Browse
Submit Data
Databases
API
Help

Dataset Information

21 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

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

ABSTRACT: 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.

SUBMITTER: Ma R

PROVIDER: S-EPMC8375316 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION.

Project description:In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies.

| S-EPMC4522432 | biostudies-literature

Logistic regression error-in-covariate models for longitudinal high-dimensional covariates.

Project description:We consider a logistic regression model for a binary response where part of its covariates are subject-specific random intercepts and slopes from a large number of longitudinal covariates. These random effect covariates must be estimated from the observed data, and therefore, the model essentially involves errors in covariates. Because of high dimension and high correlation of the random effects, we employ longitudinal principal component analysis to reduce the total number of random effects to some manageable number of random effects. To deal with errors in covariates, we extend the conditional-score equation approach to this moderate dimensional logistic regression model with random effect covariates. To reliably solve the conditional-score equations in moderate/high dimension, we apply a majorization on the first derivative of the conditional-score functions and a penalized estimation by the smoothly clipped absolute deviation. The method was evaluated through a set of simulation studies and applied to a data set with longitudinal cortical thickness of 68 regions of interest to identify biomarkers that are related to dementia transition.

| S-EPMC7654973 | biostudies-literature

LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.

Project description:This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are ?2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central ?2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ? at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

| S-EPMC6750760 | biostudies-literature

Linear Hypothesis Testing in Linear Models With High-Dimensional Responses.

Project description:In this paper, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this paper. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example.

| S-EPMC9996668 | biostudies-literature

Testing a single regression coefficient in high dimensional linear models.

Project description:In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

| S-EPMC5484175 | biostudies-literature

Change point testing in logistic regression models with interaction term.

Project description:A threshold effect takes place in situations where the relationship between an outcome variable and a predictor variable changes as the predictor value crosses a certain threshold/change point. Threshold effects are often plausible in a complex biological system, especially in defining immune responses that are protective against infections such as HIV-1, which motivates the current work. We study two hypothesis testing problems in change point models. We first compare three different approaches to obtaining a p-value for the maximum of scores test in a logistic regression model with change point variable as a main effect. Next, we study the testing problem in a logistic regression model with the change point variable both as a main effect and as part of an interaction term. We propose a test based on the maximum of likelihood ratios test statistic and obtain its reference distribution through a Monte Carlo method. We also propose a maximum of weighted scores test that can be more powerful than the maximum of likelihood ratios test when we know the direction of the interaction effect. In simulation studies, we show that the proposed tests have a correct type I error and higher power than several existing methods. We illustrate the application of change point model-based testing methods in a recent study of immune responses that are associated with the risk of mother to child transmission of HIV-1.

| S-EPMC4390452 | biostudies-literature

Efficient posterior sampling for high-dimensional imbalanced logistic regression.

Project description:Classification with high-dimensional data is of widespread interest and often involves dealing with imbalanced data. Bayesian classification approaches are hampered by the fact that current Markov chain Monte Carlo algorithms for posterior computation become inefficient as the number [Formula: see text] of predictors or the number [Formula: see text] of subjects to classify gets large, because of the increasing computational time per step and worsening mixing rates. One strategy is to employ a gradient-based sampler to improve mixing while using data subsamples to reduce the per-step computational complexity. However, the usual subsampling breaks down when applied to imbalanced data. Instead, we generalize piecewise-deterministic Markov chain Monte Carlo algorithms to include importance-weighted and mini-batch subsampling. These maintain the correct stationary distribution with arbitrarily small subsamples and substantially outperform current competitors. We provide theoretical support for the proposed approach and demonstrate its performance gains in simulated data examples and an application to cancer data.

| S-EPMC7799181 | biostudies-literature

A modern maximum-likelihood theory for high-dimensional logistic regression.

Project description:Students in statistics or data science usually learn early on that when the sample size n is large relative to the number of variables p, fitting a logistic model by the method of maximum likelihood produces estimates that are consistent and that there are well-known formulas that quantify the variability of these estimates which are used for the purpose of statistical inference. We are often told that these calculations are approximately valid if we have 5 to 10 observations per unknown parameter. This paper shows that this is far from the case, and consequently, inferences produced by common software packages are often unreliable. Consider a logistic model with independent features in which n and p become increasingly large in a fixed ratio. We prove that (i) the maximum-likelihood estimate (MLE) is biased, (ii) the variability of the MLE is far greater than classically estimated, and (iii) the likelihood-ratio test (LRT) is not distributed as a χ2 The bias of the MLE yields wrong predictions for the probability of a case based on observed values of the covariates. We present a theory, which provides explicit expressions for the asymptotic bias and variance of the MLE and the asymptotic distribution of the LRT. We empirically demonstrate that these results are accurate in finite samples. Our results depend only on a single measure of signal strength, which leads to concrete proposals for obtaining accurate inference in finite samples through the estimate of this measure.

| S-EPMC6642380 | biostudies-literature

Inference for the Case Probability in High-dimensional Logistic Regression.

Project description:Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and unstructured electronic health record data. A major hurdle currently is a lack of valid statistical inference methods for the case probability. In this paper, considering high-dimensional sparse logistic regression models for prediction, we propose a novel bias-corrected estimator for the case probability through the development of linearization and variance enhancement techniques. We establish asymptotic normality of the proposed estimator for any loading vector in high dimensions. We construct a confidence interval for the case probability and propose a hypothesis testing procedure for patient case-control labelling. We demonstrate the proposed method via extensive simulation studies and application to real-world electronic health record data.

| S-EPMC9354733 | biostudies-literature

On high-dimensional Poisson models with measurement error: Hypothesis testing for nonlinear nonconvex optimization.

Project description:We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a non-convex target function to minimize. Treating the high dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L1 and L2 convergence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardinality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear functions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.

| S-EPMC10438917 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data