Prioritizing genetic variants in GWAS with lasso using permutation-assisted tuning

MOTIVATION

Large scale genome-wide association studies (GWAS) have resulted in the identification of a wide range of genetic variants related to a host of complex traits and disorders. Despite their success, the individual single-nucleotide polymorphism (SNP) analysis approach adopted in most current GWAS can be limited in that it is usually biologically simple to elucidate a comprehensive genetic architecture of phenotypes and statistically underpowered due to heavy multiple-testing correction burden. On the other hand, multiple-SNP analyses (e.g. gene-based or region-based SNP-set analysis) are usually more powerful to examine the joint effects of a set of SNPs on the phenotype of interest. However, current multiple-SNP approaches can only draw an overall conclusion at the SNP-set level and does not directly inform which SNPs in the SNP-set are driving the overall genotype-phenotype association.

RESULTS

In this article, we propose a new permutation-assisted tuning procedure in lasso (plasso) to identify phenotype-associated SNPs in a joint multiple-SNP regression model in GWAS. The tuning parameter of lasso determines the amount of shrinkage and is essential to the performance of variable selection. In the proposed plasso procedure, we first generate permutations as pseudo-SNPs that are not associated with the phenotype. Then, the lasso tuning parameter is delicately chosen to separate true signal SNPs and non-informative pseudo-SNPs. We illustrate plasso using simulations to demonstrate its superior performance over existing methods, and application of plasso to a real GWAS dataset gains new additional insights into the genetic control of complex traits.

AVAILABILITY AND IMPLEMENTATION

R codes to implement the proposed methodology is available at https://github.com/xyz5074/plasso.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Double Empirical Bayes Testing

Analyzing data from large-scale, multi-experiment studies requires scientists to both analyze each experiment and to assess the results as a whole. In this article, we develop double empirical Bayes testing (DEBT), an empirical Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. DEBT is a two-stage method: in the first stage, it reports which experiments yielded significant outcomes; in the second stage, it hypothesizes which covariates drive the experimental significance. In both of its stages, DEBT builds on Efron (2008), which lays out an elegant empirical Bayes approach to testing. DEBT enhances this framework by learning a series of black box predictive models to boost power and control the false discovery rate (FDR). In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, it uses an empirical Bayes version of the knockoff filter (Candes et al., 2018) to select covariates that have significant predictive power of Stage-1 significance. In both simulated and real data, DEBT increases the proportion of discovered significant outcomes and selects more features when signals are weak. In a real study of cancer cell lines, DEBT selects a robust set of biologically-plausible genomic drivers of drug sensitivity and resistance in cancer.

Robust data-driven identification of risk factors and their interactions: A simulation and a study of parental and demographic risk factors for schizophrenia

OBJECTIVES

Few interactions between risk factors for schizophrenia have been replicated, but fitting all such interactions is difficult due to high-dimensionality. Our aims are to examine significant main and interaction effects for schizophrenia and the performance of our approach using simulated data.

METHODS

We apply the machine learning technique elastic net to a high-dimensional logistic regression model to produce a sparse set of predictors, and then assess the significance of odds ratios (OR) with Bonferroni-corrected p-values and confidence intervals (CI). We introduce a simulation model that resembles a Finnish nested case-control study of schizophrenia which uses national registers to identify cases (n = 1,468) and controls (n = 2,975). The predictors include nine sociodemographic factors and all interactions (31 predictors).

RESULTS

In the simulation, interactions with OR = 3 and prevalence = 4% were identified with <5% false positive rate and ≥80% power. None of the studied interactions were significantly associated with schizophrenia, but main effects of parental psychosis (OR = 5.2, CI 2.9-9.7; p < .001), urbanicity (1.3, 1.1-1.7; p = .001), and paternal age ≥35 (1.3, 1.004-1.6; p = .04) were significant.

CONCLUSIONS

We have provided an analytic pipeline for data-driven identification of main and interaction effects in case-control data. We identified highly replicated main effects for schizophrenia, but no interactions.

Beyond Target-Decoy Competition: Stable Validation of Peptide and Protein Identifications in Mass Spectrometry-Based Discovery Proteomics

In bottom-up discovery proteomics, target-decoy competition (TDC) is the most popular method for false discovery rate (FDR) control. Despite unquestionable statistical foundations, this method has drawbacks, including its hitherto unknown intrinsic lack of stability vis-à-vis practical conditions of application. Although some consequences of this instability have already been empirically described, they may have been misinterpreted. This article provides evidence that TDC has become less reliable as the accuracy of modern mass spectrometers improved. We therefore propose to replace TDC by a totally different method to control the FDR at the spectrum, peptide, and protein levels, while benefiting from the theoretical guarantees of the Benjamini-Hochberg framework. As this method is simpler to use, faster to compute, and more stable than TDC, we argue that it is better adapted to the standardization and throughput constraints of current proteomic platforms.

Statistical Hypothesis Testing versus Machine Learning Binary Classification: Distinctions and Guidelines

Making binary decisions is a common data analytical task in scientific research and industrial applications. In data sciences, there are two related but distinct strategies: hypothesis testing and binary classification. In practice, how to choose between these two strategies can be unclear and rather confusing. Here, we summarize key distinctions between these two strategies in three aspects and list five practical guidelines for data analysts to choose the appropriate strategy for specific analysis needs. We demonstrate the use of those guidelines in a cancer driver gene prediction example.

On order determination by predictor augmentation

In many dimension reduction problems in statistics and machine learning, such as in principal component analysis, canonical correlation analysis, independent component analysis and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this article, we propose a novel and highly effective order-determination method based on the idea of predictor augmentation. We show that if the predictor is augmented by an artificially generated random vector, then the parts of the eigenvectors of the matrix induced by the augmentation display a pattern that reveals information about the order to be determined. This information, when combined with the information provided by the eigenvalues of the matrix, greatly enhances the accuracy of order determination.

TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA

This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic decorrelated inference function approach, which simultaneously removes the impact of nuisance parameters and incorporates the correlation to enhance the efficiency of the estimation procedure. When the parameter of interest is of fixed dimension, we prove that the proposed estimator is asymptotically normal and attains the semiparametric information bound, based on which we can construct an optimal Wald test statistic. We further extend this result and establish the limiting distribution of the estimator under the setting with the dimension of the parameter of interest growing with the sample size at a polynomial rate. Finally, we study how to control the false discovery rate (FDR) when a vector of high-dimensional regression parameters is of interest. We prove that applying the Storey (2002)'s procedure to the proposed test statistics for each regression parameter controls FDR asymptotically in longitudinal data. We conduct simulation studies to assess the finite sample performance of the proposed procedures. Our simulation results imply that the newly proposed procedure can control both Type I error for testing a low dimensional parameter of interest and the FDR in the multiple testing problem. We also apply the proposed procedure to a real data example.

An assumption-free exact test for fixed-design linear models with exchangeable errors

We propose the cyclic permutation test to test general linear hypotheses for linear models. The test is nonrandomized and valid in finite samples with exact Type I error $\alpha$ for an arbitrary fixed design matrix and arbitrary exchangeable errors, whenever $1 / \alpha$ is an integer and $n / p \geqslant 1 / \alpha - 1$, where $n$ is the sample size and $p$ is the number of parameters. The test involves applying the marginal rank test to $1 / \alpha$ linear statistics of the outcome vector, where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a nonstandard cyclic permutation group under the null hypothesis. The power can be further enhanced by solving a secondary nonlinear travelling salesman problem, for which the genetic algorithm can find a reasonably good solution. Extensive simulation studies show that the cyclic permutation test has comparable power to existing tests. When testing for a single contrast of coefficients, an exact confidence interval can be obtained by inverting the test.

Causal inference in genetic trio studies

We introduce a method to draw causal inferences-inferences immune to all possible confounding-from genetic data that include parents and offspring. Causal conclusions are possible with these data because the natural randomness in meiosis can be viewed as a high-dimensional randomized experiment. We make this observation actionable by developing a conditional independence test that identifies regions of the genome containing distinct causal variants. The proposed digital twin test compares an observed offspring to carefully constructed synthetic offspring from the same parents to determine statistical significance, and it can leverage any black-box multivariate model and additional nontrio genetic data to increase power. Crucially, our inferences are based only on a well-established mathematical model of recombination and make no assumptions about the relationship between the genotypes and phenotypes. We compare our method to the widely used transmission disequilibrium test and demonstrate enhanced power and localization.

An embedded gene selection method using knockoffs optimizing neural network

Background

Gene selection refers to find a small subset of discriminant genes from the gene expression profiles. How to select genes that affect specific phenotypic traits effectively is an important research work in the field of biology. The neural network has better fitting ability when dealing with nonlinear data, and it can capture features automatically and flexibly. In this work, we propose an embedded gene selection method using neural network. The important genes can be obtained by calculating the weight coefficient after the training is completed. In order to solve the problem of black box of neural network and further make the training results interpretable in neural network, we use the idea of knockoffs to construct the knockoff feature genes of the original feature genes. This method not only make each feature gene to compete with each other, but also make each feature gene compete with its knockoff feature gene. This approach can help to select the key genes that affect the decision-making of neural networks.

Results

We use maize carotenoids, tocopherol methyltransferase, raffinose family oligosaccharides and human breast cancer dataset to do verification and analysis.

Conclusions

The experiment results demonstrate that the knockoffs optimizing neural network method has better detection effect than the other existing algorithms, and specially for processing the nonlinear gene expression and phenotype data.

A general interactive framework for false discovery rate control under structural constraints

We propose a general framework based on selectively traversed accumulation rules for interactive multiple testing with generic structural constraints on the rejection set. It combines accumulation tests from ordered multiple testing with data-carving ideas from post-selection inference, allowing highly flexible adaptation to generic structural information. Our procedure defines an interactive protocol for gradually pruning a candidate rejection set, beginning with the set of all hypotheses and shrinking the set with each step. By restricting the information at each step via a technique we call masking, our protocol enables interaction while controlling the false discovery rate in finite samples for any data-adaptive update rule that the analyst may choose. We suggest update rules for a variety of applications with complex structural constraints, demonstrate that selectively traversed accumulation rules perform well in problems ranging from convex region detection to false discovery rate control on directed acyclic graphs, and show how to extend the framework to regression problems where knockoff statistics are available in lieu of $p$-values.

Revealing False Positive Features in Epileptic EEG Identification

Feature selection plays a vital role in the detection and discrimination of epileptic seizures in electroencephalogram (EEG) signals. The state-of-the-art EEG classification techniques commonly entail the extraction of the multiple features that would be fed into classifiers. For some techniques, the feature selection strategies have been used to reduce the dimensionality of the entire feature space. However, most of these approaches focus on the performance of classifiers while neglecting the association between the feature and the EEG activity itself. To enhance the inner relationship between the feature subset and the epileptic EEG task with a promising classification accuracy, we propose a machine learning-based pipeline using a novel feature selection algorithm built upon a knockoff filter. First, a number of temporal, spectral, and spatial features are extracted from the raw EEG signals. Second, the proposed feature selection algorithm is exploited to obtain the optimal subgroup of features. Afterwards, three classifiers including [Formula: see text]-nearest neighbor (KNN), random forest (RF) and support vector machine (SVM) are used. The experimental results on the Bonn dataset demonstrate that the proposed approach outperforms the state-of-the-art techniques, with accuracy as high as 99.93% for normal and interictal EEG discrimination and 98.95% for interictal and ictal EEG classification. Meanwhile, it has achieved satisfactory sensitivity (95.67% in average), specificity (98.83% in average), and accuracy (98.89% in average) over the Freiburg dataset.

A powerful procedure that controls the false discovery rate with directional information

In many multiple testing applications in genetics, the signs of the test statistics provide useful directional information, such as whether genes are potentially up- or down-regulated between two experimental conditions. However, most existing procedures that control the false discovery rate (FDR) are P-value based and ignore such directional information. We introduce a novel procedure, the signed-knockoff procedure, to utilize the directional information and control the FDR in finite samples. We demonstrate the power advantage of our procedure through simulation studies and two real applications.

Hellinger distance-based stable sparse feature selection for high-dimensional class-imbalanced data

Background

Feature selection in class-imbalance learning has gained increasing attention in recent years due to the massive growth of high-dimensional class-imbalanced data across many scientific fields. In addition to reducing model complexity and discovering key biomarkers, feature selection is also an effective method of combating overlapping which may arise in such data and become a crucial aspect for determining classification performance. However, ordinary feature selection techniques for classification can not be simply used for addressing class-imbalanced data without any adjustment. Thus, more efficient feature selection technique must be developed for complicated class-imbalanced data, especially in the context of high-dimensionality.

Results

We proposed an algorithm called sssHD to achieve stable sparse feature selection applied it to complicated class-imbalanced data. sssHD is based on the Hellinger distance (HD) coupled with sparse regularization techniques. We stated that Hellinger distance is not only class-insensitive but also translation-invariant. Simulation result indicates that HD-based selection algorithm is effective in recognizing key features and control false discoveries for class-imbalance learning. Five gene expression datasets are also employed to test the performance of the sssHD algorithm, and a comparison with several existing selection procedures is performed. The result shows that sssHD is highly competitive in terms of five assessment metrics. In addition, sssHD presents limited differences between performing and not performing re-balance preprocessing.

Conclusions

sssHD is a practical feature selection method for high-dimensional class-imbalanced data, which is simple and can be an alternative for performing feature selection in class-imbalanced data. sssHD can be easily extended by connecting it with different re-balance preprocessing, different sparse regularization structures as well as different classifiers. As such, the algorithm is extremely general and has a wide range of applicability.

Multi-resolution localization of causal variants across the genome

In the statistical analysis of genome-wide association data, it is challenging to precisely localize the variants that affect complex traits, due to linkage disequilibrium, and to maximize power while limiting spurious findings. Here we report on KnockoffZoom: a flexible method that localizes causal variants at multiple resolutions by testing the conditional associations of genetic segments of decreasing width, while provably controlling the false discovery rate. Our method utilizes artificial genotypes as negative controls and is equally valid for quantitative and binary phenotypes, without requiring any assumptions about their genetic architectures. Instead, we rely on well-established genetic models of linkage disequilibrium. We demonstrate that our method can detect more associations than mixed effects models and achieve fine-mapping precision, at comparable computational cost. Lastly, we apply KnockoffZoom to data from 350k subjects in the UK Biobank and report many new findings.

ncHMR detector: a computational framework to systematically reveal non-classical functions of histone modification regulators

Recently, several non-classical functions of histone modification regulators (HMRs), independent of their known histone modification substrates and products, have been reported to be essential for specific cellular processes. However, there is no framework designed for identifying such functions systematically. Here, we develop ncHMR detector, the first computational framework to predict non-classical functions and cofactors of a given HMR, based on ChIP-seq data mining. We apply ncHMR detector in ChIP-seq data-rich cell types and predict non-classical functions of HMRs. Finally, we experimentally reveal that the predicted non-classical function of CBX7 is biologically significant for the maintenance of pluripotency.

High-dimensional variable selection for ordinal outcomes with error control

Many high-throughput genomic applications involve a large set of potential covariates and a response which is frequently measured on an ordinal scale, and it is crucial to identify which variables are truly associated with the response. Effectively controlling the false discovery rate (FDR) without sacrificing power has been a major challenge in variable selection research. This study reviews two existing variable selection frameworks, model-X knockoffs and a modified version of reference distribution variable selection (RDVS), both of which utilize artificial variables as benchmarks for decision making. Model-X knockoffs constructs a 'knockoff' variable for each covariate to mimic the covariance structure, while RDVS generates only one null variable and forms a reference distribution by performing multiple runs of model fitting. Herein, we describe how different importance measures for ordinal responses can be constructed that fit into these two selection frameworks, using either penalized regression or machine learning techniques. We compared these measures in terms of the FDR and power using simulated data. Moreover, we applied these two frameworks to high-throughput methylation data for identifying features associated with the progression from normal liver tissue to hepatocellular carcinoma to further compare and contrast their performances.

Big data analytics for smart factories of the future

Continued advancement of sensors has led to an ever-increasing amount of data of various physical nature to be acquired from production lines. As rich information relevant to the machines and processes are embedded within these "big data", how to effectively and efficiently discover patterns in the big data to enhance productivity and economy has become both a challenge and an opportunity. This paper discusses essential elements of and promising solutions enabled by data science that are critical to processing data of high volume, velocity, variety, and low veracity, towards the creation of added-value in smart factories of the future.

IPAD: Stable Interpretable Forecasting with Knockoffs Inference

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in statistics, economics, and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Candès, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods.

Predicting gene expression in the human malaria parasite Plasmodium falciparum using histone modification, nucleosome positioning, and 3D localization features

Empirical evidence suggests that the malaria parasite Plasmodium falciparum employs a broad range of mechanisms to regulate gene transcription throughout the organism's complex life cycle. To better understand this regulatory machinery, we assembled a rich collection of genomic and epigenomic data sets, including information about transcription factor (TF) binding motifs, patterns of covalent histone modifications, nucleosome occupancy, GC content, and global 3D genome architecture. We used these data to train machine learning models to discriminate between high-expression and low-expression genes, focusing on three distinct stages of the red blood cell phase of the Plasmodium life cycle. Our results highlight the importance of histone modifications and 3D chromatin architecture in Plasmodium transcriptional regulation and suggest that AP2 transcription factors may play a limited regulatory role, perhaps operating in conjunction with epigenetic factors.

False Discovery Rate Control in Cancer Biomarker Selection Using Knockoffs

The discovery of biomarkers that are informative for cancer risk assessment, diagnosis, prognosis and treatment predictions is crucial. Recent advances in high-throughput genomics make it plausible to select biomarkers from the vast number of human genes in an unbiased manner. Yet, control of false discoveries is challenging given the large number of genes versus the relatively small number of patients in a typical cancer study. To ensure that most of the discoveries are true, we employ a knockoff procedure to control false discoveries. Our method is general and flexible, accommodating arbitrary covariate distributions, linear and nonlinear associations, and survival models. In simulations, our method compares favorably to the alternatives; its utility of identifying important genes in real clinical applications is demonstrated by the identification of seven genes associated with Breslow thickness in skin cutaneous melanoma patients.

An Adaptive Multivariate Two-Sample Test With Application to Microbiome Differential Abundance Analysis

Differential abundance analysis is a crucial task in many microbiome studies, where the central goal is to identify microbiome taxa associated with certain biological or clinical conditions. There are two different modes of microbiome differential abundance analysis: the individual-based univariate differential abundance analysis and the group-based multivariate differential abundance analysis. The univariate analysis identifies differentially abundant microbiome taxa subject to multiple correction under certain statistical error measurements such as false discovery rate, which is typically complicated by the high-dimensionality of taxa and complex correlation structure among taxa. The multivariate analysis evaluates the overall shift in the abundance of microbiome composition between two conditions, which provides useful preliminary differential information for the necessity of follow-up validation studies. In this paper, we present a novel Adaptive multivariate two-sample test for Microbiome Differential Analysis (AMDA) to examine whether the composition of a taxa-set are different between two conditions. Our simulation studies and real data applications demonstrated that the AMDA test was often more powerful than several competing methods while preserving the correct type I error rate. A free implementation of our AMDA method in R software is available at https://github.com/xyz5074/AMDA.

RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-X knockoffs procedure introduced recently in Candès, Fan, Janson and Lv (2018) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-X knockoffs method called graphical nonlin-ear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.

MULTILAYER KNOCKOFF FILTER: CONTROLLED VARIABLE SELECTION AT MULTIPLE RESOLUTIONS

We tackle the problem of selecting from among a large number of variables those that are "important" for an outcome. We consider situations where groups of variables are also of interest. For example, each variable might be a genetic polymorphism, and we might want to study how a trait depends on variability in genes, segments of DNA that typically contain multiple such polymorphisms. In this context, to discover that a variable is relevant for the outcome implies discovering that the larger entity it represents is also important. To guarantee meaningful results with high chance of replicability, we suggest controlling the rate of false discoveries for findings at the level of individual variables and at the level of groups. Building on the knockoff construction of Barber and Candès [Ann. Statist. 43 (2015) 2055-2085] and the multilayer testing framework of Barber and Ramdas [J. Roy. Statist. Soc. Ser. B 79 (2017) 1247-1268], we introduce the multilayer knockoff filter (MKF). We prove that MKF simultaneously controls the FDR at each resolution and use simulations to show that it incurs little power loss compared to methods that provide guarantees only for the discoveries of individual variables. We apply MKF to analyze a genetic dataset and find that it successfully reduces the number of false gene discoveries without a significant reduction in power.