scholarly journals Permutation Testing in the Presence of Polygenic Variation

2015 ◽  
Author(s):  
Mark Abney
Keyword(s):  
Quantitative Trait ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Permutation Test ◽  
Statistical Significance ◽  
Null Distribution ◽  
Polygenic Effect ◽  
Permutation Testing ◽  
Test Statistic ◽  
Omnibus Test

This article discusses problems with and solutions to performing valid permutation tests for quantitative trait loci in the presence of polygenic effects. Although permutation testing is a popular approach for determining statistical significance of a test statistic with an unknown distribution--for instance, the maximum of multiple correlated statistics or some omnibus test statistic for a gene, gene-set or pathway--naive application of permutations may result in an invalid test. The risk of performing an invalid permutation test is particularly acute in complex trait mapping where polygenicity may combine with a structured population resulting from the presence of families, cryptic relatedness, admixture or population stratification. I give both analytical derivations and a conceptual understanding of why typical permutation procedures fail and suggest an alternative permutation based algorithm, MVNpermute, that succeeds. In particular, I examine the case where a linear mixed model is used to analyze a quantitative trait and show that both phenotype and genotype permutations may result in an invalid permutation test. I provide a formula that predicts the amount of inflation of the type 1 error rate depending on the degree of misspecification of the covariance structure of the polygenic effect and the heritability of the trait. I validate this formula by doing simulations, showing that the permutation distribution matches the theoretical expectation, and that my suggested permutation based test obtains the correct null distribution. Finally, I discuss situations where naive permutations of the phenotype or genotype are valid and the applicability of the results to other test statistics.

scholarly journals Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

2021 ◽  
Author(s):  
Anna L Tyler ◽  
Baha El Kassaby ◽  
Georgi Kolishovski ◽  
Jake Emerson ◽  
Ann E Wells ◽  
...  
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Genetic Interaction ◽  
Recombinant Inbred Lines ◽  
Test Statistics ◽  
Test Statistic ◽  
Kinship Matrix ◽  
Main Effect ◽  
Main Effects ◽  
Interaction Test

Abstract It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

scholarly journals Novel Fiber Formulation Does Not Alter Cardiometabolic Profiles in Overweight Participants Consuming Low-Fiber Diets

2020 ◽  
Vol 4 (Supplement_2) ◽  
pp. 757-757
Author(s):  
Jea Woo Kang ◽  
Chenghao Zhu ◽  
Christopher Rhodes ◽  
Hannah Houts ◽  
Jingyuan Zheng ◽  
...  
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Statistical Significance ◽  
Rice Flour ◽  
Lipid Profiles ◽  
Funding Sources ◽  
Fiber Diet ◽  
High Interindividual Variability ◽  
Dietary Records ◽  
Fiber Consumption

Abstract Objectives The objective of this study was to determine whether a novel fiber formulation improves glucose, insulin, and lipid profiles in overweight men and women consuming a low fiber diet. Methods Twenty individuals were enrolled in this randomized order, placebo-controlled, cross-over study. Participants were young, healthy, overweight (BMI 23.0–32.0) and consumed <15 g/day of fiber. All participants consumed the fiber and placebo supplement for a period of 4 weeks each, with a 4-week washout between intervention arms. Participants recorded their diet for 3 days using dietary records twice during each 4-week segment. They consumed either fiber and/or placebo packet containing a total of 12 g/serving per day. The Fiber and/or Placebo was given out as powder form which include mostly dietary fiber (resistant starch, fructooligosaccharide, sugarcane fiber, and inulin), rice flour, xanthan gum, and fruit powders that was mixed with water for consumption. Questionnaires, anthropometric measurements, blood draws, and stool samples were collected at each study visit. Changes in glucose, insulin, and lipid profile (total cholesterol (TC), triacylglycerols (TG), HDL-C and calculated LDL-C) were assessed using a linear mixed model. Results The mean change in fasted glucose, insulin, and lipid profiles showed a tendency to decrease in response to fiber consumption compared with the placebo but did not meet statistical significance (P = 0.29, 0.42, and 0.61) due to high interindividual variability. This clinical trial was registered at clinicaltrials.gov as NCT03785860. Conclusions Cardiometabolic profiles did not change in response to the fiber supplement. Funding Sources I would like to acknowledge Usana Health Sciences, Inc. for the support in this research.

Application of the Lasso to Expression Quantitative Trait Loci Mapping

2011 ◽  
Vol 10 (1) ◽  
Author(s):  
Andrew Anand Brown ◽  
Sylvia Richardson ◽  
John Whittaker
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Visual Inspection ◽  
Statistical Significance ◽  
Genetic Regulation ◽  
Simulation Studies ◽  
Test Statistic ◽  
Multiple Signals ◽  
Trait Loci ◽  
Shrinkage Method

Univariate methods have frequently been used to discover Quantitative Trait Loci for gene expression measurements, often with much success. However, correlations caused by Linkage Disequilibrium as well as chance correlations, which are functions of the large number of markers typically used in such studies, mean that causative regions can often cause multiple signals. Traditional investigations into the number of QTL for a given phenotype, such as visual inspection of likelihood plots, are not feasible when considering thousands of phenotypes. Stepwise methods have been suggested to counter this, but these are known to produce unstable models and there are difficulties in deriving significance estimates. The Lasso is a shrinkage method which has often been employed to discover true signals when the number of variables exceeds the number of observations. We propose a test statistic based on the threshold at which variables enter the Lasso model, prove analytic properties of this statistic which demonstrate parallels with univariate methods and demonstrate its utility in proposing candidate QTL. We show that this method controls for LD structure, and the estimates of statistical significance produced have superior properties when compared to those derived by stepwise methods. We study the performance of our method using simulation studies. These simulations find that the ratio of true discoveries to false positives is often superior for our method compared to univariate and stepwise approaches. Finally, we apply the derived method to data from a previous eQTL mapping experiment to investigate the nature of genetic regulation in this population.

Estimation of Genetic Variance Contributed by a Quantitative Trait Locus — Correcting the Bias Associated with Significance Tests

Genetics ◽  
2021 ◽  
Author(s):  
Fangjie Xie ◽  
Shibo Wang ◽  
William D Beavis ◽  
Shizhong Xu
Keyword(s):  
Qtl Mapping ◽  
Effect Size ◽  
Bias Correction ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Association Studies ◽  
Chromosome 9 ◽  
Genome Wide Association Studies ◽  
Test Statistic ◽  
Chi Square

Abstract The Beavis effect in QTL mapping describes a phenomenon that the estimated effect size of a statistically significant QTL (measured by the QTL variance) is greater than the true effect size of the QTL if the sample size is not sufficiently large. This is a typical example of the Winners’ curse applied to molecular quantitative genetics. Theoretical evaluation and correction for the Winners’ curse have been studied for interval mapping. However, similar technologies have not been available for current models of QTL mapping and genome-wide association studies where a polygene is often included in the linear mixed models to control the genetic background effect. In this study, we developed the theory of the Beavis effect in a linear mixed model using a truncated non-central Chi-square distribution. We equated the observed Wald test statistic of a significant QTL to the expectation of a truncated non-central Chi-square distribution to obtain a bias-corrected estimate of the QTL variance. The results are validated from replicated Monte Carlo simulation experiments. We applied the new method to the grain width (GW) trait of a rice population consisting of 524 homozygous varieties with over 300k single nucleotide polymorphism (SNPs) markers. Two loci were identified and the estimated QTL heritability were corrected for the Beavis effect. Bias correction for the larger QTL on chromosome 5 (GW5) with an estimated heritability of 12% did not change the QTL heritability due to the extremely large test score and estimated QTL effect. The smaller QTL on chromosome 9 (GW9) had an estimated QTL heritability of 9% reduced to 6% after the bias-correction.

scholarly journals Using the mixed model for interval mapping of quantitative trait loci in outbred line crosses

2001 ◽  
Vol 77 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Y. NAGAMINE ◽  
C. S. HALEY
Keyword(s):  
Animal Model ◽  
Quantitative Trait Loci ◽  
Qtl Analysis ◽  
Quantitative Trait ◽  
Fixed Effects ◽  
Mixed Model ◽  
Interval Mapping ◽  
Estimation Methods ◽  
Polygenic Effect ◽  
Trait Loci

Interval mapping by simple regression is a powerful method for the detection of quantitative trait loci (QTLs) in line crosses such as F2 populations. Due to the ease of computation of the regression approach, relatively complex models with multiple fixed effects, interactions between QTLs or between QTLs and fixed effects can easily be accommodated. However, polygenic effects, which are not targeted in QTL analysis, cannot be treated as random effects in a least squares analysis. In a cross between true inbred lines this is of no consequence, as the polygenic effect contributes just to the residual variance. In a cross between outbred lines, however, if a trait has high polygenic heritability, the additive polygenic effect has a large influence on variation in the population. Here we extend the fixed model for the regression interval mapping method to a mixed model using an animal model. This makes it possible to use not only the observations from progeny (e.g. F2), but also those from the parents (F1) to evaluate QTLs and polygenic effects. We show how the animal model using parental observations can be applied to an outbred cross and so increase the power and accuracy of QTL analysis. Three estimation methods, i.e. regression and an animal model either with or without parental observations, are applied to simulated data. The animal model using parental observations is shown to have advantages in estimating QTL position and additive genotypic value, especially when the polygenic heritability is large and the number of progeny per parent is small.

Multiple Group Comparisons of the Fixed and Random Effects From the Generalized Linear Mixed Model

2021 ◽  
pp. 004912412098618
Author(s):  
Daniel Kasper ◽  
Katrin Schulz-Heidorf ◽  
Knut Schwippert
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Asymptotic Properties ◽  
Generalized Linear Mixed Model ◽  
Test Statistic ◽  
Multiple Group ◽  
Fixed And Random Effects ◽  
Group Comparisons

In this article, we extend Liao’s test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be applied when the fixed and random effects are multivariate normally distributed, and it works well for any link function and conditional distribution of the dependent variable of the GLMM. We also derived the asymptotic properties of this test, and because power information does not exist for either our new test statistic or Liao’s test, we implemented a power study to demonstrate the superiority of these tests over the alternatively proposed F test. Using an example, we show the application of the test and then discuss its possible restrictions with respect to the distribution of the random effects.

scholarly journals Gonadotropin Response to Insulin and Lipid Infusion Reproduces the Reprometabolic Syndrome of Obesity in Lean Women

2021 ◽  
Vol 5 (Supplement_1) ◽  
pp. A732-A733
Author(s):  
Nanette F Santoro ◽  
Nanette F Santoro
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Statistical Significance ◽  
Area Under The Curve ◽  
Pulse Amplitude ◽  
Normal Weight ◽  
Obese Women ◽  
Mixed Model Analysis ◽  
Early Follicular Phase ◽  
Very High

Abstract Introduction: The reprometabolic syndrome of obesity is associated with reduced gonadotropins and impaired LH and FSH response to gonadotropin releasing hormone (GnRH). We sought to reproductive the reprometabolic syndrome in normal weight, eumenorrheic women by infusing a combination of insulin and lipid. Materials and Methods: 15 women, mean age 32 (IQR 26,36) and BMI 21.9 (20.2, 22.9) were recruited with intent to perform early follicular phase, 6-hour infusions of insulin (20-40mg/mU/m2/min) and lipid (Intralipid) or saline infusion (controls); 12 women completed both intended studies and an additional 3 women completed only one of the two studies. The first 4 hours of each study assessed endogenous gonadotropins; at 4hrs, a 75 ng/kg GnRH bolus was administered and sampling continued until 6hrs. Linear mixed model analysis was used to determine differences between Intralipid versus saline on endogenous LH pulse amplitude (primary outcomes), mean FSH, and area under the curve (AUC) response to GnRH (secondary outcomes). Results: LH pulse amplitude, mean FSH, and both AUC responses to GnRH were all reduced by Intralipid/insulin; mean FSH (P=0.03) and AUC for LH (P=0.05) were at or near statistical significance. LH pulse amplitude and response to GnRH were significantly reduced (P=0.04 and 0.02) when one participant with very high LH and AMH levels was excluded. Discussion: Acute infusion of insulin/lipid to eumenorrheic, normal weight women recapitulated the reprometabolic syndrome of obesity. These findings imply that specific circulating factors in obese women contribute to their sub fertility and thus may be amenable to discovery and treatment.

scholarly journals Estimation of Effects of Quantitative Trait Loci in Large Complex Pedigrees

Genetics ◽  
1997 ◽  
Vol 146 (1) ◽  
pp. 409-416 ◽  
Author(s):  
T H E Meuwissen ◽  
M E Goddard
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Simulated Data ◽  
Data Set ◽  
Genotype Information ◽  
Trait Loci ◽  
Basic Equations ◽  
Marker Information

A method was derived to estimate effects of quantitative trait loci (QTL) using incomplete genotype information in large outbreeding populations with complex pedigrees. The method accounts for background genes by estimating polygenic effects. The basic equations used are very similar to the usual linear mixed model equations for polygenic models, and segregation analysis was used to estimate the probabilities of the QTL genotypes for each animal. Method R was used to estimate the polygenic heritability simultaneously with the QTL effects. Also, initial allele frequencies were estimated. The method was tested in a simulated data set of 10,000 animals evenly distributed over 10 generations, where 0, 400 or 10,000 animals were genotyped for a candidate gene. In the absence of selection, the bias of the QTL estimates was <2%. Selection biased the estimate of the Aa genotype slightly, when zero animals were genotyped. Estimates of the polygenic heritability were 0.251 and 0.257, in absence and presence of selection, respectively, while the simulated value was 0.25. Although not tested in this study, marker information could be accommodated by adjusting the transmission probabilities of the genotypes from parent to offspring according to the marker information. This renders a QTL mapping study in large multi-generation pedigrees possible.

The Volume Behavior of Autogenous Iliac Bone Grafts After Sinus Floor Elevation: A Clinical Pilot Study

2015 ◽  
Vol 41 (3) ◽  
pp. 276-283 ◽  
Author(s):  
Marcus Gerressen ◽  
Dieter Riediger ◽  
Ralf-Dieter Hilgers ◽  
Frank Hölzle ◽  
Nelson Noroozi ◽  
...  
Keyword(s):  
Bone Graft ◽  
Mixed Model ◽  
Iliac Crest ◽  
Linear Mixed Model ◽  
Statistical Significance ◽  
Bone Grafts ◽  
Iliac Bone ◽  
Optimal Timing ◽  
Sinus Floor Elevation ◽  
Sinus Floor

Iliac crest is still regarded as one of the most viable source of autogenous graft materials for extensive sinus floor elevation. Three-dimensional resorption behavior has to be taken into account in anticipation of the subsequent insertion of dental implants. We performed 3-dimensional volume measurements of the inserted bone transplants in 11 patients (6 women and 5 men; mean age = 2.3 years) who underwent bilateral sinus floor elevation with autogenous iliac crest grafts. In order to determine the respective bone graft volumes, cone-beam computerized tomography studies of the maxillary sinuses were carried out directly after the operation (T0), as well as 3 months (T1) and 6 months (T2) postoperatively. The acquired DICOM (Digital Imaging and Communications in Medicine) data sets were evaluated using suitable analysis software. We evaluated statistical significance of graft volumes changes using a linear mixed model with the grouping factors for time, age, side, and sex with a significance level of P = .05. 38.9% of the initial bone graft volume, which amounted to 4.2 cm3, was resorbed until T1. At T2, the average volume again decreased significantly by 18.9 % to finally reach 1.8 cm3. The results show neither age nor side dependency and apply equally to both sexes. Without functional load, iliac bone grafts feature low-volume stability in sinus-augmentation surgery. Further clinical and animal studies should be done to detect the optimal timing for implant placement.

scholarly journals Screening feature modules and pathways in glioma using EgoNet

2017 ◽  
Vol 12 (1) ◽  
pp. 277-284
Author(s):  
Li He ◽  
Xian-Xu Song ◽  
Mei Wang ◽  
Ben-Zhuo Zhang
Keyword(s):  
Classification Accuracy ◽  
Permutation Test ◽  
Statistical Significance ◽  
Enrichment Analysis ◽  
Random Permutation ◽  
Future Research ◽  
Pathway Enrichment Analysis ◽  
Permutation Testing ◽  
Ego Networks ◽  
Network Modules

AbstractBackgroundTo investigate differential egonetwork modules and pathways in glioma using EgoNet algorithm.MethodologyBased on microarray data, EgoNet algorithm mainly comprised three stages: construction of differential co-expression network (DCN); EgoNet algorithm used to identify candidate ego-network modules based on the increased classification accuracy; statistical significance for candidate modules using random permutation testing. After that, pathway enrichment analysis for differential ego-network modules was implemented to illuminate the biological processes.ResultsWe obtained 109 ego genes. From every ego gene, we progressively grew the ego-networks by levels; we extracted 109 ego-networks and the mean node size in an ego-network was 6. By setting the classification accuracy threshold at 0.90 and the count of nodes in an ego-network module at 10, we extracted 8 candidate ego-network modules. After random permutation test with 1000 times, 5 modules including module 59, 72, 78, 86, and 90 were identified to be significant. Of note, the genes of module 90 and 86 were enriched in the pathway of resolution of sister chromatid cohesion and mitotic prometaphase, respectively.ConclusionThe identified modules and their corresponding ego genes might be beneficial in revealing the pathology underlying glioma and give insight for future research of glioma.

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