Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

A Simple Density-Based Empirical Likelihood Ratio Test for Independence.

ABSTRACT: We develop a novel nonparametric likelihood ratio test for independence between two random variables using a technique that is free of the common constraints of defining a given set of specific dependence structures. Our methodology revolves around an exact density-based empirical likelihood ratio test statistic that approximates in a distribution-free fashion the corresponding most powerful parametric likelihood ratio test. We demonstrate that the proposed test is very powerful in detecting general structures of dependence between two random variables, including non-linear and/or random-effect dependence structures. An extensive Monte Carlo study confirms that the proposed test is superior to the classical nonparametric procedures across a variety of settings. The real-world applicability of the proposed test is illustrated using data from a study of biomarkers associated with myocardial infarction.

SUBMITTER: Vexler A

PROVIDER: S-EPMC4191747 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

A Simple Density-Based Empirical Likelihood Ratio Test for Independence.

Vexler Albert A Tsai Wan-Min WM Hutson Alan D AD

The American statistician 20140101 3

We develop a novel nonparametric likelihood ratio test for independence between two random variables using a technique that is free of the common constraints of defining a given set of specific dependence structures. Our methodology revolves around an exact density-based empirical likelihood ratio test statistic that approximates in a distribution-free fashion the corresponding most powerful parametric likelihood ratio test. We demonstrate that the proposed test is very powerful in detecting gen ...[more]

PMID: 25308974

Similar Datasets

MARGINAL EMPIRICAL LIKELIHOOD AND SURE INDEPENDENCE FEATURE SCREENING.

Project description:We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal empirical likelihood approach.

| S-EPMC3887322 | biostudies-literature

Cancer outlier detection based on likelihood ratio test.

Project description:MotivationMicroarray experiments can be used to help study the role of chromosomal translocation in cancer development through cancer outlier detection. The aim is to identify genes that are up- or down-regulated in a subset of cancer samples in comparison to normal samples.ResultsWe propose a likelihood-based approach which targets detecting the change of point in mean expression intensity in the group of cancer samples. A desirable property of the proposed approach is the availability of theoretical significance-level results. Simulation studies showed that the performance of the proposed approach is appealing in terms of both detection power and false discovery rate. And the real data example also favored the likelihood-based approach in terms of the biological relevance of the results.AvailabilityR code to implement the proposed method in the statistical package R is available at: http://odin.mdacc.tmc.edu/~jhhu/cod-analysis/.

| S-EPMC2732272 | biostudies-literature

A density based empirical likelihood approach for testing bivariate normality.

Project description:Sample entropy based tests, methods of sieves and Grenander estimation type procedures are known to be very efficient tools for assessing normality of underlying data distributions, in one-dimensional nonparametric settings. Recently, it has been shown that the density based empirical likelihood (EL) concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics, in a distribution-free manner. In this paper, we discuss difficulties related to constructing density based EL ratio techniques for testing bivariate normality and propose a solution regarding this problem. Toward this end, a novel bivariate sample entropy expression is derived and shown to satisfy the known concept related to bivariate histogram density estimations. Monte Carlo results show that the new density based EL ratio tests for bivariate normality behave very well for finite sample sizes. In order to exemplify the excellent applicability of the proposed approach, we demonstrate a real data example related to a study of biomarkers associated with myocardial infarction.

| S-EPMC6586021 | biostudies-literature

Empirical likelihood ratio tests with power one.

Project description:In the 1970s, Professor Robbins and his coauthors extended the Vile and Wald inequality in order to derive the fundamental theoretical results regarding likelihood ratio based sequential tests with power one. The law of the iterated logarithm confirms an optimal property of the power one tests. In parallel with Robbins's decision-making procedures, we propose and examine sequential empirical likelihood ratio (ELR) tests with power one. In this setting, we develop the nonparametric one- and two-sided ELR tests. It turns out that the proposed sequential ELR tests significantly outperform the classical nonparametric t-statistic-based counterparts in many scenarios based on different underlying data distributions.

| S-EPMC6217850 | biostudies-literature

An empirical likelihood ratio test robust to individual heterogeneity for differential expression analysis of RNA-seq.

Project description:The individual sample heterogeneity is one of the biggest obstacles in biomarker identification for complex diseases such as cancers. Current statistical models to identify differentially expressed genes between disease and control groups often overlook the substantial human sample heterogeneity. Meanwhile, traditional nonparametric tests lose detailed data information and sacrifice the analysis power, although they are distribution free and robust to heterogeneity. Here, we propose an empirical likelihood ratio test with a mean-variance relationship constraint (ELTSeq) for the differential expression analysis of RNA sequencing (RNA-seq). As a distribution-free nonparametric model, ELTSeq handles individual heterogeneity by estimating an empirical probability for each observation without making any assumption about read-count distribution. It also incorporates a constraint for the read-count overdispersion, which is widely observed in RNA-seq data. ELTSeq demonstrates a significant improvement over existing methods such as edgeR, DESeq, t-tests, Wilcoxon tests and the classic empirical likelihood-ratio test when handling heterogeneous groups. It will significantly advance the transcriptomics studies of cancers and other complex disease.

| S-EPMC5875907 | biostudies-literature

Powers of the likelihood ratio test and the correlation test using empirical bayes estimates for various shrinkages in population pharmacokinetics.

Project description:We compared the powers of the likelihood ratio test (LRT) and the Pearson correlation test (CT) from empirical Bayes estimates (EBEs) for various designs and shrinkages in the context of nonlinear mixed-effect modeling. Clinical trial simulation was performed with a simple pharmacokinetic model with various weight (WT) effects on volume (V). Data sets were analyzed with NONMEM 7.2 using first-order conditional estimation with interaction and stochastic approximation expectation maximization algorithms. The powers of LRT and CT in detecting the link between individual WT and V or clearance were computed to explore hidden or induced correlations, respectively. Although the different designs and variabilities could be related to the large shrinkage of the EBEs, type 1 errors and powers were similar in LRT and CT in all cases. Power was mostly influenced by covariate effect size and, to a lesser extent, by the informativeness of the design. Further studies with more models are needed.

| S-EPMC4011164 | biostudies-literature

A Likelihood Ratio Test for Gene-Environment Interaction Based on the Trend Effect of Genotype Under an Additive Risk Model Using the Gene-Environment Independence Assumption.

Project description:Several statistical methods have been proposed for testing gene-environment (G-E) interactions under additive risk models using data from genome-wide association studies. However, these approaches have strong assumptions from underlying genetic models, such as dominant or recessive effects that are known to be less robust when the true genetic model is unknown. We aimed to develop a robust trend test employing a likelihood ratio test for detecting G-E interaction under an additive risk model, while incorporating the G-E independence assumption to increase power. We used a constrained likelihood to impose 2 sets of constraints for: 1) the linear trend effect of genotype and 2) the additive joint effects of gene and environment. To incorporate the G-E independence assumption, a retrospective likelihood was used versus a standard prospective likelihood. Numerical investigation suggests that the proposed tests are more powerful than tests assuming dominant, recessive, or general models under various parameter settings and under both likelihoods. Incorporation of the independence assumption enhances efficiency by 2.5-fold. We applied the proposed methods to examine the gene-smoking interaction for lung cancer and gene-apolipoprotein E $\varepsilon$4 interaction for Alzheimer disease, which identified 2 interactions between apolipoprotein E $\varepsilon$4 and loci membrane-spanning 4-domains subfamily A (MS4A) and bridging integrator 1 (BIN1) genes at genome-wide significance that were replicated using independent data.

| S-EPMC8979298 | biostudies-literature

Likelihood ratio test for detecting gene (G)-environment (E) interactions under an additive risk model exploiting G-E independence for case-control data.

Project description:There has been a long-standing controversy in epidemiology with regard to an appropriate risk scale for testing interactions between genes (G) and environmental exposure (E?). Although interaction tests based on the logistic model-which approximates the multiplicative risk for rare diseases-have been more widely applied because of its convenience in statistical modeling, interactions under additive risk models have been regarded as closer to true biologic interactions and more useful in intervention-related decision-making processes in public health. It has been well known that exploiting a natural assumption of G-E independence for the underlying population can dramatically increase statistical power for detecting multiplicative interactions in case-control studies. However, the implication of the independence assumption for tests for additive interaction has not been previously investigated. In this article, the authors develop a likelihood ratio test for detecting additive interactions for case-control studies that incorporates the G-E independence assumption. Numerical investigation of power suggests that incorporation of the independence assumption can enhance the efficiency of the test for additive interaction by 2- to 2.5-fold. The authors illustrate their method by applying it to data from a bladder cancer study.

| S-EPMC3571244 | biostudies-literature

Empirical likelihood-based tests for stochastic ordering.

Project description:This paper develops an empirical likelihood approach to testing for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by integrating a localized empirical likelihood statistic with respect to the empirical distribution of the pooled sample. The asymptotic null distribution of this test statistic is found to have a simple distribution-free representation in terms of standard Brownian bridge processes. The approach is used to compare the lengths of rule of Roman Emperors over various historical periods, including the "decline and fall" phase of the empire. In a simulation study, the power of the proposed test is found to improve substantially upon that of a competing test due to El Barmi and Mukerjee.

| S-EPMC3716296 | biostudies-literature

Real time QRS detection based on M-ary likelihood ratio test on the DFT coefficients.

Project description:This paper shows an adaptive statistical test for QRS detection of electrocardiography (ECG) signals. The method is based on a M-ary generalized likelihood ratio test (LRT) defined over a multiple observation window in the Fourier domain. The motivations for proposing another detection algorithm based on maximum a posteriori (MAP) estimation are found in the high complexity of the signal model proposed in previous approaches which i) makes them computationally unfeasible or not intended for real time applications such as intensive care monitoring and (ii) in which the parameter selection conditions the overall performance. In this sense, we propose an alternative model based on the independent Gaussian properties of the Discrete Fourier Transform (DFT) coefficients, which allows to define a simplified MAP probability function. In addition, the proposed approach defines an adaptive MAP statistical test in which a global hypothesis is defined on particular hypotheses of the multiple observation window. In this sense, the observation interval is modeled as a discontinuous transmission discrete-time stochastic process avoiding the inclusion of parameters that constraint the morphology of the QRS complexes.

| S-EPMC4214710 | 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