Classical testing in functional linear models

Kong, Dehan; Staicu, Ana‐Maria; Maity, Arnab

doi:10.1080/10485252.2016.1231806

Cited by 59 publications

(56 citation statements)

References 33 publications

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“…For quantitative traits, the LRT of functional linear models was found to have inflated type I error rates when sample sizes are smaller than or equal to 1,000 and to have accurate type I error rates when sample sizes are 1,500 or 2,000, while F -tests were found to have accurate type I error rates over all sample sizes examined [Fan et al 2013]. Similar results regarding type I error rates were found in Kong et al [2014].…”

Section: Discussionmentioning

confidence: 65%

Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies

Fan

Wang

Mills

et al. 2014

Genetic Epidemiology

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By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene are disease-related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease data sets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses.

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Section: Discussionmentioning

confidence: 65%

Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies

Fan

Wang

Mills

et al. 2014

Genetic Epidemiology

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“…We need to develop valid hypothesis testing procedures to test the association [Fan et al, 2013, 2014]. To our knowledge, Kong et al [2014] is the only paper to deal with the hypothesis testing of functional linear models, except for Fan et al [2013, 2014]. Kong et al [2014] calculates type I error rates at a 0.05 level, by using 5,000 simulated replicates.…”

Section: Introductionmentioning

confidence: 99%

“…To our knowledge, Kong et al [2014] is the only paper to deal with the hypothesis testing of functional linear models, except for Fan et al [2013, 2014]. Kong et al [2014] calculates type I error rates at a 0.05 level, by using 5,000 simulated replicates. In short, there has been very limited research on the hypothesis testing of functional regression models.…”

Section: Introductionmentioning

confidence: 99%

Pleiotropy Analysis of Quantitative Traits at Gene Level by Multivariate Functional Linear Models

Wang

Liu

Mills

et al. 2015

Genetic Epidemiology

111

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In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F-distribution tests based on Pillai–Bartlett trace, Hotelling–Lawley trace, and Wilks’s Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants in one genetic region. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and optimal sequence kernel association test (SKAT-O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F-distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F-distribution tests provide much more significant results than those of F-tests of univariate analysis and SKAT-O for the three biochemical traits. The approximate F-distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT-O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT-O in the univariate case.

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“…Two past approaches have commented on the potential for hypothesis tests in the FLM through the use of tests for zero variance components, but neither fully developed a method or study the properties of a hypothesis test (Reiss and Ogden, 2010;Gertheiss et al, 2012) (the former in the context of scalar-on-image regression). The theory for classical testing for H 0 : γ(s) = 0 in FLM has been developed, but still lacks computational implementability and the ability to test other null hypotheses Kong et al (2013). Tests for zero variance components, as proposed herein, are readily implementable and allow for testing a variety of null hypotheses.…”

Section: Introductionmentioning

confidence: 99%

Restricted Likelihood Ratio Tests for Functional Effects in the Functional Linear Model

Swihart¹,

Goldsmith²,

Crainiceanu³

2014

Technometrics

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The goal of our article is to provide a transparent, robust, and computationally feasible statistical approach for testing in the context of scalar-on-function linear regression models. In particular, we are interested in testing for the necessity of functional effects against standard linear models. Our methods are motivated by and applied to a large longitudinal study involving diffusion tensor imaging of intracranial white matter tracts in a susceptible cohort. In the context of this study, we conduct hypothesis tests that are motivated by anatomical knowledge and which support recent findings regarding the relationship between cognitive impairment and white matter demyelination. R-code and data are provided to reproduce the application.

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Classical testing in functional linear models

Cited by 59 publications

References 33 publications

Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies

Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies

Pleiotropy Analysis of Quantitative Traits at Gene Level by Multivariate Functional Linear Models

Restricted Likelihood Ratio Tests for Functional Effects in the Functional Linear Model

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