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1. Second-order group knockoffs with applications to genome-wide association studies

   https://doi.org/10.1093/bioinformatics/btae580  

   Chu, Benjamin B; Gu, Jiaqi; Chen, Zhaomeng; Morrison, Tim; Candès, Emmanuel; He, Zihuai; Sabatti, Chiara (October 2024, Bioinformatics)

   Gao, Xin (Ed.)

   Abstract MotivationConditional testing via the knockoff framework allows one to identify—among a large number of possible explanatory variables—those that carry unique information about an outcome of interest and also provides a false discovery rate guarantee on the selection. This approach is particularly well suited to the analysis of genome-wide association studies (GWAS), which have the goal of identifying genetic variants that influence traits of medical relevance. ResultsWhile conditional testing can be both more powerful and precise than traditional GWAS analysis methods, its vanilla implementation encounters a difficulty common to all multivariate analysis methods: it is challenging to distinguish among multiple, highly correlated regressors. This impasse can be overcome by shifting the object of inference from single variables to groups of correlated variables. To achieve this, it is necessary to construct “group knockoffs.” While successful examples are already documented in the literature, this paper substantially expands the set of algorithms and software for group knockoffs. We focus in particular on second-order knockoffs, for which we describe correlation matrix approximations that are appropriate for GWAS data and that result in considerable computational savings. We illustrate the effectiveness of the proposed methods with simulations and with the analysis of albuminuria data from the UK Biobank. Availability and implementationThe described algorithms are implemented in an open-source Julia package Knockoffs.jl. R and Python wrappers are available as knockoffsr and knockoffspy packages. 

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2. Self-Discrepancy Conditional Independence Test

   Lee, Sanghack; Honavar, Vasant G (January 2017, Uncertainty in artificial intelligence)

   Tests of conditional independence (CI) of ran- dom variables play an important role in ma- chine learning and causal inference. Of partic- ular interest are kernel-based CI tests which allow us to test for independence among ran- dom variables with complex distribution func- tions. The efficacy of a CI test is measured in terms of its power and its calibratedness. We show that the Kernel CI Permutation Test (KCIPT) suffers from a loss of calibratedness as its power is increased by increasing the number of bootstraps. To address this limita- tion, we propose a novel CI test, called Self- Discrepancy Conditional Independence Test (SDCIT). SDCIT uses a test statistic that is a modified unbiased estimate of maximum mean discrepancy (MMD), the largest difference in the means of features of the given sample and its permuted counterpart in the kernel-induced Hilbert space. We present results of experi- ments that demonstrate SDCIT is, relative to the other methods: (i) competitive in terms of its power and calibratedness, outperforming other methods when the number of condition- ing variables is large; (ii) more robust with re- spect to the choice of the kernel function; and (iii) competitive in run time. 

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3. Phylogenetic association analysis with conditional rank correlation

   https://doi.org/10.1093/biomet/asad075  

   Wang, Shulei; Yuan, Bo; Tony_Cai, T.; Li, Hongzhe (December 2023, Biometrika)

   Summary Phylogenetic association analysis plays a crucial role in investigating the correlation between microbial compositions and specific outcomes of interest in microbiome studies. However, existing methods for testing such associations have limitations related to the assumption of a linear association in high-dimensional settings and the handling of confounding effects. Hence, there is a need for methods capable of characterizing complex associations, including nonmonotonic relationships. This article introduces a novel phylogenetic association analysis framework and associated tests to address these challenges by employing conditional rank correlation as a measure of association. The proposed tests account for confounders in a fully nonparametric manner, ensuring robustness against outliers and the ability to detect diverse dependencies. The proposed framework aggregates conditional rank correlations for subtrees using weighted sum and maximum approaches to capture both dense and sparse signals. The significance level of the test statistics is determined by calibration through a nearest-neighbour bootstrapping method, which is straightforward to implement and can accommodate additional datasets when these are available. The practical advantages of the proposed framework are demonstrated through numerical experiments using both simulated and real microbiome datasets. 

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4. Graphical Gaussian process models for highly multivariate spatial data

   https://doi.org/10.1093/biomet/asab061  

   Dey, Debangan; Datta, Abhirup; Banerjee, Sudipto (December 2021, Biometrika)

   Summary For multivariate spatial Gaussian process models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence between the variables. This is undesirable, especially in highly multivariate settings, where popular cross-covariance functions, such as multivariate Matérn functions, suffer from a curse of dimensionality as the numbers of parameters and floating-point operations scale up in quadratic and cubic order, respectively, with the number of variables. We propose a class of multivariate graphical Gaussian processes using a general construction called stitching that crafts cross-covariance functions from graphs and ensures process-level conditional independence between variables. For the Matérn family of functions, stitching yields a multivariate Gaussian process whose univariate components are Matérn Gaussian processes, and which conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matérn Gaussian process to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling. 

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5. A Poisson reduced-rank regression model for association mapping in sequencing data

   https://doi.org/10.1186/s12859-022-05054-6  

   Fitzgerald, Tiana; Jones, Andrew; Engelhardt, Barbara_E (December 2022, BMC Bioinformatics)

   Abstract BackgroundSingle-cell RNA-sequencing (scRNA-seq) technologies allow for the study of gene expression in individual cells. Often, it is of interest to understand how transcriptional activity is associated with cell-specific covariates, such as cell type, genotype, or measures of cell health. Traditional approaches for this type of association mapping assume independence between the outcome variables (or genes), and perform a separate regression for each. However, these methods are computationally costly and ignore the substantial correlation structure of gene expression. Furthermore, count-based scRNA-seq data pose challenges for traditional models based on Gaussian assumptions. ResultsWe aim to resolve these issues by developing a reduced-rank regression model that identifies low-dimensional linear associations between a large number of cell-specific covariates and high-dimensional gene expression readouts. Our probabilistic model uses a Poisson likelihood in order to account for the unique structure of scRNA-seq counts. We demonstrate the performance of our model using simulations, and we apply our model to a scRNA-seq dataset, a spatial gene expression dataset, and a bulk RNA-seq dataset to show its behavior in three distinct analyses. ConclusionWe show that our statistical modeling approach, which is based on reduced-rank regression, captures associations between gene expression and cell- and sample-specific covariates by leveraging low-dimensional representations of transcriptional states. 

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