MULTILAYER KNOCKOFF FILTER: CONTROLLED VARIABLE SELECTION AT MULTIPLE RESOLUTIONS

Transcriptome data are insufficient to control false discoveries in regulatory network inference

Inference of causal transcriptional regulatory networks (TRNs) from transcriptomic data suffers notoriously from false positives. Approaches to control the false discovery rate (FDR), for example, via permutation, bootstrapping, or multivariate Gaussian distributions, suffer from several complications: difficulty in distinguishing direct from indirect regulation, nonlinear effects, and causal structure inference requiring "causal sufficiency," meaning experiments that are free of any unmeasured, confounding variables. Here, we use a recently developed statistical framework, model-X knockoffs, to control the FDR while accounting for indirect effects, nonlinear dose-response, and user-provided covariates. We adjust the procedure to estimate the FDR correctly even when measured against incomplete gold standards. However, benchmarking against chromatin immunoprecipitation (ChIP) and other gold standards reveals higher observed than reported FDR. This indicates that unmeasured confounding is a major driver of FDR in TRN inference. A record of this paper's transparent peer review process is included in the supplemental information.

Summary statistics knockoffs inference with family-wise error rate control

Testing multiple hypotheses of conditional independence with provable error rate control is a fundamental problem with various applications. To infer conditional independence with family-wise error rate (FWER) control when only summary statistics of marginal dependence are accessible, we adopt GhostKnockoff to directly generate knockoff copies of summary statistics and propose a new filter to select features conditionally dependent on the response. In addition, we develop a computationally efficient algorithm to greatly reduce the computational cost of knockoff copies generation without sacrificing power and FWER control. Experiments on simulated data and a real dataset of Alzheimer's disease genetics demonstrate the advantage of the proposed method over existing alternatives in both statistical power and computational efficiency.

Beyond guilty by association at scale: searching for causal variants on the basis of genome-wide summary statistics

Understanding the causal genetic architecture of complex phenotypes is essential for future research into disease mechanisms and potential therapies. Here, we present a novel framework for genome-wide detection of sets of variants that carry non-redundant information on the phenotypes and are therefore more likely to be causal in a biological sense. Crucially, our framework requires only summary statistics obtained from standard genome-wide marginal association testing. The described approach, implemented in open-source software, is also computationally efficient, requiring less than 15 minutes on a single CPU to perform genome-wide analysis. Through extensive genome-wide simulation studies, we show that the method can substantially outperform usual two-stage marginal association testing and fine-mapping procedures in precision and recall. In applications to a meta-analysis of ten large-scale genetic studies of Alzheimer's disease (AD), we identified 82 loci associated with AD, including 37 additional loci missed by conventional GWAS pipeline. The identified putative causal variants achieve state-of-the-art agreement with massively parallel reporter assays and CRISPR-Cas9 experiments. Additionally, we applied the method to a retrospective analysis of 67 large-scale GWAS summary statistics since 2013 for a variety of phenotypes. Results reveal the method's capacity to robustly discover additional loci for polygenic traits and pinpoint potential causal variants underpinning each locus beyond conventional GWAS pipeline, contributing to a deeper understanding of complex genetic architectures in post-GWAS analyses.

A generic model-free feature screening procedure for ultra-high dimensional data with categorical response

BACKGROUND AND OBJECTIVE

Identifying active features from ultra-high dimensional data is one of the primary and vital tasks in statistical learning and biological discovery.

METHODS

In this paper, we develop a generic concordance index screening (CI-SIS) procedure to wrestle with ultra-high dimensional data with categorical response. The proposed procedure is model-free and nonparametric based on the concordance index measure. It enjoys both sure screening and ranking consistency properties under some relatively weak assumptions. We investigate the flexibility of this procedure by considering some commonly-encountered challenging settings in biomedical studies, such as category-adaptive data and extremely unbalanced response distributions. A data-driven threshold selection procedure via knockoff features is also presented.

RESULTS

On the real lung dataset, our method achieves a lower prediction error with a mean error of 0.107 with linear discriminant analysis (LDA) and 0.117 with random forest (RF), respectively. In addition, we obtain an accuracy improvement of 3% with LDA and 5% with RF compared to the runner-up method. In a more challenging real data of SRBCT (Small round blue cell tumours), CI-SIS brings about a amazing performance improvement, which is at least 8% higher than all other competing methods.

CONCLUSION

Experimental results show that the proposed method can efficiently identify genes that are associated with certain types of diseases. Therefore, survived features (filtering out irrelevant features) selected by our procedure can help doctors make precision diagnoses and refined treatments of patients.

GhostKnockoff inference empowers identification of putative causal variants in genome-wide association studies

Recent advances in genome sequencing and imputation technologies provide an exciting opportunity to comprehensively study the contribution of genetic variants to complex phenotypes. However, our ability to translate genetic discoveries into mechanistic insights remains limited at this point. In this paper, we propose an efficient knockoff-based method, GhostKnockoff, for genome-wide association studies (GWAS) that leads to improved power and ability to prioritize putative causal variants relative to conventional GWAS approaches. The method requires only Z-scores from conventional GWAS and hence can be easily applied to enhance existing and future studies. The method can also be applied to meta-analysis of multiple GWAS allowing for arbitrary sample overlap. We demonstrate its performance using empirical simulations and two applications: (1) a meta-analysis for Alzheimer's disease comprising nine overlapping large-scale GWAS, whole-exome and whole-genome sequencing studies and (2) analysis of 1403 binary phenotypes from the UK Biobank data in 408,961 samples of European ancestry. Our results demonstrate that GhostKnockoff can identify putatively functional variants with weaker statistical effects that are missed by conventional association tests.

Grace-AKO: a novel and stable knockoff filter for variable selection incorporating gene network structures

Motivation

Variable selection is a common statistical approach to identifying genes associated with clinical outcomes of scientific interest. There are thousands of genes in genomic studies, while only a limited number of individual samples are available. Therefore, it is important to develop a method to identify genes associated with outcomes of interest that can control finite-sample false discovery rate (FDR) in high-dimensional data settings.

Results

This article proposes a novel method named Grace-AKO for graph-constrained estimation (Grace), which incorporates aggregation of multiple knockoffs (AKO) with the network-constrained penalty. Grace-AKO can control FDR in finite-sample settings and improve model stability simultaneously. Simulation studies show that Grace-AKO has better performance in finite-sample FDR control than the original Grace model. We apply Grace-AKO to the prostate cancer data in The Cancer Genome Atlas program by incorporating prostate-specific antigen (PSA) pathways in the Kyoto Encyclopedia of Genes and Genomes as the prior information. Grace-AKO finally identifies 47 candidate genes associated with PSA level, and more than 75% of the detected genes can be validated.

Smoothed Nested Testing on Directed Acyclic Graphs

We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-level test statistics using the known logical constraints. Within this framework, we study a smoothing procedure that combines each node with all of its descendants to form a more powerful statistic. We prove a broad class of smoothing strategies can be used with existing selection procedures to control the familywise error rate, false discovery exceedance rate, or false discovery rate, so long as the original test statistics are independent under the null. When the null statistics are not independent but are derived from positively-correlated normal observations, we prove control for all three error rates when the smoothing method is arithmetic averaging of the observations. Simulations and an application to a real biology dataset demonstrate that smoothing leads to substantial power gains.

A High-Dimensional Power Analysis of the Conditional Randomization Test and Knockoffs

In many scientific problems, researchers try to relate a response variable Y to a set of potential explanatory variables X  = (X1,…,Xp), and start by trying to identify variables that contribute to this relationship. In statistical terms, this goal can be posed as trying to identify the Xj’s upon which Y is conditionally dependent. Sometimes it is of value to simultaneously test for each j, which is more commonly known as variable selection. The conditional randomization test, CRT, and model-X knockoffs are two recently proposed methods that respectively perform conditional independence testing and variable selection by, for each Xj, computing any test statistic on the data and assessing that test statistic’s significance by comparing it to test statistics computed on synthetic variables generated using knowledge of X’s distribution. Our main contribution is to analyse their power in a high-dimensional linear model where the ratio of the dimension p and the sample size n converge to a positive constant. We give explicit expressions for the asymptotic power of the CRT, variable selection with CRT p-values, and model-X knockoffs, each with a test statistic based on either the marginal covariance, the least squares coefficient, or the lasso. One useful application of our analysis is the direct theoretical comparison of the asymptotic powers of variable selection with CRT p-values and model-X knockoffs; in the instances with independent covariates that we consider, the CRT provably dominates knockoffs. We also analyse the power gain from using unlabelled data in the CRT when limited knowledge of X’s distribution is available, and the power of the CRT when samples are collected retrospectively.

False discovery rate control in genome-wide association studies with population structure

We present a comprehensive statistical framework to analyze data from genome-wide association studies of polygenic traits, producing interpretable findings while controlling the false discovery rate. In contrast with standard approaches, our method can leverage sophisticated multivariate algorithms but makes no parametric assumptions about the unknown relation between genotypes and phenotype. Instead, we recognize that genotypes can be considered as a random sample from an appropriate model, encapsulating our knowledge of genetic inheritance and human populations. This allows the generation of imperfect copies (knockoffs) of these variables that serve as ideal negative controls, correcting for linkage disequilibrium and accounting for unknown population structure, which may be due to diverse ancestries or familial relatedness. The validity and effectiveness of our method are demonstrated by extensive simulations and by applications to the UK Biobank data. These analyses confirm our method is powerful relative to state-of-the-art alternatives, while comparisons with other studies validate most of our discoveries. Finally, fast software is made available for researchers to analyze Biobank-scale datasets.

False discovery rate control in genome-wide association studies with population structure

We present a comprehensive statistical framework to analyze data from genome-wide association studies of polygenic traits, producing interpretable findings while controlling the false discovery rate. In contrast with standard approaches, our method can leverage sophisticated multivariate algorithms but makes no parametric assumptions about the unknown relation between genotypes and phenotype. Instead, we recognize that genotypes can be considered as a random sample from an appropriate model, encapsulating our knowledge of genetic inheritance and human populations. This allows the generation of imperfect copies (knockoffs) of these variables that serve as ideal negative controls, correcting for linkage disequilibrium and accounting for unknown population structure, which may be due to diverse ancestries or familial relatedness. The validity and effectiveness of our method are demonstrated by extensive simulations and by applications to the UK Biobank data. These analyses confirm our method is powerful relative to state-of-the-art alternatives, while comparisons with other studies validate most of our discoveries. Finally, fast software is made available for researchers to analyze Biobank-scale datasets.

Interpretable Classification of Bacterial Raman Spectra with Knockoff Wavelets

Deep neural networks and other machine learning models are widely applied to biomedical signal data because they can detect complex patterns and compute accurate predictions. However, the difficulty of interpreting such models is a limitation, especially for applications involving high-stakes decision, including the identification of bacterial infections. This paper considers fast Raman spectroscopy data and demonstrates that a logistic regression model with carefully selected features achieves accuracy comparable to that of neural networks, while being much simpler and more transparent. Our analysis leverages wavelet features with intuitive chemical interpretations, and performs controlled variable selection with knockoffs to ensure the predictors are relevant and non-redundant. Although we focus on a particular data set, the proposed approach is broadly applicable to other types of signal data for which interpretability may be important.

Deep-gKnock: Nonlinear group-feature selection with deep neural networks

Feature selection is central to contemporary high-dimensional data analysis. Group structure among features arises naturally in various scientific problems. Many methods have been proposed to incorporate the group structure information into feature selection. However, these methods are normally restricted to a linear regression setting. To relax the linear constraint, we design a new Deep Neural Network (DNN) architecture and integrating it with the recently proposed knockoff technique to perform nonlinear group-feature selection with controlled group-wise False Discovery Rate (gFDR). Experimental results on high-dimensional synthetic data demonstrate that our method achieves the highest power and accurate gFDR control compared with state-of-the-art methods. The performance of Deep-gKnock is especially superior in the following five situations: (1) nonlinearity relationship; (2) dimension p greater than sample size n; (3) high between-group correlation; (4) high within-group correlation; (5) large number of associated groups. And Deep-gKnock is also demonstrated to be robust to the misspecification of the feature distribution and the change of network architecture. Moreover, Deep-gKnock achieves scientifically meaningful group-feature selection results for cutting-edge real world datasets.

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.

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.