Association and linkage with quantitative traits

This paper examines two approaches for the analysis of quantitative traits: (1) association studies and (2) linkage studies. The trait studied was Q1 from simulated Problem 2 data set in Genetic Analysis Workshop 9. Our purpose was to evaluate associations present in the data, to identify nongenetic and genetic predictors of the trait, and to explore the simulated genome for linkage. Through the association study, we found evidence for the primary major gene associated with this trait. The linkage study found evidence of residual genetic effect acting through other traits. Adjustments of Q1 for Q2 and Q3 led to a failure to find significant effects of MG2 and MG3. This supports the suggestion that adjustment for genetically influenced traits for effects of other genetic traits can reduce the power to detect major gene effects. In summary, we detected the major gene directly associated with the trait of interest through association studies. Linkage analysis detected evidence for two other genes associated to a lesser degree with the trait. © 1995 Wiley-Liss, Inc.     

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.     

Modeling Age×Major Gene Interaction by a Variance Component Approach

The variance component method has become popular for linkage analysis due to its computational simplicity and generally high power. In this paper we model phenotypic variability of an individual as a mixed effects model in which both the major gene as well as the polygene effects interact with age. We applied the proposed model to the simulated data of Genetic Analysis Workshop 12. We considered the quantitative trait, Q₄, in the outbred population. Two major genes influence this trait, each interacting with age independently. Consequently, trait variability is a function of age and also there is interaction of major gene effects with age. By using our model we were able to detect interaction between the major gene effects and age for this trait. © 2001 Wiley‐Liss, Inc.     

Identification of susceptibility loci contributing to a complex disease using conventional segregation,linkage, and association methods

We set out to apply conventional analytic methods to a GAW data set of nuclear families with an oligogenic disease that has a population prevalence of 0.023. We chose methods generally applied to disorders with at least one major gene. Our approaches included: (1) complex segregation analysis under two models of ascertainment, (2) linkage analysis assuming either a single-locus trait with possible genetic heterogeneity or a two-locus trait, and (3) allelic association studies using both a case/control approach and the haplotype relative risk (HRR) test. The association study was the only analysis of the three that provided evidence for genes playing a role in the etiology of this disorder. ©1995 Wiley-Liss, Inc.     

Identification and mapping of mendelian subtypes of disease

We took as our working hypothesis the premise that there could be a single locus of major effect underlying a subset of cases in the simulated Problem 2 data set, and took as our primary goal the task of mapping that locus. Treating the disease as dichotomous and using discriminant function analysis, we were able to separate affected individuals into two disease categories: Disease Type I (DT-I) cases, whose disease was by hypothesis caused by the major locus; and Disease Type II (DT-II) cases, whose disease was by hypothesis produced by other causes. Segregation analysis showed evidence of simple recessive inheritance among the DT-I individuals. Linkage analysis under the best-fitting recessive model gave clear evidence of linkage to D1G2. In the generating model, this marker is linked to a major gene for disease with recombination fraction θ = 0, and the mode of inheritance at that locus is recessive (when the trait is considered as a dichotomy). We conclude that when the true model is complex, focussing on subtypes of disease that show evidence of simple Mendelian inheritance may be a useful first step in determining the underlying model and mapping major genes. © 1995 Wiley-Liss, Inc.     

Linkage Disequilibrium Structure and Its Impact on the Localization of a Candidate Functional Mutation

We have used the unblinded MG1/Q1 Genetic Analysis Workshop 12 simulated data as a model system for investigating the use of linkage disequilibrium structure and simple genotype‐phenotype associations to identify candidate functional mutations within a gene of interest. Analysis of the pattern of pair‐wise linkage disequilibrium indicated three groups of single‐nucleotide polymorphisms for which the linkage disequilibrium was high between sites within a group, but lower between sites of different groups. Using linear regression to predict levels of the trait Q1 showed that the known functional site, 5782, was usually not the best genetic predictor of Q1, but sites belonging to the same group as 5782 (i.e., group 2) were always included in the prediction model. In 49 out of the 50 replicates, the functional site was not the best predictor of the trait. Finally, more detailed analyses demonstrate that the relationship between the adjusted R² for the marker in the prediction model and its disequilibrium with 5782 was linear with the intercept at the origin and terminating at the R² value for the known functional mutation when the disequilibrium is maximal. These data indicate that simple association studies will not identify the functional mutation, but rather will identify candidate functional mutations that are in very tight linkage disequilibrium with the functional mutation. © 2001 Wiley‐Liss, Inc.     

Power to Localize the Major Gene for Disease Liability Is Increased After Accounting for the Effects of Related Quantitative Phenotypes

We used the simulated general population data for Genetic Analysis Workshop 12 to test whether power to localize the major gene for liability to disease is increased after accounting for the effects of correlated quantitative phenotypes. We performed the multipoint variance‐component linkage analyses for the discrete trait twice: first analysis with age, sex, and EF1 as covariates, and the second analysis with age, sex, EF1, and Q1–Q5 as covariates. Major locus heritability (h²_q,) (0.80 ± 0.06) and lod score (6.4) averaged over the number of replicates used are significantly higher in the second analysis compared with the first analysis (h²_q= 0.39 ± 0.12, lod = 2.6). Thus, in the present analysis, power to detect linkage and localize the genes for liability to disease appears to be increased after accounting for the effects of five quantitative traits that are correlated with the liability. © 2001 Wiley‐Liss, Inc.     

Weighted pairwise correlation and transmission disequilibrium in a common oligogenic disease

Weighted pairwise correlation (WPC) linkage analysis and the transmission disequilibrium test (TDT) for allelic association were applied to simulated family data for a common oligogenic disorder in order to localize genes that increase levels of Q1. Preliminary linear models indicated that Q1 increases with age, Q2, Q3, and the occurrence of D5G28 allele 3 (D5G28(3). WPC provided evidence for linkage of Q1 to Major Gene 1, D5G28 (p < 0.0001), and to other loci when ranks based on age and affection status (Q1 < or > 87.5) were used to define the phenotype. D5G28 was the only locus linked to Q1 (p = 0.01) when the phenotype was defined as Q1 adjusted for age, Q2, Q3, and D5G28(3). The TDT indicated linkage disequilibirum between a gene for elevated Q1 (> 87.5) and alleles at loci adjacent to D5G28: D5G29(2) was apparently protective (p = 0.008) while allele 8 was associated with risk (p = 0.007); D5G30(7) was also apparently protective (p = 0.02). However, significant disequilibirum was not found for D5G28(3), possibly due to lack of adjustment of Q1 and small sample size. These results imply that the combined use of WPC and the TDT may be an effective strategy for genomic screens in complex disorders defined by quantitative traits, especially when the trait can be adjusted for age and other relevant factors. © 1995 Wiley-Liss, Inc.     

Covariate effects on linkage and association using a general pair method

The “general pair method” (GPM) is a nonparametric, identity-by-state (IBS) method of assessing linkage between a chromosomal marker and a binary phenotype. It is applicable to any pedigree structure, and uses marker information from affected as well as unaffected individuals. Results obtained here from nuclear families (Problem 2A) are contrasted with those from extended pedigrees (Problem 2B). Test statistics for chromosomal linkage between each marker and disease status are contrasted with tests for “direct association” which test the hypothesis that a particular allele is associated disease status across all pedigrees. A novel extension of the GPM is presented here for testing whether the strength of linkage (and/or association) depends on the levels of a covariate (i.e., dependency on gender, age, the levels of the “environmental factor,” or the levels of the “quantitative phenotypes” supplied). The GPM is seen to have some power to detect major gene 1 on chromosome 5, and major gene 3 on chromosome 4. The gender interaction effects proved too small to detect. No direct associations are found. © 1997 Wiley-Liss, Inc.     

Assessing linkage on chromosome 5 using components of variance approach: Univariate versus multivariate

We report results when one disease related quantitative trait (Q1) is analyzed versus multiple related quantitative traits using a components of variance approach [Amos, 1994; de Andrade and Amos, 1996]. In both cases, we used age, sex and environmental factor (EF) as covariates. Analysis with ascertainment correction of samples selected through probands with extremely high trait values was also performed and is presented. Testing procedures to detect linkage using the components of variance approach are discussed. The univariate and multivariate analyses showed effects of locus 15 on chromosome 5 only for Q1. This result was confirmed when using ascertainment correction. © 1997 Wiley-Liss, Inc.     

Guess LOD approach: Sufficient conditions for robustness

Analysis of genetic linkage between a disease and a marker locus requires specifying a genetic model describing both the inheritance pattern and the gene frequencies of the marker and trait loci. Misspecification of the genetic model is likely for etiologically complex diseases. In previous work we have shown through analytic studies that misspecifying the genetic model for disease inheritance does not lead to excess false-positive evidence for genetic linkage provided the genetic marker alleles of all pedigree members are known, or can be inferred without bias from the data. Here, under various selection or ascertainment schemes we extend these previous results to situations in which the genetic model for the marker locus may be incorrect. We provide sufficient conditions for the asymptotic unbiased estimation of the recombination fraction under the null hypothesis of no linkage, and also conditions for the limiting distribution of the likelihood ratio test for no linkage to be chi-squared. Through simulation studies we document some situations under which asymptotic bias can result when the genetic model is misspecified. Among those situations under which an excess of false-positive evidence for genetic linkage can be generated, the most common is failure to provide accurate estimates of the marker allele frequencies. We show that in most cases false-positive evidence for genetic linkage is unlikely to result solely from the misspecification of the genetic model for disease or trait inheritance. © 1995 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.     

Multivariate genetic analysis of an oligogenic disease

Joint multivariate segregation and linkage analysis provides a method for simultaneously analyzing data on affection status, correlated phenotypic traits, environmental risk factors, and other covariates. The power of this approach for mapping disease susceptibility loci of small effect (oligogenes) was evaluated by analyzing the GAW9 Problem 2 data set. The program REGRESS, which assumes a pleiotropy model in which one locus influences both affection status (AF) and a quantitative trait, was used to conduct joint segregation and linkage analysis of bivariate phenotypes, each comprising AF and one quantitative trait (Q2,Q3,Q4). A genome-wide search using markers spaced approximately 10 cM apart was conducted and regions on chromosomes 1, 2, and 5 were identified as demonstrating linkage with three respective bivariate phenotypes at the following markers: AF/Q2 - D1G2; AF/Q3 - D2G10; and AF/Q4 - D5G18. The effects of other loci were included in a general model by specifying the quantitative traits they influenced as covariates along with age, sex, and an environmental effect. Use of covariate and quantitative trait data in each analysis resulted in respective χ² values with 1 df of 38.4, 65.4, and 22.0 to reject the no linkage hypothesis at $ {\rm \hat \theta } $ = 0, with respective equivalent lod scores of 8.3, 14.2, and 4.8. Rejection at p < 0.0002 occurred using markers as far away as 20 cM. These loci were not detected when AF alone was analyzed. © 1995 Wiley-Liss, Inc.     

Assessing the Effect of Sampling Strategies on the Power of Linkage Analysis to Identify Pathway‐Specific Loci Underlying a Complex Disease

Using the simulated general population data sets, we first examined the effect of sampling strategies on the power of identifying linkage by selecting samples with (A) two affected sibs in a nuclear family and (B) one affected sib and one sib with an intermediate trait value in the upper quantiles. Second, we evaluated the improvement in power when analyzing correlated traits simultaneously. Under each selection criteria, 100 replicates of 300 nuclear families were sampled and analyzed with two‐point linkage analysis for ten markers (1 cM apart) from each of the candidate regions. Different genes were identified under different sampling strategies. When a gene has a pleitropic effect, it is more powerful to analyze correlated traits simultaneously, either by using a linear combination or the larger value of standardized traits, than to analyze each trait separately. © 2001 Wiley‐Liss, Inc.     

The method of sib-pair linkage analysis in context of case-control design

We used sib-pair linkage analysis as part of an epidemiologic approach to solving Problem 2 of the GAW10 data set of nuclear families. We recoded the quantitative trait Q1 into a dichotomous trait using Q1 ≥ 40 as the cut-point. In a case-control design of sib-pair analysis, the affected siblings of the proband were the case subjects and the unaffected siblings were the control subjects. Case and control subjects were compared with respect to the number of alleles at one or more loci (0,1,2) that were identical-by-descent (IBD) with those of the proband. Odds ratios (Ors) and 95% confidence intervals (95% CI) were then computed with subjects sharing no alleles (share-0) serving as the reference group. Significantly high ORs were taken as indication of linkage between a marker locus and a suspected disease-susceptibility locus. The case-control sib-pair analysis identified marker D5G15 as associated with disease susceptibility (OR of sharing two alleles [share-2] = 7.7 [95% CI 2.5-23.9]). Our results were consistent with the results from Kruglyak and Lander's method of complete multipoint sib-pair analysis for linkage. For the marker (D5G15) identified through sib-pair analysis, we examined the effects of other covariates and evaluated gene-environment interaction using conditional logistic regression. © 1997 Wiley-Liss, Inc.     

A Versatile Omnibus Test for Detecting Mean and Variance Heterogeneity

Recent research has revealed loci that display variance heterogeneity through various means such as biological disruption, linkage disequilibrium (LD), gene‐by‐gene (G × G), or gene‐by‐environment interaction. We propose a versatile likelihood ratio test that allows joint testing for mean and variance heterogeneity (LRT_MV) or either effect alone (LRT_M or LRT_V) in the presence of covariates. Using extensive simulations for our method and others, we found that all parametric tests were sensitive to nonnormality regardless of any trait transformations. Coupling our test with the parametric bootstrap solves this issue. Using simulations and empirical data from a known mean‐only functional variant, we demonstrate how LD can produce variance‐heterogeneity loci (vQTL) in a predictable fashion based on differential allele frequencies, high D′, and relatively low r² values. We propose that a joint test for mean and variance heterogeneity is more powerful than a variance‐only test for detecting vQTL. This takes advantage of loci that also have mean effects without sacrificing much power to detect variance only effects. We discuss using vQTL as an approach to detect G × G interactions and also how vQTL are related to relationship loci, and how both can create prior hypothesis for each other and reveal the relationships between traits and possibly between components of a composite trait.     

The elusive goal of pedigree weights

Non-parametric linkage analysis methods generally involve calculating an allele-sharing statistic for each pedigree in a data set, then standardizing and summing the statistics over pedigrees. Pedigrees of different sizes can be weighted differently in the sum, though it is perhaps most common to weight all standardized pedigree statistics equally. Most other common weighting schemes are based on the number of affected individuals in the pedigree. It is also possible to derive optimal weights, which maximize power to detect linkage under particular trait models. We started by investigating three different analytical and simulation-based methods to calculate power and derive optimal weights. We found that simulation methods produce noticeably more accurate power calculations than the other methods. However, although the different calculation methods give different "optimal" weights, the power at those weights is very similar. That is, the analytical calculation methods are sufficient for finding good weights even though the simulation methods are most appropriate for calculating power. In comparing optimal weights for different trait models, we found that the weights vary quite a bit with the model, such that optimal weights for one model are not necessarily powerful at all for other models. Finally, we studied the power of a number of general weighting schemes, and of some new ones that incorporate information on how closely the affected individuals are related. We were able to find some schemes that performed well in the sense of giving reasonably powerful weights for most of the trait models and pedigree types we considered.     

Impact of Preadjusting a Quantitative Phenotype Prior to Sib‐Pair Linkage Analysis when Gene×Environment Interaction Exists

The investigation of potential gene×environment (G×E) interactions is an important facet in the study of complex diseases. When G×E interaction exists, linkage analyses of the interacting gene must treat the environmental factor appropriately. Specifically, the common approach of regressing out an environmental factor prior to linkage analysis may be inappropriate if that factor has an interaction with the gene. This is explored here in the Genetic Analysis Workshop 12 simulated data set using the G×E interaction between major gene four (MG4) and environmental factor two (E2). The analysis shows that preadjusting the quantitative trait three (Q3) phenotype for the main effects of several environmental variables, including one (E2) that interacts with MG4, affects the results of a Haseman‐Elston linkage analysis. In particular, the agreement in detecting linkage between preadjusting versus not preadjusting was only 78% and 66% using alpha levels of 0.05 and 0.10, respectively. For both approaches, incorporating an interaction term in the regression models enabled linkage to be detected where the evidence was either minimal or not present in an identical‐by‐descent main effects‐only model. Furthermore, preadjustment for E2 did not appear to account for the major discrepancies between the approaches. © 2001 Wiley‐Liss, Inc.     

Sample size required for predefined linkage decision quality

A method for estimating the sample size required to attain a predefined linkage decision quality (type I and type II errors) is proposed using the linkage test power estimate developed by Ginsburg et al. [(1996) Genet Epidemiol 13:355–366]. The method is applicable for samples of arbitrarily structured pedigrees collected via proband. Comparison of different ascertainment schemes and pedigree structures by their consequent minimal sample size was performed. For recessive and dominant inheritance with complete penetrance, the relative ranks of the ascertainment schemes are invariant regardless of the true recombination fraction value and the trait and marker gene frequencies, which enables one to point out the better scheme. The feasibility of evaluating a sampling strategy by the cost of pedigree collection is also considered, and comparison between these two methods of sample planning is performed. Genet. Epidemiol. 14:479–491,1997. © 1997 Wiley-Liss, Inc.     

A brute force dichotomization approach to quantitative trait linkage analysis

The effect of dichotomizing a continuous phenotype in linkage analysis of a simulated oligogenic trait is explored. We conclude that dichotomization does not in itself preclude the detection of loci which account for as little as 16% of the genetic variance of the disease. The effects of inclusion of known covariates and quantitative trait linkage analysis are also discussed. © 1995 Wiley-Liss, Inc.