
Category : Dogma
Languages : en
Pages : 554
Book Description
Using the Partitioning Principle to Control Generalized Familywise Error Rate
Author: Haiyan XuPublisher:
ISBN:
Category : Bioinformatics
Languages : en
Pages :
Book Description
Abstract: In multiple testing, strong control of the familywise error rate (FWER) may be unnecessarily stringent in some situations such as bioinformatic studies. An alternative is to control the false discovery rate (FDR), the expected proportion of true null hypotheses among all rejected null hypotheses. However, in bioinformatic studies, the loss or cost of false discoveries often corresponds to the number rather than the proportion of false discoveries. Controlling the generalized familywise error rate (gFWER) controls the probability of incorrectly rejecting strictly more than m hypotheses. In this dissertation, we propose the generalized partitioning principle for constructing multiple tests that control gFWER. A set of sufficient conditions to shortcut generalized partitioning tests as step-down tests is provided. We show that, by being able to use information on the joint distribution of test statistics, step-down tests we propose can be more powerful than stepdown tests that ignore such information.
Balanced Control of Generalized Error Rates
Author: Joseph P. RomanoMultiple Testing Problems in Pharmaceutical Statistics
Author: Alex DmitrienkoPublisher: 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
New Step Down Procedures for Control of the Familywise Error Rate
Author: Zijiang YangPublisher:
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.
Familywise Robustness Criteria Revisited for Newer Multiple Testing Procedures
Author: Charles W. MillerPublisher:
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.
Selected Works of E. L. Lehmann
Author: Javier RojoPublisher: Springer Science & Business Media
ISBN: 1461414113
Category : Mathematics
Languages : en
Pages : 1103
Book Description
These volumes present a selection of Erich L. Lehmann’s monumental contributions to Statistics. These works are multifaceted. His early work included fundamental contributions to hypothesis testing, theory of point estimation, and more generally to decision theory. His work in Nonparametric Statistics was groundbreaking. His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature. The two volumes are divided into chapters of related works. Invited contributors have critiqued the papers in each chapter, and the reprinted group of papers follows each commentary. A complete bibliography that contains links to recorded talks by Erich Lehmann – and which are freely accessible to the public – and a list of Ph.D. students are also included. These volumes belong in every statistician’s personal collection and are a required holding for any institutional library.
Multiple Testing and False Discovery Rate Control
Author: Shiyun ChenPublisher:
ISBN:
Category :
Languages : en
Pages : 142
Book Description
Multiple testing, a situation where multiple hypothesis tests are performed simultaneously, is a core research topic in statistics that arises in almost every scientific field. When more hypotheses are tested, more errors are bound to occur. Controlling the false discovery rate (FDR) [BH95], which is the expected proportion of falsely rejected null hypotheses among all rejections, is an important challenge for making meaningful inferences. Throughout the dissertation, we analyze the asymptotic performance of several FDR-controlling procedures under different multiple testing settings. In Chapter 1, we study the famous Benjamini-Hochberg (BH) method [BH95] which often serves as benchmark among FDR-controlling procedures, and show that it is asymptotic optimal in a stylized setting. We then prove that a distribution-free FDR control method of Barber and Candès [FBC15], which only requires the (unknown) null distribution to be symmetric, can achieve the same asymptotic performance as the BH method, thus is also optimal. Chapter 2 proposes an interval-type procedure which identifies the longest interval with the estimated FDR under a given level and rejects the corresponding hypotheses with P-values lying inside the interval. Unlike the threshold approaches, this procedure scans over all intervals with the left point not necessary being zero. We show that this scan procedure provides strong control of the asymptotic false discovery rate. In addition, we investigate its asymptotic false non-discovery rate (FNR), deriving conditions under which it outperforms the BH procedure. In Chapter 3, we consider an online multiple testing problem where the hypotheses arrive sequentially in a stream, and investigate two procedures proposed by Javanmard and Montanari [JM15] which control FDR in an online manner. We quantify their asymptotic performance in the same location models as in Chapter 1 and compare their power with the (static) BH method. In Chapter 4, we propose a new class of powerful online testing procedures which incorporates the available contextual information, and prove that any rule in this class controls the online FDR under some standard assumptions. We also derive a practical algorithm that can make more empirical discoveries in an online fashion, compared to the state-of-the-art procedures.