958 research outputs found
Familywise Error Rate Control via Knockoffs
We present a novel method for controlling the -familywise error rate
(-FWER) in the linear regression setting using the knockoffs framework first
introduced by Barber and Cand\`es. Our procedure, which we also refer to as
knockoffs, can be applied with any design matrix with at least as many
observations as variables, and does not require knowing the noise variance.
Unlike other multiple testing procedures which act directly on -values,
knockoffs is specifically tailored to linear regression and implicitly accounts
for the statistical relationships between hypothesis tests of different
coefficients. We prove that knockoffs controls the -FWER exactly in finite
samples and show in simulations that it provides superior power to alternative
procedures over a range of linear regression problems. We also discuss
extensions to controlling other Type I error rates such as the false exceedance
rate, and use it to identify candidates for mutations conferring
drug-resistance in HIV.Comment: 15 pages, 3 figures. Updated reference
A robust procedure for comparing multiple means under heteroscedasticity in unbalanced designs.
Investigating differences between means of more than two groups or experimental conditions is a routine research question addressed in biology. In order to assess differences statistically, multiple comparison procedures are applied. The most prominent procedures of this type, the Dunnett and Tukey-Kramer test, control the probability of reporting at least one false positive result when the data are normally distributed and when the sample sizes and variances do not differ between groups. All three assumptions are non-realistic in biological research and any violation leads to an increased number of reported false positive results. Based on a general statistical framework for simultaneous inference and robust covariance estimators we propose a new statistical multiple comparison procedure for assessing multiple means. In contrast to the Dunnett or Tukey-Kramer tests, no assumptions regarding the distribution, sample sizes or variance homogeneity are necessary. The performance of the new procedure is assessed by means of its familywise error rate and power under different distributions. The practical merits are demonstrated by a reanalysis of fatty acid phenotypes of the bacterium Bacillus simplex from the "Evolution Canyons" I and II in Israel. The simulation results show that even under severely varying variances, the procedure controls the number of false positive findings very well. Thus, the here presented procedure works well under biologically realistic scenarios of unbalanced group sizes, non-normality and heteroscedasticity
Recent developments towards optimality in multiple hypothesis testing
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.Comment: Published at http://dx.doi.org/10.1214/074921706000000374 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates
We present a unifying approach to multiple testing procedures for sequential
(or streaming) data by giving sufficient conditions for a sequential multiple
testing procedure to control the familywise error rate (FWER), extending to the
sequential domain the work of Goeman and Solari (2010) who accomplished this
for fixed sample size procedures. Together we call these conditions the
"rejection principle for sequential tests," which we then apply to some
existing sequential multiple testing procedures to give simplified
understanding of their FWER control. Next the principle is applied to derive
two new sequential multiple testing procedures with provable FWER control, one
for testing hypotheses in order and another for closed testing. Examples of
these new procedures are given by applying them to a chromosome aberration data
set and to finding the maximum safe dose of a treatment
Statistical significance in high-dimensional linear models
We propose a method for constructing p-values for general hypotheses in a
high-dimensional linear model. The hypotheses can be local for testing a single
regression parameter or they may be more global involving several up to all
parameters. Furthermore, when considering many hypotheses, we show how to
adjust for multiple testing taking dependence among the p-values into account.
Our technique is based on Ridge estimation with an additional correction term
due to a substantial projection bias in high dimensions. We prove strong error
control for our p-values and provide sufficient conditions for detection: for
the former, we do not make any assumption on the size of the true underlying
regression coefficients while regarding the latter, our procedure might not be
optimal in terms of power. We demonstrate the method in simulated examples and
a real data application.Comment: Published in at http://dx.doi.org/10.3150/12-BEJSP11 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Genome-Wide Significance Levels and Weighted Hypothesis Testing
Genetic investigations often involve the testing of vast numbers of related
hypotheses simultaneously. To control the overall error rate, a substantial
penalty is required, making it difficult to detect signals of moderate
strength. To improve the power in this setting, a number of authors have
considered using weighted -values, with the motivation often based upon the
scientific plausibility of the hypotheses. We review this literature, derive
optimal weights and show that the power is remarkably robust to
misspecification of these weights. We consider two methods for choosing weights
in practice. The first, external weighting, is based on prior information. The
second, estimated weighting, uses the data to choose weights.Comment: Published in at http://dx.doi.org/10.1214/09-STS289 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Adaptive, Group Sequential Designs that Balance the Benefits and Risks of Wider Inclusion Criteria
We propose a new class of adaptive randomized trial designs aimed at gaining the advantages of wider generalizability and faster recruitment, while mitigating the risks of including a population for which there is greater a priori uncertainty. Our designs use adaptive enrichment, i.e., they have preplanned decision rules for modifying enrollment criteria based on data accrued at interim analyses. For example, enrollment can be restricted if the participants from predefined subpopulations are not benefiting from the new treatment. To the best of our knowledge, our designs are the first adaptive enrichment designs to have all of the following features: the multiple testing procedure fully leverages the correlation among statistics for different populations; the familywise Type I error rate is strongly controlled; for outcomes that are binary, normally distributed, or Poisson distributed, the decision rule and multiple testing procedure are functions of the data only through minimal sufficient statistics. The advantage of relying solely on minimal sufficient statistics is that not doing so can lead to losses in power. Our designs incorporate standard group sequential boundaries for each population of interest; this may be helpful in communicating our designs, since many clinical investigators are familiar with such boundaries, which can be summarized succinctly in a single table or graph. We demonstrate these adaptive designs in the context of a Phase III trial of a new treatment for stroke, and provide user-friendly, free software implementing these designs
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