Controlled Variable Selection from Summary Statistics Only? A Solution via GhostKnockoffs and Penalized Regression

Identifying which variables do influence a response while controlling false positives pervades statistics and data science. In this paper, we consider a scenario in which we only have access to summary statistics, such as the values of marginal empirical correlations between each dependent variable of potential interest and the response. This situation may arise due to privacy concerns, e.g., to avoid the release of sensitive genetic information. We extend GhostKnockoffs He et al. [2022] and introduce variable selection methods based on penalized regression achieving false discovery rate (FDR) control. We report empirical results in extensive simulation studies, demonstrating enhanced performance over previous work. We also apply our methods to genome-wide association studies of Alzheimer's disease, and evidence a significant improvement in power.

Competition-based control of the false discovery proportion

Recently, Barber and Candès laid the theoretical foundation for a general framework for false discovery rate (FDR) control based on the notion of "knockoffs." A closely related FDR control methodology has long been employed in the analysis of mass spectrometry data, referred to there as "target-decoy competition" (TDC). However, any approach that aims to control the FDR, which is defined as the expected value of the false discovery proportion (FDP), suffers from a problem. Specifically, even when successfully controlling the FDR at level α, the FDP in the list of discoveries can significantly exceed α. We offer FDP-SD, a new procedure that rigorously controls the FDP in the knockoff/TDC competition setup by guaranteeing that the FDP is bounded by α at a desired confidence level. Compared with the recently published framework of Katsevich and Ramdas, FDP-SD generally delivers more power and often substantially so in simulated and real data.

Identification of significant gene expression changes in multiple perturbation experiments using knockoffs

Large-scale multiple perturbation experiments have the potential to reveal a more detailed understanding of the molecular pathways that respond to genetic and environmental changes. A key question in these studies is which gene expression changes are important for the response to the perturbation. This problem is challenging because (i) the functional form of the nonlinear relationship between gene expression and the perturbation is unknown and (ii) identification of the most important genes is a high-dimensional variable selection problem. To deal with these challenges, we present here a method based on the model-X knockoffs framework and Deep Neural Networks to identify significant gene expression changes in multiple perturbation experiments. This approach makes no assumptions on the functional form of the dependence between the responses and the perturbations and it enjoys finite sample false discovery rate control for the selected set of important gene expression responses. We apply this approach to the Library of Integrated Network-Based Cellular Signature data sets which is a National Institutes of Health Common Fund program that catalogs how human cells globally respond to chemical, genetic and disease perturbations. We identified important genes whose expression is directly modulated in response to perturbation with anthracycline, vorinostat, trichostatin-a, geldanamycin and sirolimus. We compare the set of important genes that respond to these small molecules to identify co-responsive pathways. Identification of which genes respond to specific perturbation stressors can provide better understanding of the underlying mechanisms of disease and advance the identification of new drug targets.

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.

DeepLINK: Deep learning inference using knockoffs with applications to genomics

We propose a deep learning-based knockoffs inference framework, DeepLINK, that guarantees the false discovery rate (FDR) control in high-dimensional settings. DeepLINK is applicable to a broad class of covariate distributions described by the possibly nonlinear latent factor models. It consists of two major parts: an autoencoder network for the knockoff variable construction and a multilayer perceptron network for feature selection with the FDR control. The empirical performance of DeepLINK is investigated through extensive simulation studies, where it is shown to achieve FDR control in feature selection with both high selection power and high prediction accuracy. We also apply DeepLINK to three real data applications to demonstrate its practical utility.

Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data

Recent discoveries suggest that our gut microbiome plays an important role in our health and wellbeing. However, the gut microbiome data are intricate; for example, the microbial diversity in the gut makes the data high-dimensional. While there are dedicated high-dimensional methods, such as the lasso estimator, they always come with the risk of false discoveries. Knockoffs are a recent approach to control the number of false discoveries. In this paper, we show that knockoffs can be aggregated to increase power while retaining sharp control over the false discoveries. We support our method both in theory and simulations, and we show that it can lead to new discoveries on microbiome data from the American Gut Project. In particular, our results indicate that several phyla that have been overlooked so far are associated with obesity.

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.