arXiv subjects

Hongzhe Li

Publications and source records attributed to Hongzhe Li.

At least 37 records · Page 2Linked to original sources

arXiv2023

A Regression-based Approach to Robust Estimation and Inference for Genetic Covariance

Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex traits, and some variants are shown to be associated with multiple complex traits. Genetic covariance between two traits is defined as the underlying covariance of genetic effects and can be used to measure the shared genetic architecture. The data used to estimate such a genetic covariance can be from the same group or different groups of individuals, and the traits can be of different types or collected based on different study designs. This paper proposes a unified regression-based approach to robust estimation and inference for genetic covariance of general traits that may be associated with genetic variants nonlinearly. The asymptotic properties of the proposed estimator are provided and are shown to be robust under certain model mis-specification. Our method under linear working models provides a robust inference for the narrow-sense genetic covariance, even when both linear models are mis-specified. Numerical experiments are performed to support the theoretical results. Our method is applied to an outbred mice GWAS data set to study the overlapping genetic effects between the behavioral and physiological phenotypes. The real data results reveal interesting genetic covariance among different mice developmental traits.

stat.ME↗

arXiv2023

Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data

Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with blockwise missing covariates and a partially observed response variable. Under this framework, we propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations and a blockwise imputation procedure, and obtain its rate of convergence. Furthermore, building upon an innovative projected estimating equation technique that intrinsically achieves bias-correction of the initial estimator, we propose a nearly unbiased estimator for each individual regression coefficient, which is asymptotically normally distributed under mild conditions. Based on these debiased estimators, asymptotically valid confidence intervals and statistical tests about each regression coefficient are constructed. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods.

stat.ME↗

arXiv2023

Transfer Learning with Random Coefficient Ridge Regression

Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction of random coefficient ridge regression in the setting of transfer learning, where in addition to observations from the target model, source samples from different but possibly related regression models are available. The informativeness of the source model to the target model can be quantified by the correlation between the regression coefficients. This paper proposes two estimators of regression coefficients of the target model as the weighted sum of the ridge estimates of both target and source models, where the weights can be determined by minimizing the empirical estimation risk or prediction risk. Using random matrix theory, the limiting values of the optimal weights are derived under the setting when $p/n \rightarrow γ$, where $p$ is the number of the predictors and $n$ is the sample size, which leads to an explicit expression of the estimation or prediction risks. Simulations show that these limiting risks agree very well with the empirical risks. An application to predicting the polygenic risk scores for lipid traits shows such transfer learning methods lead to smaller prediction errors than the single sample ridge regression or Lasso-based transfer learning.

stat.ML↗

arXiv2023

HT-MMIOW: A Hypothesis Test approach for Microbiome Mediation using Inverse Odds Weighting

The human microbiome has an important role in determining health. Mediation analyses quantify the contribution of the microbiome in the causal path between exposure and disease; however, current mediation models cannot fully capture the high dimensional, correlated, and compositional nature of microbiome data and do not typically accommodate dichotomous outcomes. We propose a novel approach that uses inverse odds weighting to test for the mediating effect of the microbiome. We use simulation to demonstrate that our approach gains power for high dimensional mediators, and it is agnostic to the effect of interactions between the exposure and mediators. Our application to infant gut microbiome data from the New Hampshire Birth Cohort Study revealed a mediating effect of 6-week infant gut microbiome on the relationship between maternal prenatal antibiotic use during pregnancy and incidence of childhood allergy by 5 years of age.

stat.AP↗

arXiv2022

An Empirical Bayes Regression for Multi-tissue eQTL Data Analysis

The Genotype-Tissue Expression (GTEx) project collects samples from multiple human tissues to study the relationship between genetic variation or single nucleotide polymorphisms (SNPs) and gene expression in each tissue. However, most existing eQTL analyses only focus on single tissue information. In this paper, we develop a multi-tissue eQTL analysis that improves the single tissue cis-SNP gene expression association analysis by borrowing information across tissues. Specifically, we propose an empirical Bayes regression model for SNP-expression association analysis using data across multiple tissues. To allow the effects of SNPs to vary greatly among tissues, we use a mixture distribution as the prior, which is a mixture of a multivariate Gaussian distribution and a Dirac mass at zero. The model allows us to assess the cis-SNP gene expression association in each tissue by calculating the Bayes factors. We show that the proposed estimator of the cis-SNP effects on gene expression achieves the minimum Bayes risk among all estimators. Analyses of the GTEx data show that our proposed method is superior to traditional simple regression methods in terms of predicting accuracy for gene expression levels using cis-SNPs in testing data sets. Moreover, we find that although genetic effects on expression are extensively shared among tissues, effect sizes still vary greatly across tissues.

stat.ME↗

arXiv2022

Statistical Inference for Genetic Relatedness Based on High-Dimensional Logistic Regression

This paper studies the problem of statistical inference for genetic relatedness between binary traits based on individual-level genome-wide association data. Specifically, under the high-dimensional logistic regression models, we define parameters characterizing the cross-trait genetic correlation, the genetic covariance and the trait-specific genetic variance. A novel weighted debiasing method is developed for the logistic Lasso estimator and computationally efficient debiased estimators are proposed. The rates of convergence for these estimators are studied and their asymptotic normality is established under mild conditions. Moreover, we construct confidence intervals and statistical tests for these parameters, and provide theoretical justifications for the methods, including the coverage probability and expected length of the confidence intervals, as well as the size and power of the proposed tests. Numerical studies are conducted under both model generated data and simulated genetic data to show the superiority of the proposed methods. By analyzing a real data set on autoimmune diseases, we demonstrate its ability to obtain novel insights about the shared genetic architecture between ten pediatric autoimmune diseases.

stat.ME↗

arXiv2022

Mediation analysis with densities as mediators with an application to iCOMPARE trial

Physical activity has long been shown to be associated with biological and physiological performance and risk of diseases. It is of great interest to assess whether the effect of an exposure or intervention on an outcome is mediated through physical activity measured by modern wearable devices such as actigraphy. However, existing methods for mediation analysis focus almost exclusively on mediation variable that is in the Euclidean space, which cannot be applied directly to the actigraphy data of physical activity. Such data is best summarized in the form of an histogram or density. In this paper, we extend the structural equation models (SEMs) to the settings where a density is treated as the mediator to study the indirect mediation effect of physical activity on an outcome. We provide sufficient conditions for identifying the average causal effects of density mediator and present methods for estimating the direct and mediating effects of density on an outcome. We apply our method to the data set from the iCOMPARE trial that compares flexible duty-hour policies and standard duty-hour policies on interns' sleep related outcomes to explore the mediation effect of physical activity on the causal path between flexible duty-hour policies and sleep related outcomes.

stat.AP↗

arXiv2022

Truncated Rank-Based Tests for Two-Part Models with Excessive Zeros and Applications to Microbiome Data

High-throughput sequencing technology allows us to test the compositional difference of bacteria in different populations. One important feature of human microbiome data is that it often includes a large number of zeros. Such data can be treated as being generated from a two-part model that includes a zero point-mass. Motivated by analysis of such non-negative data with excessive zeros, we introduce several truncated rank-based two-group and multi-group tests for such data, including a truncated rank-based Wilcoxon rank-sum test for two-group comparison and two truncated Kruskal-Wallis tests for multi-group comparison. We show both analytically through asymptotic relative efficiency analysis and by simulations that the proposed tests have higher power than the standard rank-based tests, especially when the proportion of zeros in the data is high. The tests can also be applied to repeated measurements of compositional data via simple within-subject permutations. In a simple before-and-after treatment experiment, the within-subject permutation is similar to the paired rank test. However, the proposed tests handle the excessive zeros, which leads to a better power. We apply the tests to the analysis of a gut microbiome data set to compare the microbiome compositions of healthy and pediatric Crohn's disease patients and to assess the treatment effects on microbiome compositions. We identify several bacterial genera that are missed by the standard rank-based tests.

stat.ME↗

arXiv2022

Estimation and Inference with Proxy Data and its Genetic Applications

Existing high-dimensional statistical methods are largely established for analyzing individual-level data. In this work, we study estimation and inference for high-dimensional linear models where we only observe "proxy data", which include the marginal statistics and sample covariance matrix that are computed based on different sets of individuals. We develop a rate optimal method for estimation and inference for the regression coefficient vector and its linear functionals based on the proxy data. Moreover, we show the intrinsic limitations in the proxy-data based inference: the minimax optimal rate for estimation is slower than that in the conventional case where individual data are observed; the power for testing and multiple testing does not go to one as the signal strength goes to infinity. These interesting findings are illustrated through simulation studies and an analysis of a dataset concerning the genetic associations of hindlimb muscle weight in a mouse population.

stat.ME↗

arXiv2021

Inference of Microbial Interactions Using Copula Models with Mixture Margins

Quantification of microbial interactions from 16S rRNA and meta-genomic sequencing data is difficult due to their sparse nature, as well as the fact that the data only provides measures of relative abundance. In this paper, we propose using copula models with mixed zero-beta margins for estimation of taxon-taxon interactions using the normalized microbial relative abundances. Copulas allow for separate modeling of the dependence structure from the margins, marginal covariate adjustment, and uncertainty measurement. Our method shows that a two-stage maximum likelihood approach provides accurate estimation of the model parameters. A corresponding two-stage likelihood-ratio test for the dependence parameter is derived. Simulation studies show that the test is valid and more powerful than tests based upon Pearson's and rank correlations. Furthermore, we demonstrate that our method can be used to build biologically meaningful microbial networks based on the data set of the American Gut Project.

stat.ME↗

arXiv2021

Inference for Individual Mediation Effects and Interventional Effects in Sparse High-Dimensional Causal Graphical Models

We consider the problem of identifying intermediate variables (or mediators) that regulate the effect of a treatment on a response variable. While there has been significant research on this classical topic, little work has been done when the set of potential mediators is high-dimensional (HD). A further complication arises when these mediators are interrelated (with unknown dependencies). In particular, we assume that the causal structure of the treatment, the confounders, the potential mediators and the response is a (possibly unknown) directed acyclic graph (DAG). HD DAG models have previously been used for the estimation of causal effects from observational data. In particular, methods called IDA and joint-IDA have been developed for estimating the effects of single and multiple simultaneous interventions, respectively. In this paper, we propose an IDA-type method called MIDA for estimating so-called individual mediation effects from HD observational data. Although IDA and joint-IDA estimators have been shown to be consistent in certain sparse HD settings, their asymptotic properties such as convergence in distribution and inferential tools in such settings have remained unknown. In this paper, we prove HD consistency of MIDA for linear structural equation models with sub-Gaussian errors. More importantly, we derive distributional convergence results for MIDA in similar HD settings, which are applicable to IDA and joint-IDA estimators as well. To our knowledge, these are the first such distributional convergence results facilitating inference for IDA-type estimators. These are built on our novel theoretical results regarding uniform bounds for linear regression estimators over varying subsets of HD covariates which may be of independent interest. Finally, we empirically validate our asymptotic theory for MIDA and demonstrate its usefulness via simulations and a real data application.

stat.ME↗

arXiv2021

Two-sample tests for repeated measurements of histogram objects with applications to wearable device data

Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over multiple days. It remains of great interest to appropriately evaluate how the daily distribution of biosignals might differ across disease groups and demographics. Hence these data could be formulated as multivariate complex object data such as probability densities, histograms, and observations on a tree. Traditional statistical methods would often fail to apply as they are sampled from an arbitrary non-Euclidean metric space. In this paper, we propose novel non-parametric graph-based two-sample tests for object data with repeated measures. A set of test statistics are proposed to capture various possible alternatives. We derive their asymptotic null distributions under the permutation null. These tests exhibit substantial power improvements over the existing methods while controlling the type I errors under finite samples as shown through simulation studies. The proposed tests are demonstrated to provide additional insights on the location, inter- and intra-individual variability of the daily physical activity distributions in a sample of studies for mood disorders.

stat.AP↗

arXiv2021

Multi-sample estimation of centered log-ratio matrix in microbiome studies

In microbiome studies, one of the ways of studying bacterial abundances is to estimate bacterial composition based on the sequencing read counts. Various transformations are then applied to such compositional data for downstream statistical analysis, among which the centered log-ratio (clr) transformation is most commonly used. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which makes clr transformation infeasible. This paper proposes a multi-sample approach to estimation of the clr matrix directly in order to borrow information across samples and across species. Empirical results from real datasets suggest that the clr matrix over multiple samples is approximately low rank, which motivates a regularized maximum likelihood estimation with a nuclear norm penalty. An efficient optimization algorithm using the generalized accelerated proximal gradient is developed. Theoretical upper bounds of the estimation errors and of its corresponding singular subspace errors are established. Simulation studies demonstrate that the proposed estimator outperforms the naive estimators. The method is analyzed on Gut Microbiome dataset and the American Gut project.

stat.ME↗

arXiv2021

Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional fixed effects. The proposed method is applicable to general settings where the dimension of the random effects and the cluster sizes are possibly large. Regarding the fixed effects, we provide rate optimal estimators and valid inference procedures that do not rely on the structural information of the variance components. We also study the estimation of variance components with high-dimensional fixed effects in general settings. The algorithms are easy to implement and computationally fast. The proposed methods are assessed in various simulation settings and are applied to a real study regarding the associations between body mass index and genetic polymorphic markers in a heterogeneous stock mice population.

stat.ME↗

arXiv2021

Information content of high-order associations of the human gut microbiota network

The human gastrointestinal tract is an environment that hosts an ecosystem of microorganisms essential to human health. Vital biological processes emerge from fundamental inter- and intra-species molecular interactions that influence the assembly and composition of the gut microbiota ecology. Here we quantify the complexity of the ecological relationships within the human infant gut microbiota ecosystem as a function of the information contained in the nonlinear associations of a sequence of increasingly-specified maximum entropy representations of the system. Our paradigm frames the ecological state, in terms of the presence or absence of individual microbial ecological units that are identified by amplicon sequence variants (ASV) in the gut microenvironment, as a function of both the ecological states of its neighboring units and, in a departure from standard graphical model representations, the associations among the units within its neighborhood. We characterize the order of the system based on the relative quantity of statistical information encoded by high-order statistical associations of the infant gut microbiota.

q-bio.QM↗

arXiv2020

Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal over some sparsity range. For testing the individual coefficients simultaneously, multiple testing procedures are proposed and shown to control the false discovery rate (FDR) and falsely discovered variables (FDV) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed tests and their superiority over existing methods. The testing procedures are also illustrated by analyzing a data set of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn's disease and the effects of treatment on such associations.

stat.ME↗

arXiv2020

Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates

Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general structured principal subspace estimation problem which includes as special cases non-negative PCA/SVD, sparse PCA/SVD, subspace constrained PCA/SVD, and spectral clustering. General minimax lower and upper bounds are established to characterize the interplay between the information-geometric complexity of the structural set for the principal subspaces, the signal-to-noise ratio (SNR), and the dimensionality. The results yield interesting phase transition phenomena concerning the rates of convergence as a function of the SNRs and the fundamental limit for consistent estimation. Applying the general results to the specific settings yields the minimax rates of convergence for those problems, including the previous unknown optimal rates for non-negative PCA/SVD, sparse SVD and subspace constrained PCA/SVD.

math.ST↗

arXiv2020

Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regression

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random covariates. Building upon a high-dimensional EM algorithm, we propose an iterative procedure for estimating the two regression vectors and establish their rates of convergence. Based on the iterative estimators, we further construct debiased estimators and establish their asymptotic normality. For individual coordinates, confidence intervals centered at the debiased estimators are constructed. Furthermore, a large-scale multiple testing procedure is proposed for testing the regression coefficients and is shown to control the false discovery rate (FDR) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed methods and their superiority over existing methods. The proposed methods are further illustrated through an analysis of a dataset of multiplex image cytometry, which investigates the interaction networks among the cellular phenotypes that include the expression levels of 20 epitopes or combinations of markers.

stat.ME↗