Power of multipoint identity-by-descent methods to detect linkage using variance component models.

Multipoint linkage analysis gives increased power over single-point analysis to detect linkage for quantitative trait loci (QTL). Besides increased power, the use of multipoint methods makes it possible to estimate not only the location but also the magnitude of the QTL. Currently, two methods are commonly used for calculating multipoint identity-by-descent (IBD) allele-sharing estimates for pedigrees of moderate sizes. The method of Fulker et al. is based on multiple regression of the IBD status at the observed marker loci, whereas the hidden Markov model approach of Kruglyak and Lander estimates the true inheritance distribution at each chromosomal location. Simulation studies of full sibs and nuclear pedigrees show that the two methods for estimating multipoint IBD scores may give very different estimates for a pair of relatives and that a small increase in power to detect linkage can be obtained by using the hidden Markov model compared with the regression method.     

Detecting linkage for a complex disease using simulated extended pedigrees

The simulated extended pedigree data of the Genetic Analysis Workshop 10 were used to examine the relationship between several quantitative traits (Q1-Q5), an environmental factor, age and sex and to identify genes contributing to the quantitative traits. A forward selection procedure was used to identify regression models for each trait. Residuals from these regression models were used as quantitative traits in linkage analysis. Two-point sib-pair analysis was performed on Replicate 1 of the data set using SIBPAL. Sixteen regions on 8 chromosomes yielded two-point p-values < 0.005 in Replicate 1. Two strategies for utilizing a second data set were evaluated. In a two-stage approach, only those regions with p-value < 0.005 in Replicate 1 were followed up in the second data set. Nine of these regions had p-values < 0.05 in Replicate 2; four were associated with major genes included in the generating model and the remaining five regions were false positives. An alternative strategy was to perform a repeat genome wide screen in the second data set. This strategy resulted in the identification of 20 regions with p-values < 0.05 in both replicates; five of which included major genes included in the generating model. Although the false positive rate increased when a complete genome screen was performed on both data sets, the two-stage screen, with a more stringent initial criterion for identifying suggestive linkages, had a higher rate of false negatives. For some studies, conducting two complete genome screens in a split-sample design may be worthwhile. © 1997 Wiley-Liss, Inc.     

Analysis of quantitative risk factors for a common oligogenic disease

All three simulated loci influencing the quantitative variables Q1, Q2, and Q3 were successfully mapped by using a strategy of covariate adjustment and segregation analysis, coupled with association analyses and lod-score analyses. © 1995 Wiley-Liss, Inc.     

The role of smoothing techniques in the interpretation of results from genomic scans using sib-pair data

We compare the results of genomic scans conducted with the Haseman-Elston sib- pair method using either (1) the average marker information from several adjacent loci or (2) each marker individually. Under smoothing, the squared sib-pair trait difference is regressed on the average number of alleles shared identical by descent averaged at several adjacent loci. This results in a significant decrease in the number of false-positives when compared to the individual marker approach. Linkage of Q4 to MG4 was found only with smoothing but not the individual marker approach. Overall, smoothing resulted in the loss of two true linkages. © 1997 Wiley-Liss, Inc.     

Detection of major genes underlying several quantitative traits associated with a common disease using different ascertainment schemes

Using the Problem 2A data sets of GAW10, we assessed the power of four ascertainment schemes to localize major genes underlying a disease trait; the schemes were based on disease or quantitative trait status of nuclear families. MAPMAKER/SIBS was used to perform sib-pair analysis for all four data sets using marker data from three chromosomes, 4,5 and 8. Each scheme varied in power to identify major genes underlying the quantitative traits depending on the genetic architecture of the data set. Three different methods, Haseman-Elston quantitative trait locus (QTL) regression analysis, maximum likelihood variance estimation and a non-parametric method, were used to assess the strength of linkage in all four data sets. False positive mappings localizing to the same region of the genome, verifiable across all three methods did not occur. Two major genes, MG1 and MG2, were successfully assigned to chromosomes 5 and 8, respectively, by at least one of the ascertainment schemes. MG1 was localized under two schemes, selection of families with exactly two affected sibs and selection of families with two sibs who had extremely discordant values for Q1. Additional weak evidence of the location of MG1 was also obtained under the other two ascertainment schemes. MG2 could not be detected by analyzing data sets ascertained either by affected sib pairs or by sib pairs with extremely discordant values for Q1. In the data set ascertained by a third strategy, selection of families with sib pairs extremely discordant for Q2, MG2 could be mapped to chromosome 8. A random ascertainment scheme yielded a data set in which we could find weak evidence for MG1 and no evidence for MG2. Thus our ability to detect major genes underlying the QTL depended on several factors which included the ascertainment scheme, the population allelle frequencies, linkage and epistasis. © 1997 Wiley-Liss, Inc.     

Mapping multiple genes for quantitative or complex traits

Models for complex and quantitative traits that involve multiple, possibly interacting, genes are described. Methods of linkage analysis are developed that utilize special features of these models, and their power is compared with that of simple genome scans that ignore these special features. Our calculations show that for family-based nonparametric linkage analysis in human genetics, in contrast to experimental genetics, there are limits to the increase in power that can be achieved by correctly modeling gene-gene interactions. In particular, the noncentrality parameter of likelihood-based statistics to detect single gene effects involves both single gene and interaction components of variance, so even when the interaction components of variance are relatively large, the incremental power from a statistic designed to detect both single gene and interaction effects is often quite modest. We carry out our analysis with the assistance of a parameterization that allows us to compute score statistics, noncentrality parameters, and Fisher information matrices reasonably explicitly.     

Longitudinal Association Analysis of Quantitative Traits

Longitudinal genetic studies provide a valuable resource for exploring key genetic and environmental factors that affect complex traits over time. Genetic analysis of longitudinal data that incorporate temporal variations is important for understanding genetic architecture and biological variations of common complex diseases. Although they are important, there is a paucity of statistical methods to analyze longitudinal human genetic data. In this article, longitudinal methods are developed for temporal association mapping to analyze population longitudinal data. Both parametric and nonparametric models are proposed. The models can be applied to multiple diallelic genetic markers such as single‐nucleotide polymorphisms and multiallelic markers such as microsatellites. By analytical formulae, we show that the models take both the linkage disequilibrium and temporal trends into account simultaneously. Variance‐covariance structure is constructed to model the single measurement variation and multiple measurement correlations of an individual based on the theory of stochastic processes. Novel penalized spline models are used to estimate the time‐dependent mean functions and regression coefficients. The methods were applied to analyze Framingham Heart Study data of Genetic Analysis Workshop (GAW) 13 and GAW 16. The temporal trends and genetic effects of the systolic blood pressure are successfully detected by the proposed approaches. Simulation studies were performed to find out that the nonparametric penalized linear model is the best choice in fitting real data. The research sheds light on the important area of longitudinal genetic analysis, and it provides a basis for future methodological investigations and practical applications.     

Multilocus linkage disequilibrium mapping of epistatic quantitative trait loci that regulate HIV dynamics: a simulation approach

The time-dependent change of HIV particle load, i.e. HIV dynamics, is likely to be controlled by a multitude of quantitative trait loci (QTL) that interact with each other as well as with various developmental and environmental factors in a coordinated manner. In this article, we have derived a new statistical model for mapping the epistatic QTL responsible for HIV dynamics in a natural human population. This model, constructed on the integrated theme of functional mapping and linkage disequilibrium (LD) mapping, can make use of information from multiple markers genotyped from the human genome. It allows for the test and estimation of genetic actions and interactions involved in the control of HIV progression and provides a general platform to identify the detailed genetic architecture of resistance or susceptibility of humans to HIV on a dynamic scale. We have generalized this model to accommodate various complicated clincal designs for AIDS studies. Simulation studies with different scenarios are performed to examine the statistical behaviour of the model. The genetic and statistical extensions of this mapping model to HIV/AIDS genomic research are discussed.     

Longitudinal SNP‐set association analysis of quantitative phenotypes

Many genetic epidemiological studies collect repeated measurements over time. This design not only provides a more accurate assessment of disease condition, but allows us to explore the genetic influence on disease development and progression. Thus, it is of great interest to study the longitudinal contribution of genes to disease susceptibility. Most association testing methods for longitudinal phenotypes are developed for single variant, and may have limited power to detect association, especially for variants with low minor allele frequency. We propose Longitudinal SNP‐set/sequence kernel association test (LSKAT), a robust, mixed‐effects method for association testing of rare and common variants with longitudinal quantitative phenotypes. LSKAT uses several random effects to account for the within‐subject correlation in longitudinal data, and allows for adjustment for both static and time‐varying covariates. We also present a longitudinal trait burden test (LBT), where we test association between the trait and the burden score in linear mixed models. In simulation studies, we demonstrate that LBT achieves high power when variants are almost all deleterious or all protective, while LSKAT performs well in a wide range of genetic models. By making full use of trait values from repeated measures, LSKAT is more powerful than several tests applied to a single measurement or average over all time points. Moreover, LSKAT is robust to misspecification of the covariance structure. We apply the LSKAT and LBT methods to detect association with longitudinally measured body mass index in the Framingham Heart Study, where we are able to replicate association with a circadian gene NR1D2.     

Joint linkage and segregation analysis under multiallelic trait inheritance: simplifying interpretations for complex traits

Identification of the genetic basis of common traits may be hindered by underlying complex genetic architectures that are inadequately captured by existing models, including both multiallelic and multilocus modes of inheritance (MOI). One useful approach for localizing genes underlying continuous complex traits is the joint oligogenic linkage and segregation analysis implemented in the package Loki. The method uses reversible jump Markov chain Monte Carlo to eliminate the need to prespecify the number of quantitative trait loci (QTLs) in the trait model, thus providing posterior distributions for the number of QTLs in a Bayesian framework. The current implementation assumes QTLs are diallelic, and therefore can overestimate the number of linked QTLs in the presence of a multiallelic QTL. To address the possibility of multiple alleles, we extended the QTL model to allow for a variable number of additive alleles at each locus. Application to simulated data shows that, under a diallelic MOI, the multiallelic and diallelic analysis models give similar results. Under a multiallelic MOI, the multiallelic analysis model provides better mixing and improved convergence, and leads to a more accurate estimate of the underlying trait MOI and model parameter values, than does the diallelic model. Application to real data shows the multiallelic model results in fewer estimated linked QTLs and that the predominant QTL model is similar to one of two predominant models estimated from the diallelic analysis. Our results indicate that use of a multiallelic analysis model can lead to better understanding of the genetic architecture underlying complex traits. Genet. Epidemiol. 34: 344–353, 2010. © 2010 Wiley‐Liss, Inc.     

Empirical evaluation of genome scans for linkage of a quantitative trait associated with a complex disorder

Nonparametric sib-pair analysis (Haseman-Elston) was used to search for evidence of linkage between a putative locus for a complex quantitative trait Q1 and genome-wide markers (367 markers from 10 chromosomes) for the first 100 replicates of nuclear family data. The characteristics of the statistically positive linkage results [the magnitude of p-values (p), the number of supporting flanking markers, and the percentage of positive replicates] were compared for true linkage (major and minor genes) and false positive evidence for linkage. Discriminant analysis was used to evaluate which characteristics of these statistically positive linkage results are good indicators to discriminate true linkage from false positive evidence for linkage. Sensitivity and false positive rates of several proposed criteria for linkage, as well as the criteria based on our results were evaluated. The relationship between the map location of the marker with the lowest p-value and the map location of the true underlying gene was also evaluated, which provided useful information for fine mapping and replication studies. © 1997 Wiley-Liss, Inc.     

On the utility of gene set methods in genomewide association studies of quantitative traits

In genomewide genetic association studies, prior biological knowledge may help distinguish variation that is truly associated with a quantitative trait from the vast majority of unassociated variation that may be significant in hypothesis testing due to chance. However, formal methods for integrating prior biological knowledge into association studies have only been proposed recently, and their potential utility has not been thoroughly evaluated. Herein, gene set methods from genomewide analysis of gene expression data are adapted for application to genomewide genetic analysis of quantitative traits. The proposed gene set method was tested in simulations with gene sets that included up to 500 total variants, among which up to 20 collectively explained 5% of the variance. In a population of 1,000 individuals, the gene set method was largely more efficient at detecting truly associated variants in these gene sets than a comparably calibrated conventional approach relying on P-values alone. While extremely strong associations remain best identified by conventional methods, the gene set approach may provide a complementary mode of analysis for revealing the full spectrum of genes that influence a quantitative trait.     

A statistical model for high-resolution mapping of quantitative trait loci determining HIV dynamics

Are there specific genes that control the pathogenesis of HIV infection? This question, which is of fundamental importance in designing personalized strategies of gene therapy to control HIV infection, can be examined by genetic mapping approaches. In this article, we present a new statistical model for unravelling the genetic mechanisms for the dynamic change of HIV that causes AIDS by marker‐based linkage disequilibrium (LD) analyses. This new model is the extension of our functional mapping theory to integrate viral load trajectories within a genetic mapping framework. Earlier studies of HIV dynamics have led to various mathematical functions for modelling the kinetic curves of plasma virions and CD4 lymphocytes in HIV patients. Through incorporating these functions into the LD‐based mapping procedure, we can identify and map individual quantitative trait loci (or QTL) responsible for viral pathogenesis. We derive a closed‐form solution for estimating QTL allele frequency and marker‐QTL linkage disequilibrium in the context of EM algorithm and implement the simplex algorithm to estimate the mathematical parameters describing the curve shapes of HIV pathogenesis. We performed different simulation scenarios based on currently used clinical designs in AIDS/HIV research to illustrate the utility and power of our model for genetic mapping of HIV dynamics. The implications of our model for genetic and genomic research into AIDS pathogenesis are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

一种新的调控型遗传变异与中国人群肺癌发病风险的关系：两阶段病例-对照研究

目的 调控型数量性状位点（regQTL）理论可以帮助研究者从三维角度评估单核苷酸多态性（SNPs）对重要生物信号的调控作用。本研究拟探讨regQTL-SNPs对肺癌易感性的影响。方法 基于regQTL理论，利用已知的肺癌regQTL-SNPs数据库，筛选出全基因组关联研究（GWAS）报道的肺癌易感区域中发挥regQTL功能的SNPs。并通过两阶段病例-对照研究（初筛阶段：2 331例肺癌病例和3 077例健康对照；验证阶段：626例肺癌病例和667例健康对照），进一步明确上述regQTL-SNPs与肺癌易感性的关联。结果 在肺癌GWAS已报道的易感区域中，共筛选出8个regQTL-SNPs。人群易感性分析的初筛阶段，研究结果显示3个regQTL-SNPs与肺癌的发病风险存在统计学关联（P<0.05），验证阶段结果显示，位于ADRA1A基因上的rs6998591突变等位基因T可以显著增加肺癌的发病风险（相加模型：OR=1.33，95%CI：1.01~1.74，P=0.040），而位于ACTA2基因上的rs11202916突变等位基因G可以明显降低肺癌的发病风险（隐性模型：OR=0.71，95%CI：0.52~0.96，P=0.026）。分层分析结果显示，rs6998591的突变等位基因T显著增加肺鳞癌的发病风险（相加模型：OR=1.53，95%CI：1.01~2.32，P=0.043），而rs11202916的突变等位基因G显著降低肺腺癌的发病风险（相加模型：OR=0.83，95%CI：0.69~0.98，P=0.031）。基因环境交互作用分析显示携带rs6998591突变等位基因T且吸烟的个体与不携带rs6998591突变等位基因T且不吸烟的个体相比，肺癌的发病风险增加235%（OR=3.35，95%CI：2.10~5.34，P<0.001）。结论 肺癌GWAS已报道的易感区域中存在2个发挥regQTL功能的SNPs，并且可以显著影响肺癌的易感性。     

The utility of deviant sib pairs in the detection of linkage

A tripartite sampling design was used to help deduce the genetic structure of a complex biological system. Univariate and multivariate population parameters were estimated from an age/sex stratified sample of unrelated individuals. Estimates of familial resemblance between and within continuous variables were obtained from a sample of randomly ascertained nuclear families. Finally, a sample of highly deviant concordant and discordant independent sib pairs facilitated the discovery of major genes through multipoint linkage analysis. No false positive signals were inferred. The pleiotropic effects of major genes, however, became obscured when linkage analysis was performed on adjusted quantitative variables. © 1997 Wiley-Liss, Inc.     

Comparison of Sib Pair‐Based Approaches for Identifying Quantitative Trait Loci Underlying Asthma in the Busselton Families

The goal of this study is to determine the linkage relationship between IgE levels and the 269 microsatellite markers using the Genetic Analysis Workshop 12 Busselton data set. Analyses were carried out using both traditional and new Haseman‐Elston methods, the maximum likelihood quantitative trait locus estimation (MLE QTL) method and the nonparametric (NP QTL) method. Our analyses confirmed some of the signals reported by Daniels et al. [Nature 383:247–50, 1996]. We also observed that several significant signals reported in the original report became insignificant (D6S76 and D11S96) and several new signals showed up after the data were reanalyzed using the new Haseman‐Elston method, the MLE QTL method, and the NP QTL method. Based on the original and the current analyses, we recommend that follow‐up studies of three regions including D7S2250, FCER1B, D11S901, and six markers on chromosome 16 be given higher priority. © 2001 Wiley‐Liss, Inc.     

Functional Linear Models for Association Analysis of Quantitative Traits

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F‐distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT‐O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT‐O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study.     

A review of kernel methods for genetic association studies

Evaluating the association of multiple genetic variants with a trait of interest by use of kernel-based methods has made a significant impact on how genetic association analyses are conducted. An advantage of kernel methods is that they tend to be robust when the genetic variants have effects that are a mixture of positive and negative effects, as well as when there is a small fraction of causal variants. Another advantage is that kernel methods fit within the framework of mixed models, providing flexible ways to adjust for additional covariates that influence traits. Herein, we review the basic ideas behind the use of kernel methods for genetic association analysis as well as recent methodological advancements for different types of traits, multivariate traits, pedigree data, and longitudinal data. Finally, we discuss opportunities for future research.     

A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits

In association studies of complex traits, fixed‐effect regression models are usually used to test for association between traits and major gene loci. In recent years, variance‐component tests based on mixed models were developed for region‐based genetic variant association tests. In the mixed models, the association is tested by a null hypothesis of zero variance via a sequence kernel association test (SKAT), its optimal unified test (SKAT‐O), and a combined sum test of rare and common variant effect (SKAT‐C). Although there are some comparison studies to evaluate the performance of mixed and fixed models, there is no systematic analysis to determine when the mixed models perform better and when the fixed models perform better. Here we evaluated, based on extensive simulations, the performance of the fixed and mixed model statistics, using genetic variants located in 3, 6, 9, 12, and 15 kb simulated regions. We compared the performance of three models: (i) mixed models that lead to SKAT, SKAT‐O, and SKAT‐C, (ii) traditional fixed‐effect additive models, and (iii) fixed‐effect functional regression models. To evaluate the type I error rates of the tests of fixed models, we generated genotype data by two methods: (i) using all variants, (ii) using only rare variants. We found that the fixed‐effect tests accurately control or have low false positive rates. We performed simulation analyses to compare power for two scenarios: (i) all causal variants are rare, (ii) some causal variants are rare and some are common. Either one or both of the fixed‐effect models performed better than or similar to the mixed models except when (1) the region sizes are 12 and 15 kb and (2) effect sizes are small. Therefore, the assumption of mixed models could be satisfied and SKAT/SKAT‐O/SKAT‐C could perform better if the number of causal variants is large and each causal variant contributes a small amount to the traits (i.e., polygenes). In major gene association studies, we argue that the fixed‐effect models perform better or similarly to mixed models in most cases because some variants should affect the traits relatively large. In practice, it makes sense to perform analysis by both the fixed and mixed effect models and to make a comparison, and this can be readily done using our R codes and the SKAT packages.     

How can maximum likelihood methods reveal candidate gene effects on a quantitative trait?

Different maximum likelihood approaches were used to explore the role of candidate genes in the variability of quantitative trait Q1 while accounting for the effects of age, Q2, and Q3. Segregation analysis, under the class D regressive model, provides evidence for a Mendelian gene effect on the adjusted trait Q1. Results of gene mapping through lod-score analyses remain puzzling. Pairwise lod scores indicate a possible linkage with the candidate gene C5 which is excluded when using tightly linked informative marker loci. Finally, our combined segregation and linkage analysis clearly shows that a C5 linked gene is involved in Q1 variability. However, given the lod-score results within the C5 region, we postulate a more complex mechanism for Q1 than a single di-allelic C5 linked gene. The knowledge of the true model (C5 is MG1 and has three alleles) permits a partial explanation of our results. This study demonstrates the advantages of using complementary approaches to reveal the role of candidate genes in complex traits, and the value of simultaneous estimation of linkage and segregation parameters. © 1995 Wiley-Liss, Inc.