Dataset Information

Hypothesis testing in functional linear models.

ABSTRACT: Functional data arise frequently in biomedical studies, where it is often of interest to investigate the association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not systematically studied. In this article, we first investigate the power performance of the Wald-type test with varying thresholds in selecting the number of PCs for the functional covariates, and show that the power is sensitive to the choice of thresholds. To circumvent the issue, we propose a new method of ordering and selecting principal components to construct test statistics. The proposed method takes into account both the association with the response and the variation along each eigenfunction. We establish its theoretical properties and assess the finite sample properties through simulations. Our simulation results show that the proposed test is more robust against the choice of threshold while being as powerful as, and often more powerful than, the existing method. We then apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study.

SUBMITTER: Su YR

PROVIDER: S-EPMC5518697 | biostudies-literature | 2017 Jun

REPOSITORIES: biostudies-literature

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Hypothesis testing in functional linear models.

Su Yu-Ru YR Di Chong-Zhi CZ Hsu Li L

Biometrics 20170310 2

Functional data arise frequently in biomedical studies, where it is often of interest to investigate the association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its po ...[more]

PMID: 28295175

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Project description:BackgroundModern biology has shifted from "one gene" approaches to methods for genomic-scale analysis like microarray technology, which allow simultaneous measurement of thousands of genes. This has created a need for tools facilitating interpretation of biological data in "batch" mode. However, such tools often leave the investigator with large volumes of apparently unorganized information. To meet this interpretation challenge, gene-set, or cluster testing has become a popular analytical tool. Many gene-set testing methods and software packages are now available, most of which use a variety of statistical tests to assess the genes in a set for biological information. However, the field is still evolving, and there is a great need for "integrated" solutions.ResultsGeneTools is a web-service providing access to a database that brings together information from a broad range of resources. The annotation data are updated weekly, guaranteeing that users get data most recently available. Data submitted by the user are stored in the database, where it can easily be updated, shared between users and exported in various formats. GeneTools provides three different tools: i) NMC Annotation Tool, which offers annotations from several databases like UniGene, Entrez Gene, SwissProt and GeneOntology, in both single- and batch search mode. ii) GO Annotator Tool, where users can add new gene ontology (GO) annotations to genes of interest. These user defined GO annotations can be used in further analysis or exported for public distribution. iii) eGOn, a tool for visualization and statistical hypothesis testing of GO category representation. As the first GO tool, eGOn supports hypothesis testing for three different situations (master-target situation, mutually exclusive target-target situation and intersecting target-target situation). An important additional function is an evidence-code filter that allows users, to select the GO annotations for the analysis.ConclusionGeneTools is the first "all in one" annotation tool, providing users with a rapid extraction of highly relevant gene annotation data for e.g. thousands of genes or clones at once. It allows a user to define and archive new GO annotations and it supports hypothesis testing related to GO category representations. GeneTools is freely available through www.genetools.no

Dataset Information

Hypothesis testing in functional linear models.

Publications

Hypothesis testing in functional linear models.

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