A Powerful Global Test Statistic for Functional Statistical Inference

We consider the problem of performing an association test between functional data and scalar variables in a varying coefficient model setting. We propose a functional projection regression model and an associated global test statistic to aggregate relatively weak signals across the domain of functional data, while reducing the dimension. An optimal functional projection direction is selected to maximize signal-to-noise ratio with ridge penalty. Theoretically, we systematically study the asymptotic distribution of the global test statistic and provide a strategy to adaptively select the optimal tuning parameter. We use simulations to show that the proposed test outperforms all existing state-of-the-art methods in functional statistical inference. Finally, we apply the proposed testing method to the genome-wide association analysis of imaging genetic data in UK Biobank dataset.

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A Robust Rerank Approach for Feature Selection and Its Application to Pooling-Based GWA Studies

Computational and Mathematical Methods in Medicine ◽

10.1155/2013/860673 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Jia-Rou Liu ◽

Po-Hsiu Kuo ◽

Hung Hung

Keyword(s):

Characteristic Curve ◽

Real Data ◽

Tuning Parameter ◽

Practical Implementation ◽

Tuning Parameters ◽

Genome Wide ◽

Feature Based ◽

The Difference ◽

Gwa Studies ◽

Selection Of

Large-p-small-ndatasets are commonly encountered in modern biomedical studies. To detect the difference between two groups, conventional methods would fail to apply due to the instability in estimating variances int-test and a high proportion of tied values in AUC (area under the receiver operating characteristic curve) estimates. The significance analysis of microarrays (SAM) may also not be satisfactory, since its performance is sensitive to the tuning parameter, and its selection is not straightforward. In this work, we propose a robust rerank approach to overcome the above-mentioned diffculties. In particular, we obtain a rank-based statistic for each feature based on the concept of “rank-over-variable.” Techniques of “random subset” and “rerank” are then iteratively applied to rank features, and the leading features will be selected for further studies. The proposed re-rank approach is especially applicable for large-p-small-ndatasets. Moreover, it is insensitive to the selection of tuning parameters, which is an appealing property for practical implementation. Simulation studies and real data analysis of pooling-based genome wide association (GWA) studies demonstrate the usefulness of our method.

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The Effects of Manifest Residual Variances, Indicator Communality, and Sample Size on the χ2-Test Statistic of the Metric Invariance Model

10.31234/osf.io/4vmku ◽

2019 ◽

Author(s):

Eric Klopp ◽

Stefan Klößner

Keyword(s):

Sample Size ◽

Measurement Invariance ◽

Signal To Noise Ratio ◽

Practical Implication ◽

Residual Variance ◽

Test Statistic ◽

Monte Carlo Studies ◽

Key Factor ◽

Metric Measurement ◽

Invariance Model

In this contribution, we investigate the effects of manifest residual variance, indicator communality and sample size on the χ2-test statistic of the metric measurement invariance model, i.e. the model with equality constraints on all loadings. We demonstrate by means of Monte Carlo studies that the χ2-test statistic relates inversely to manifest residual variance, whereas sample size and χ2-test statistic show the well-known pro- portional relation. Moreover, we consider indicator communality as a key factor for the size of the χ2-test statistic. In this context, we introduce the concept of signal-to-noise ratio as a tool for studying the effects of manifest residual error and indicator commu- nality and demonstrate its use with some examples. Finally, we discuss the limitations of this contribution and its practical implication for the analysis of metric measurement invariance models.

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A method for identifying genetic heterogeneity within phenotypically-defined disease subgroups

10.1101/037713 ◽

2016 ◽

Cited By ~ 1

Author(s):

James Liley ◽

John A Todd ◽

Chris Wallace

Keyword(s):

Genetic Variants ◽

Genetic Architecture ◽

Effect Sizes ◽

Thyroid Peroxidase ◽

Global Test ◽

Genome Wide ◽

Thyroid Peroxidase Antibody ◽

Antibody Positivity ◽

Post Hoc

AbstractMany common diseases show wide phenotypic variation. We present a statistical method for determining whether phenotypically defined subgroups of disease cases represent different genetic architectures, in which disease-associated variants have different effect sizes in the two subgroups. Our method models the genome-wide distributions of genetic association statistics with mixture Gaussians. We apply a global test without requiring explicit identification of disease-associated variants, thus maximising power in comparison to a standard variant by variant subgroup analysis. Where evidence for genetic subgrouping is found, we present methods for post-hoc identification of the contributing genetic variants.We demonstrate the method on a range of simulated and test datasets where expected results are already known. We investigate subgroups of type 1 diabetes (T1D) cases defined by autoantibody positivity, establishing evidence for differential genetic architecture with thyroid peroxidase antibody positivity, driven generally by variants in known T1D associated regions.

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An approach to gene-based testing accounting for dependence of tests among nearby genes

10.1101/2021.05.24.445494 ◽

2021 ◽

Author(s):

Ronald J Yurko ◽

Kathryn Roeder ◽

Bernie Devlin ◽

Max G'Sell

Keyword(s):

Multiple Testing ◽

Association Studies ◽

Autism Spectrum ◽

P Value ◽

Genome Wide Association Studies ◽

Strongly Correlated ◽

Test Statistics ◽

Test Statistic ◽

Genome Wide ◽

Insight Into

In genome-wide association studies (GWAS), it has become commonplace to test millions of SNPs for phenotypic association. Gene-based testing can improve power to detect weak signal by reducing multiple testing and pooling signal strength. While such tests account for linkage disequilibrium (LD) structure of SNP alleles within each gene, current approaches do not capture LD of SNPs falling in different nearby genes, which can induce correlation of gene-based test statistics. We introduce an algorithm to account for this correlation. When a gene's test statistic is independent of others, it is assessed separately; when test statistics for nearby genes are strongly correlated, their SNPs are agglomerated and tested as a locus. To provide insight into SNPs and genes driving association within loci, we develop an interactive visualization tool to explore localized signal. We demonstrate our approach in the context of weakly powered GWAS for autism spectrum disorder, which is contrasted to more highly powered GWAS for schizophrenia and educational attainment. To increase power for these analyses, especially those for autism, we use adaptive p-value thresholding (AdaPT), guided by high-dimensional metadata modeled with gradient boosted trees, highlighting when and how it can be most useful. Notably our workflow is based on summary statistics.

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On “Field Significance” and the False Discovery Rate

Journal of Applied Meteorology and Climatology ◽

10.1175/jam2404.1 ◽

2006 ◽

Vol 45 (9) ◽

pp. 1181-1189 ◽

Cited By ~ 280

Author(s):

D. S. Wilks

Keyword(s):

False Discovery Rate ◽

Statistical Power ◽

Statistical Significance ◽

Significance Test ◽

P Value ◽

Test Statistic ◽

Global Test ◽

Additional Advantage ◽

Counting Procedure ◽

False Discovery

Abstract The conventional approach to evaluating the joint statistical significance of multiple hypothesis tests (i.e., “field,” or “global,” significance) in meteorology and climatology is to count the number of individual (or “local”) tests yielding nominally significant results and then to judge the unusualness of this integer value in the context of the distribution of such counts that would occur if all local null hypotheses were true. The sensitivity (i.e., statistical power) of this approach is potentially compromised both by the discrete nature of the test statistic and by the fact that the approach ignores the confidence with which locally significant tests reject their null hypotheses. An alternative global test statistic that has neither of these problems is the minimum p value among all of the local tests. Evaluation of field significance using the minimum local p value as the global test statistic, which is also known as the Walker test, has strong connections to the joint evaluation of multiple tests in a way that controls the “false discovery rate” (FDR, or the expected fraction of local null hypothesis rejections that are incorrect). In particular, using the minimum local p value to evaluate field significance at a level αglobal is nearly equivalent to the slightly more powerful global test based on the FDR criterion. An additional advantage shared by Walker’s test and the FDR approach is that both are robust to spatial dependence within the field of tests. The FDR method not only provides a more broadly applicable and generally more powerful field significance test than the conventional counting procedure but also allows better identification of locations with significant differences, because fewer than αglobal × 100% (on average) of apparently significant local tests will have resulted from local null hypotheses that are true.

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Global spectral clustering in dynamic networks

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1718449115 ◽

2018 ◽

Vol 115 (5) ◽

pp. 927-932 ◽

Cited By ~ 28

Author(s):

Fuchen Liu ◽

David Choi ◽

Lu Xie ◽

Kathryn Roeder

Keyword(s):

Community Detection ◽

Spectral Clustering ◽

Signal To Noise Ratio ◽

Dynamic Networks ◽

Brain Regions ◽

Tuning Parameter ◽

Expression Data ◽

Dynamic Community Detection ◽

Dynamic Community ◽

Better Than

Community detection is challenging when the network structure is estimated with uncertainty. Dynamic networks present additional challenges but also add information across time periods. We propose a global community detection method, persistent communities by eigenvector smoothing (PisCES), that combines information across a series of networks, longitudinally, to strengthen the inference for each period. Our method is derived from evolutionary spectral clustering and degree correction methods. Data-driven solutions to the problem of tuning parameter selection are provided. In simulations we find that PisCES performs better than competing methods designed for a low signal-to-noise ratio. Recently obtained gene expression data from rhesus monkey brains provide samples from finely partitioned brain regions over a broad time span including pre- and postnatal periods. Of interest is how gene communities develop over space and time; however, once the data are divided into homogeneous spatial and temporal periods, sample sizes are very small, making inference quite challenging. Applying PisCES to medial prefrontal cortex in monkey rhesus brains from near conception to adulthood reveals dense communities that persist, merge, and diverge over time and others that are loosely organized and short lived, illustrating how dynamic community detection can yield interesting insights into processes such as brain development.

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Inference for Support Vector Regression under ℓ1 Regularization

AEA Papers and Proceedings ◽

10.1257/pandp.20211035 ◽

2021 ◽

Vol 111 ◽

pp. 611-615

Author(s):

Yuehao Bai ◽

Hung Ho ◽

Guillaume A. Pouliot ◽

Joshua Shea

Keyword(s):

Support Vector Regression ◽

Tuning Parameter ◽

Support Vector ◽

L1 Norm ◽

Test Statistic ◽

Sample Distribution ◽

Large Sample ◽

Variance Estimate ◽

Error Bars ◽

ℓ1 Regularization

We provide large-sample distribution theory for support vector regression (SVR) with l1-norm along with error bars for the SVR regression coefficients. Although a classical Wald confidence interval obtains from our theory, its implementation inherently depends on the choice of a tuning parameter that scales the variance estimate and thus the width of the error bars. We address this shortcoming by further proposing an alternative large-sample inference method based on the inversion of a novel test statistic that displays competitive power properties and does not depend on the choice of a tuning parameter.

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TEGS-CN: A Statistical Method for Pathway Analysis of Genome-wide Copy Number Profile

Cancer Informatics ◽

10.4137/cin.s13978 ◽

2014 ◽

Vol 13s4 ◽

pp. CIN.S13978

Author(s):

Yen-Tsung Huang ◽

Thomas Hsu ◽

David C. Christiani

Keyword(s):

Copy Number ◽

Copy Number Data ◽

Copy Number Profile ◽

Test Statistic ◽

Gene Set ◽

Bonferroni Adjustment ◽

Gene Sets ◽

Genome Wide ◽

A Genome ◽

Pathway Analyses

The effects of copy number alterations make up a significant part of the tumor genome profile, but pathway analyses of these alterations are still not well established. We proposed a novel method to analyze multiple copy numbers of genes within a pathway, termed Test for the Effect of a Gene Set with Copy Number data (TEGS-CN). TEGS-CN was adapted from TEGS, a method that we previously developed for gene expression data using a variance component score test. With additional development, we extend the method to analyze DNA copy number data, accounting for different sizes and thus various numbers of copy number probes in genes. The test statistic follows a mixture of X 2 distributions that can be obtained using permutation with scaled X 2 approximation. We conducted simulation studies to evaluate the size and the power of TEGS-CN and to compare its performance with TEGS. We analyzed a genome-wide copy number data from 264 patients of non-small-cell lung cancer. With the Molecular Signatures Database (MSigDB) pathway database, the genome-wide copy number data can be classified into 1814 biological pathways or gene sets. We investigated associations of the copy number profile of the 1814 gene sets with pack-years of cigarette smoking. Our analysis revealed five pathways with significant P values after Bonferroni adjustment (<2.8 x 10-5), including the PTEN pathway (7.8 x 10-7), the gene set up-regulated under heat shock (3.6 x 10-6), the gene sets involved in the immune profile for rejection of kidney transplantation (9.2 x 10-6) and for transcriptional control of leukocytes (2.2 x 10-5), and the ganglioside biosynthesis pathway (2.7 x 10-5). In conclusion, we present a new method for pathway analyses of copy number data, and causal mechanisms of the five pathways require further study.

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Data-adaptive multi-locus association testing in subjects with arbitrary genealogical relationships

Statistical Applications in Genetics and Molecular Biology ◽

10.1515/sagmb-2018-0030 ◽

2019 ◽

Vol 18 (3) ◽

Cited By ~ 1

Author(s):

Gail Gong ◽

Wei Wang ◽

Chih-Lin Hsieh ◽

David J. Van Den Berg ◽

Christopher Haiman ◽

...

Keyword(s):

Prostate Cancer ◽

R Package ◽

Suppressor Gene ◽

Test Statistic ◽

Specific Data ◽

Association Tests ◽

Association Testing ◽

Genome Wide ◽

Genome Wide Data ◽

Data Adaptive

Abstract Genome-wide sequencing enables evaluation of associations between traits and combinations of variants in genes and pathways. But such evaluation requires multi-locus association tests with good power, regardless of the variant and trait characteristics. And since analyzing families may yield more power than analyzing unrelated individuals, we need multi-locus tests applicable to both related and unrelated individuals. Here we describe such tests, and we introduce SKAT-X, a new test statistic that uses genome-wide data obtained from related or unrelated subjects to optimize power for the specific data at hand. Simulations show that: a) SKAT-X performs well regardless of variant and trait characteristics; and b) for binary traits, analyzing affected relatives brings more power than analyzing unrelated individuals, consistent with previous findings for single-locus tests. We illustrate the methods by application to rare unclassified missense variants in the tumor suppressor gene BRCA2, as applied to combined data from prostate cancer families and unrelated prostate cancer cases and controls in the Multi-ethnic Cohort (MEC). The methods can be implemented using open-source code for public use as the R-package GATARS (Genetic Association Tests for Arbitrarily Related Subjects) <https://gailg.github.io/gatars/>.

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