Permutation Testing in the Presence of Polygenic Variation

Summary Motivated by applications in neuroanatomy, we propose a novel methodology to estimate heritability, which corresponds to the proportion of phenotypic variance that can be explained by genetic factors. Since the phenotypic variations may be due to only a small fraction of the available genetic information, we propose an estimator of heritability that can be used in sparse linear mixed models. Since the real genetic architecture is in general unknown in practice, our method enables the user to determine whether the genetic effects are very sparse: in that case, we propose a variable selection approach to recover the support of these genetic effects before estimating heritability. Otherwise, we use a classical maximum likelihood approach. We apply our method, implemented in the R package EstHer that is available on the Comprehensive R Archive Network, on neuroanatomical data from the project IMAGEN.

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“…Observe that our resampling technique is close to that proposed by Abney () for building permutation tests in linear mixed models.…”

Section: Description Of the Methodssupporting

confidence: 61%

Improving Heritability Estimation by a Variable Selection Approach in Sparse High Dimensional Linear Mixed Models

Bonnet

Lévy‐Leduc

Gassiat

et al. 2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…Permutation‐based S1.2 null design can estimate the true distribution of a test statistic

T

when applied to a real data set, and identify the correct significance threshold for

T

under the “empirical” null. But, permutation must be carried out carefully in practice, for example, in the presence of sample correlation (Abney, ).…”

Section: Discussionmentioning

confidence: 99%

Beyond the traditional simulation design for evaluating type 1 error control: From the “theoretical” null to “empirical” null

Zhang

Sun

2018

Genetic Epidemiology

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When evaluating a newly developed statistical test, an important step is to check its type 1 error (T1E) control using simulations. This is often achieved by the standard simulation design S0 under the so‐called “theoretical” null of no association. In practice, the whole‐genome association analyses scan through a large number of genetic markers ( s) for the ones associated with an outcome of interest ( ), where comes from an alternative while the majority of s are not associated with ; the relationships are under the “empirical” null. This reality can be better represented by two other simulation designs, where design S1.1 simulates from an alternative model based on , then evaluates its association with independently generated ; while design S1.2 evaluates the association between permutated and . More than a decade ago, Efron (2004) has noted the important distinction between the “theoretical” and “empirical” null in false discovery rate control. Using scale tests for variance heterogeneity, direct univariate, and multivariate interaction tests as examples, here we show that not all null simulation designs are equal. In examining the accuracy of a likelihood ratio test, while simulation design S0 suggested the method being accurate, designs S1.1 and S1.2 revealed its increased empirical T1E rate if applied in real data setting. The inflation becomes more severe at the tail and does not diminish as sample size increases. This is an important observation that calls for new practices for methods evaluation and T1E control interpretation.

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“…Because the genotype is permuted rather than the phenotype, the covariates can be regressed on the phenotypes and the residuals used for these methods as long as the covariates are not associated with the genotype (i.e., age, gender, etc.) (Abney, ; Freedman & Lane, ; Wagner, Zerbe, Mexal, & Leonard, ). Because many forms of population structure can cause confounding that can invalidate a permutation test, careful consideration needs to be given when adjusting for genetic ancestry in permutation‐based tests (Abney, ).…”

Section: Methodsmentioning

confidence: 99%

“…(Abney, ; Freedman & Lane, ; Wagner, Zerbe, Mexal, & Leonard, ). Because many forms of population structure can cause confounding that can invalidate a permutation test, careful consideration needs to be given when adjusting for genetic ancestry in permutation‐based tests (Abney, ). When a limited number of principal components can adjust for the background genetic confounding (e.g., a simple population stratification scenario), it is possible to formulate a valid permutation test (Epstein et al., ).…”

Section: Methodsmentioning

confidence: 99%

“…When a limited number of principal components can adjust for the background genetic confounding (e.g., a simple population stratification scenario), it is possible to formulate a valid permutation test (Epstein et al., ). However, in more complicated scenarios of population substructure, other methods are needed such as a parametric bootstrap or MVNpermute, a method designed for permutation testing in the presence of polygenic variation (Abney, ).…”

Section: Methodsmentioning

confidence: 99%

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A general approach to testing for pleiotropy with rare and common variants

Lutz

Fingerlin

Hokanson

et al. 2016

Genetic Epidemiology

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Through genome-wide association studies, numerous genes have been shown to be associated with multiple phenotypes. To determine the overlap of genetic susceptibility of correlated phenotypes, one can apply multivariate regression or dimension reduction techniques, such as principal components analysis, and test for the association with the principal components of the phenotypes rather than the individual phenotypes. However, as these approaches test whether there is a genetic effect for at least one of the phenotypes, a significant test result does not necessarily imply pleiotropy. Recently, a method called Pleiotropy Estimation and Test Bootstrap (PET-B) has been proposed to specifically test for pleiotropy, (i.e. that 2 normally distributed phenotypes are both associated with the single nucleotide polymorphism (SNP) of interest). While the method examines the genetic overlap between the 2 quantitative phenotypes, the extension to binary phenotypes, 3 or more phenotypes, and rare variants is not straightforward. We provide two approaches to formally test this pleiotropic relationship in multiple scenarios. These approaches depend on permuting the phenotypes of interest and comparing the set of observed p-values to the set of permuted p-values in relation to the origin (e.g. a vector of zeros) either using the Hausdorff metric or a cut-off based approach. These approaches are appropriate for categorical and quantitative phenotypes, more than 2 phenotypes, common variants and rare variants. We evaluate these approaches under various simulation scenarios and apply them to the COPDGene study, a case-control study of Chronic Obstructive Pulmonary Disease (COPD) in current and former smokers.

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Permutation Testing in the Presence of Polygenic Variation

Cited by 8 publications

References 28 publications

Improving Heritability Estimation by a Variable Selection Approach in Sparse High Dimensional Linear Mixed Models

Improving Heritability Estimation by a Variable Selection Approach in Sparse High Dimensional Linear Mixed Models

Beyond the traditional simulation design for evaluating type 1 error control: From the “theoretical” null to “empirical” null

A general approach to testing for pleiotropy with rare and common variants

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