A variance components/major locus likelihood approximation on quantitative data

The variance components/major locus model encompasses a major locus, a polygenic component, and shared environmental effects. The model attributes familial correlations to polygenic and shared environmental effects when testing for major locus inheritance or accounts for the major locus when estimating variance components. Because exact computation of the likelihood of the variance components/major locus model on quantitative data requires excessive computer time, I developed an approximation. The approximation retained the general shape of the likelihood surface. Accuracy of the approximation did not vary consistently with allele frequency or the size of the major locus effect.     

Comparison of variance components and sibpair-based approaches to quantitative trait linkage analysis in unselected samples

We compared the statistical performance of sibpair-based and variance components approaches to multipoint linkage analysis of a quantitative trait in unselected samples. As a benchmark dataset, we used the simulated family data from Genetic Analysis Workshop 10 [Goldin et al., 1997], and each method was used to screen all 200 replications of the GAW10 genome for evidence of linkage to quantitative trait Q1. The sibpair and variance components methods were each applied to datasets comprising single-sibpairs and complete sibships, and for further comparison we also applied the variance components method to the nuclear family and extended pedigree datasets. For each analysis, the unbiasedness and efficiency of parameter estimation, the power to detect linkage, and the Type I error rate were estimated empirically. Sibpair and variance components methods exhibited comparable performance in terms of the unbiasedness of the estimate of QTL location and the Type I error rate. Within the single-sibpair and sibship sampling units, the variance components approach gave consistently superior power and efficiency of parameter estimation. Within each method, the statistical performance was improved by the use of the larger and more informative sampling units.     

Effects of model misspecification in the estimation of variance components and intraclass correlation for paired data

Paired data occur in many experimental situations. When one views the subjects as a random sample from some large population, it may seem reasonable to model the data according to the typical one-way random effects analysis of variance (ANOVA). It is then usually of interest to estimate variance components and intraclass correlation. These estimators can be biased if key assumptions are violated, leading to erroneous interpretations and conclusions. We focus upon assumptions about the equality or inequality of means and/or variances of the two measures on each subject. In the framework of the one-way random effects ANOVA model, and three generalizations of it, we document estimators obtained as solutions to the likelihood equations. We consider the potentially serious effects of mistaken assumptions. Our findings suggest that the most general model considered is most desirable if consistent and efficient estimation of the between-subject variance component and intraclass correlation is the main goal. We also briefly connect our exposition to the study of reliability or agreement.     

A multivariate model for the analysis of sibship covariance structure using marker information and multiple quantitative traits

A model was developed to detect effects of quantitative trait loci (QTLs) in sibships from simulated nuclear family data using the full covariance structure of the data and analyzing all five quantitative traits simultaneously in a multivariate model. Evidence of the presence of loci was detected on chromosomes 4,8,9, and 10. The method provided stable results and is worth further exploration for its performance and optimal sample size requirements under realistic conditions. © 1997 Wiley-Liss, Inc.     

Statistical properties of a variance components method for quantitative trait linkage analysis in nuclear families and extended pedigrees

We investigated the statistical properties of a variance components method for quantitative trait linkage analysis using nuclear families and extended pedigrees. © 1997 Wiley-Liss, Inc.     

Identifying influential individuals in linkage analysis: application to a quantitative trait locus detected in the COGA data

Once linkage is detected to a quantitative trait locus (QTL), the next step towards localizing the gene involved may be to identify those families, or individuals, in whom the putative mutations are segregating. In this paper, we describe a jackknife procedure for identifying individuals (and families) who contribute disproportionately to the linkage. Following initial detection of linkage to a QTL, the strategy involves sequentially removing each individual (or each family) from the analysis and recomputing the lod score associated with the linked region using data from all remaining subjects (or families). This procedure can be used to determine if particular observations have substantial impact on evidence for linkage. Identification of such observations may provide insights for further efforts to localize the QTL.     

Quantitative trait linkage analysis by generalized estimating equations: unification of variance components and Haseman-Elston regression

Two of the major approaches for linkage analysis with quantitative traits in humans include variance components and Haseman-Elston regression. Previously, these were viewed as quite separate methods. We describe a general model, fit by use of generalized estimating equations (GEE), for which the variance components and Haseman-Elston methods (including many of the extensions to the original Haseman-Elston method) are special cases, corresponding to different choices for a working covariance matrix. We also show that the regression-based test of Sham et al. ([2002] Am. J. Hum. Genet. 71:238-253) is equivalent to a robust score statistic derived from our GEE approach. These results have several important implications. First, this work provides new insight regarding the connection between these methods. Second, asymptotic approximations for power and sample size allow clear comparisons regarding the relative efficiency of the different methods. Third, our general framework suggests important extensions to the Haseman-Elston approach which make more complete use of the data in extended pedigrees and allow a natural incorporation of environmental and other covariates.     

Use of robust statistical methods to determine the effect of fragile X on means and variance components of a quantitative trait

Owing to the presence of outliers, an estimated 3.5% in the ridge breadth data and 1.7% in the height data, the effect of fragile X on height and ridge breadth was examined using robust statistical techniques for data collected from 54 families afflicted with this disorder. It is shown that fragile X affects ridge breadth and height in a different manner. Fragile X women had a greater mean ridge breadth than normal women, whereas there was a similar trend, but no significant difference, between normal and fragile X men. Fragile X men were shorter than normal men, but no significant difference between the mean height of normal and fragile X women was observed. However, fragile X girls were shown to grow more quickly and to stop growing earlier than normal girls. An examination of the covariance between relatives classified according to fragile X status showed that for both traits the effect of fragile X was to reduce the covariance between parents and offspring, which produced the effect of departure from an additive polygenic model of inheritance. ©1995 Wiley-Liss, Inc.     

The impact of random‐effect misspecification on percentile estimation for longitudinal growth data

Identifying unusual growth‐related measurements or longitudinal patterns in growth is often the focus in fetal and pediatric medicine. For example, the goal of the ongoing National Fetal Growth Study is to develop both cross‐sectional and longitudinal reference curves for ultrasound fetal growth measurements that can be used for this purpose. Current methodology for estimating cross‐sectional and longitudinal reference curves relies mainly on the linear mixed model. The focus of this paper is on examining the robustness of percentile estimation to the assumptions with respect to the Gaussian random‐effect assumption implicitly made in the standard linear mixed model. We also examine a random‐effects distribution based on mixtures of normals and compare the two approaches under both correct and misspecified random‐effects distributions. In general, we find that the standard linear mixed model is relatively robust for cross‐sectional percentile estimation but less robust for longitudinal or ‘personalized’ reference curves based on the conditional distribution given prior ultrasound measurements. The methodology is illustrated with data from a longitudinal fetal growth study. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Asymptotic power of likelihood-ratio tests for detecting quantitative trait loci using the COGA data

We investigated the asymptotic power of the likelihood-ratio test for detecting linkage to a quantitative trait locus (QTL) using the data set from the Collaborative Study on the Genetics of Alcoholism (COGA). Assuming a total trait heritability of 50% as determined for the COGA Cz P300 phenotype, we determined the minimum QTL heritability required at each point in the genome to achieve 80% power to detect linkage with a lod of 3.0. We find that there are regions of the genome where it is not possible to detect a QTL of any effect with 80% power, and that the overall minimum detectable QTL heritability for the COGA data is 0.35-0.40.     

Extension of variance components approach to incorporate temporal trends and longitudinal pedigree data analysis

Here we present a method that permits one to evaluate genetic effects and to detect genetic linkages by using serial observations of quantitative traits in pedigrees. We developed a statistical method that incorporates longitudinal family data and genetic marker information into an estimating equations framework. With this approach, we can study changes in components over time that measure polygenic and major genetic variances as well as shared and individual-specific environmental effects. Our method provides a measure of heritability from analysis of longitudinal data. Results using longitudinal family data from the Center for Preventive Medicine (Nancy, France) are presented. The results of our analysis show that the apolipoprotein E locus has no effect on interindividual variability in systolic blood pressure. We found that the longitudinal measure of heritability of systolic blood pressure is 0.32.     

Genome-wide linkage analyses of total serum IgE using variance components analysis in asthmatic families

Variance components models were used to analyze total IgE levels in families ascertained though the Collaborative Study of the Genetics of Asthma (CSGA) using a genome-wide array of polymorphic markers. While IgE levels are known to be associated with clinical asthma and recognized to be under strong genetic control (here the heritability was estimated at 44-60% in the three racial groups), specific genes influencing this trait are still largely unknown. Multipoint analysis of 323 markers yielded little indication of specific regions containing a trait locus controlling total serum IgE levels (adjusted for age and gender). Although a number of regions showed LOD statistics above 1.5 in Caucasian families (chromosome 4) and in African-American families (chromosomes 2 and 4), none yielded consistent evidence in all three racial groups. Analysis of total IgE adjusted for gender, age and Allergy Index (a quantitative score of skin test sensitivity to 14 common aeroallergens) was conducted on these data. In this analysis, a much stronger signal for a trait locus controlling adjusted log[total IgE] was seen on the telomeric end of chromosome 18, but only in Caucasian families. This region accounted for most of the genetic variation in log[total IgE], and may represent a quantitative trait locus for IgE levels independent of atopic response. Oligogenic analysis accounting simultaneously for the contribution of this locus on chromosome 18 and other chromosomal regions showing some evidence of linkage in these Caucasian families (on chromosomes 2, 4 and 20) failed to yield significant evidence for interaction.     

Methods to estimate genetic components of variance for quantitative traits in family studies

The aim of this paper was to compare several methods of estimating the genetic components of a quantitative trait in familial data. The Expectation and Maximization (E‐M) algorithm, the Newton‐Raphson method, and the scoring method were compared for estimating polygenic and environmental effects on nuclear families. We also compared scoring and quasilikelihood (QL) methods when a linked genetic marker was available to estimate effects from a major gene. Generally, all procedures performed similarly in estimating polygenic and environmental variance components. The E‐M algorithm yielded more precise estimators when heritability was low. The scoring method was much faster than the other methods and yielded slightly more precise estimates of mean effects but slightly less precise estimates of the variance components. Estimates of major gene effects were not affected by the number of alleles at the trait locus. For these relatively large sample sizes, QL and scoring had similar precision, but QL took 32 times longer than scoring. Finally, we compared the results of applying these methods to data from the Bogalusa Heart Study. Results showed larger imprecision when the QL method was applied, consistent with earlier studies that showed decreased precision of quasilikelihood compared with maximum likelihood in moderately small sample sizes. Genet. Epidemiol. 17:64–76, 1999. © 1999 Wiley‐Liss, Inc.     

Genetic analysis of personality traits and alcoholism using a mixed discrete continuous trait variance component model

Bivariate analyses can improve power to detect linkage. This paper describes one application of a bivariate variance component method for estimating joint likelihoods of a continuous and a discrete trait. This method is applied to the Collaborative Study on the Genetics of Alcoholism data set to investigate the relationship between personality traits derived from the tridimensional personality questionnaire (TPQ) and alcoholism. The results indicate that the novelty-seeking subscale of the TPQ and alcoholism share a strong and significant genetic correlation (rho G = 0.83) and modest environmental correlation (rho E = 0.31). When both traits are considered jointly in a multipoint linkage model compared with the alcoholism trait alone, there is an improvement in the ability to detect and localize a quantitative trait locus on chromosome 4.     

Genome-wide linkage analysis using genetic variance components of alcohol dependency-associated censored and continuous traits

We used variance-components analysis to investigate the additive genetic effects regulating some of the phenotypes included in the GAW11 data set. Variance-components models were fitted using Gibbs sampling methods in BUGS v 0.6. Linkage analyses for both multivariate normal (MvN) traits and right censored survival times (age-of-onset) were based upon standard Haseman-Elston identity-by-descent sib-pair methods applied directly to traits showing evidence of substantial additive genetic determination (residualized for any important covariates) and to the estimated sigma A2 residuals for those traits. Harm avoidance behavior (TPQ subscale) showed evidence of linkage to markers on chromosomes 1, 13, and 18. P300 levels at the Fp1 site showed evidence of linkage to markers on chromosomes 2, 3, 9, 12, 17, 19, and 20. Platelet monoamine oxidase B (MAOB) levels showed evidence of linkage to D4S1651. The age-of-onset for ALDX1 in those over 30 years old showed evidence of linkage to markers on chromosomes 1, 6, 14, and 15. The age-of-onset for the more strictly defined ALDX2 in those over 30 years old showed evidence of linkage to markers on chromosomes 7 and 14. These results are consistent with a complex, multifactorial susceptibility to alcohol dependency.     

Segregation and linkage analysis of a quantitative versus a qualitative trait in large pedigrees

Goals of this analysis were to map loci contributing to variation in the quantitative trait, Q1, using the lod-score method on data set 1, and to explore the difference in power to map genes when considering the discrete vs. Quantitative phenotype. Segregation analyses, after covariate adjustment, correctly suggested two contributing loci. The major gene on chromosome 5 was successfully mapped, but the major gene on chromosome 8 was not. Comparison of linkage analyses for the qualitative and quantitative traits confirmed that the quantitative trait is more informative, suggesting that localizing disease genes with a qualitative trait would be more difficult in these pedigrees. © 1997 Wiley-Liss, Inc.     

Ignoring temporal trends in genetic effects substantially reduces power of quantitative trait linkage analysis

Linkage analysis has been one of the most widely used methods for identifying regions of the human genome which contain genes responsible for human diseases. Evidence suggests that the effects of some of the trait causing genes may vary with the age of an individual, giving rise to temporal trends in genetic effects. Linkage analysis routinely tends to ignore such gene-by-age interactions. While linkage analysis methods have been proposed for analysis of longitudinal family data for exploring temporal trends, there are no models to characterize such trends nor methods for analysis of cross-sectional family data. We extend variance component linkage analysis methodology by modeling the variance components due to the quantitative trait locus (QTL) and that due to the polygenic effect to be age dependent. With this model, we investigate the power of linkage analysis in the presence of temporal trends. We show that modeling true temporal trends in QTL effects can substantially increase the power of linkage analysis even when the average locus-specific heritabilities (when trends are ignored) are quite low, thereby demonstrating that, ignoring the gene-by-age interactions, when present, could jeopardize gene discovery.     

Assessing linkage of monoamine oxidase B in a genome-wide scan using a univariate variance components approach

We report results when one alcoholism related quantitative trait, monoamine oxidase B (MAOB), is analyzed by the variance components approach for linkage [Amos, 1994; Amos et al., 1996] using the Collaborative Study on the Genetics of Alcoholism data set provided for the Genetic Analysis Workshop 11. We used two different covariate models, one with age at interview, sex, ethnicity, and smoking status and the other with age at interview, sex, and ethnicity. The univariate analysis showed 24 markers on four different chromosomes (1, 4, 9, and 12) to have evidence for linkage with the quantitative trait (single-point and multipoint linkage). However, when outliers for MAOB were removed, the significant evidence for linkage disappeared.     

Detecting differentially expressed genes in heterogeneous diseases using control-only analysis of variance

PurposeMicroarray technology allows for simultaneously screening many genes and determining which gene(s) are differentially expressed in different disease statuses or different cell types. The analysis of variance (ANOVA) (for a K-sample situation with K > 2) can be used in such occasions to gauge statistical significances. However, the test may be underpowered if the diseases under study are heterogeneous.MethodsThe authors propose the “control-only ANOVA” for detecting differentially expressed genes in heterogeneous diseases. Monte-Carlo simulation shows that the test produces quite accurate type I error rates for both normal and non-normal data. The statistical power of the control-only ANOVA is higher than that of the conventional ANOVA when the diseases under study are heterogeneous.ResultsAnalysis of a real data set shows that after Bonferroni correction, the control-only ANOVA detects three differentially expressed genes, whereas the conventional ANOVA can detect only one.ConclusionsThe control-only ANOVA is recommended for use when the diseases under study are heterogeneous.