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Register a new userFamilywise Error Rate Control by Interactive Unmasking
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Added by
Boyan Duan
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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We propose a method for multiple hypothesis testing with familywise error rate (FWER) control, called the i-FWER test. Most testing methods are predefined algorithms that do not allow modifications after observing the data. However, in practice, analysts tend to choose a promising algorithm after observing the data; unfortunately, this violates the validity of the conclusion. The i-FWER test allows much flexibility: a human (or a computer program acting on the humans behalf) may adaptively guide the algorithm in a data-dependent manner. We prove that our test controls FWER if the analysts adhere to a particular protocol of masking and unmasking. We demonstrate via numerical experiments the power of our test under structured non-nulls, and then explore new forms of masking.
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Given the cost and duration of phase III and phase IV clinical trials, the development of statistical methods for go/no-go decisions is vital. In this paper, we introduce a Bayesian methodology to compute the probability of success based on the current data of a treatment regimen for the multivariate linear model. Our approach utilizes a Bayesian seemingly unrelated regression model, which allows for multiple endpoints to be modeled jointly even if the covariates between the endpoints are different. Correlations between endpoints are explicitly modeled. This Bayesian joint modeling approach unifies single and multiple testing procedures under a single framework. We develop an approach to multiple testing that asymptotically guarantees strict family-wise error rate control, and is more powerful than frequentist approaches to multiplicity. The method effectively yields those of Ibrahim et al. and Chuang-Stein as special cases, and, to our knowledge, is the only method that allows for robust sample size determination for multiple endpoints and/or hypotheses and the only method that provides strict family-wise type I error control in the presence of multiplicity.
We develop a new class of distribution--free multiple testing rules for false discovery rate (FDR) control under general dependence. A key element in our proposal is a symmetrized data aggregation (SDA) approach to incorporating the dependence structure via sample splitting, data screening and information pooling. The proposed SDA filter first constructs a sequence of ranking statistics that fulfill global symmetry properties, and then chooses a data--driven threshold along the ranking to control the FDR. The SDA filter substantially outperforms the knockoff method in power under moderate to strong dependence, and is more robust than existing methods based on asymptotic $p$-values. We first develop finite--sample theory to provide an upper bound for the actual FDR under general dependence, and then establish the asymptotic validity of SDA for both the FDR and false discovery proportion (FDP) control under mild regularity conditions. The procedure is implemented in the R package texttt{SDA}. Numerical results confirm the effectiveness and robustness of SDA in FDR control and show that it achieves substantial power gain over existing methods in many settings.
Selecting relevant features associated with a given response variable is an important issue in many scientific fields. Quantifying quality and uncertainty of a selection result via false discovery rate (FDR) control has been of recent interest. This paper introduces a way of using data-splitting strategies to asymptotically control the FDR while maintaining a high power. For each feature, the method constructs a test statistic by estimating two independent regression coefficients via data splitting. FDR control is achieved by taking advantage of the statistics property that, for any null feature, its sampling distribution is symmetric about zero. Furthermore, we propose Multiple Data Splitting (MDS) to stabilize the selection result and boost the power. Interestingly and surprisingly, with the FDR still under control, MDS not only helps overcome the power loss caused by sample splitting, but also results in a lower variance of the false discovery proportion (FDP) compared with all other methods in consideration. We prove that the proposed data-splitting methods can asymptotically control the FDR at any designated level for linear and Gaussian graphical models in both low and high dimensions. Through intensive simulation studies and a real-data application, we show that the proposed methods are robust to the unknown distribution of features, easy to implement and computationally efficient, and are often the most powerful ones amongst competitors especially when the signals are weak and the correlations or partial correlations are high among features.
Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub structures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high dimensional graphical models and control the false discovery rate (FDR). Discovering hub nodes in the networks is challenging: there is no straightforward statistic for testing the degree of a node due to the combinatorial structures; complicated dependence in the multiple testing problem is hard to characterize and control. In methodology, the StarTrek filter overcomes this by constructing p-values based on the maximum test statistics via the Gaussian multiplier bootstrap. In theory, we show that the StarTrek filter can control the FDR by providing accurate bounds on the approximation errors of the quantile estimation and addressing the dependence structures among the maximal statistics. To this end, we establish novel Cramer-type comparison bounds for the high dimensional Gaussian random vectors. Comparing to the Gaussian comparison bound via the Kolmogorov distance established by citet{chernozhukov2014anti}, our Cramer-type comparison bounds establish the relative difference between the distribution functions of two high dimensional Gaussian random vectors. We illustrate the validity of the StarTrek filter in a series of numerical experiments and apply it to the genotype-tissue expression dataset to discover central regulator genes.
In neuroimaging, hundreds to hundreds of thousands of tests are performed across a set of brain regions or all locations in an image. Recent studies have shown that the most common family-wise error (FWE) controlling procedures in imaging, which rely on classical mathematical inequalities or Gaussian random field theory, yield FWE rates that are far from the nominal level. Depending on the approach used, the FWER can be exceedingly small or grossly inflated. Given the widespread use of neuroimaging as a tool for understanding neurological and psychiatric disorders, it is imperative that reliable multiple testing procedures are available. To our knowledge, only permutation joint testing procedures have been shown to reliably control the FWER at the nominal level. However, these procedures are computationally intensive due to the increasingly available large sample sizes and dimensionality of the images, and analyses can take days to complete. Here, we develop a parametric bootstrap joint testing procedure. The parametric bootstrap procedure works directly with the test statistics, which leads to much faster estimation of adjusted emph{p}-values than resampling-based procedures while reliably controlling the FWER in sample sizes available in many neuroimaging studies. We demonstrate that the procedure controls the FWER in finite samples using simulations, and present region- and voxel-wise analyses to test for sex differences in developmental trajectories of cerebral blood flow.
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