Phenotypic assortative mating in segregation analysis

A model of phenotypic assortative mating was developed for application in segregation analysis. The model assumed a constant spouse correlation across the range of a quantitative trait or the liability to a discrete trait. Four traits were analyzed to evaluate: (1) the feasibility of applying likelihood analysis to pedigree data in order to distinguish between assortative mating and shared environmental effects as the source of spouse correlation; and (2) the impact on segregation analysis of the failure to account for either assortative mating or shared environmental effects, as appropriate. Height ratio (the ratio of sitting to standing height) and eye color comprised the traits for which the observed spouse correlation reflected assortative mating; serum cholesterol and peptic ulcers (with genotypes defined by the ABO blood group) comprised the traits for which the observed spouse correlation reflected shared environmental effects. For all four traits the test statistics agreed with the known cause of spouse correlation; however, significance was not attained for height ratio or serum cholesterol. The ability to distinguish between the causes of spouse correlation in pedigree data presumably depends on trait and sample characteristics which remain to be delineated. Despite significant spouse correlation, its omission from the segregation analysis model did not undermine the inference of major locus inheritance for any of the four traits. However, the lack of an impact for these traits does not preclude an impact for other traits of ignoring the appropriate spouse correlation in segregation analysis. © 1995 Wiley-Liss, Inc.     

A method for identifying genes related to a quantitative trait, incorporating multiple siblings and missing parents

When studying either qualitative or quantitative traits, tests of association in the presence of linkage are necessary for fine-mapping. In a previous report, we suggested a polytomous logistic approach to testing linkage and association between a di-allelic marker and a quantitative trait locus, using genotyped triads, consisting of an individual whose quantitative trait has been measured and his or her two parents. Here we extend that approach to incorporate marker information from entire nuclear families. By computing a weighted score function instead of a maximum likelihood test, we allow for both an unspecified correlation structure between siblings and "informative" family size. Both this approach and our original approach allow for population admixture by conditioning on parental genotypes. The proposed method allows for missing parental genotype data through a multiple imputation procedure. We use simulations based on a population with admixture to compare our method to a popular non-parametric family-based association test (FBAT), testing the null of no association in the presence of linkage.     

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.     

Method for using complete and incomplete trios to identify genes related to a quantitative trait

A number of tests for linkage and association with qualitative traits have been developed, with the most well-known being the transmission/disequilibrium test (TDT). For quantitative traits, varying extensions of the TDT have been suggested. The quantitative trait approach we propose is based on extending the log-linear model for case-parent trio data (Weinberg et al. [1998] Am. J. Hum. Genet. 62:969-978). Like the log-linear approach for qualitative traits, our proposed polytomous logistic approach for quantitative traits allows for population admixture by conditioning on parental genotypes. Compared to other methods, simulations demonstrate good power and robustness of the proposed test under various scenarios of the genotype effect, distribution of the quantitative trait, and population stratification. In addition, missing parental genotype data can be accommodated through an expectation-maximization (EM) algorithm approach. The EM approach allows recovery of most of the lost power due to incomplete trios.     

An application of a model for a genotype-dependent relationship between a concomitant (age) and a quantitative trait (LDL cholesterol) in pedigree data

In most genetic studies in humans the variability in a quantitative trait is adjusted for variability in concomitants (age, sex, etc) using a single regression equation prior to analyses of pedigree data. To illustrate an alternative approach, a single locus genetic model was tested. This model incorporates genotypic effects on the level of the trait, the variability in the trait, and the relationship between a concomitant and the trait. In this study, the model was applied to measures of age and low-density lipoprotein (LDL) cholesterol in a large kindred with familial hypercholesterolemia. The application of this model to 322 individuals in four generations provided evidence that genotypic variation at a single locus influences LDL levels early in life, the rate of increase of LDL with age and the phenotypic variance. A model with genotype-dependent slope and variance fit the data significantly better than a model with slope and variance independent of genotype. The inclusion of age-specific genotypic differences contributed to identification of high-risk individuals, to statistical support for a major locus, and to evidence for genetic determination of the tracking of LDL levels. Models that incorporate genotype-specific concomitant effects have the potential to represent more realistically the relationship between genotypic variability and quantitative phenotypic variation than models that assume that these effects do not exist.     

Multipoint linkage mapping using sibpairs: non-parametric estimation of trait effects with quantitative covariates

Multipoint linkage analysis using sibpair designs remains a common approach to help investigators to narrow chromosomal regions for traits (either qualitative or quantitative) of interest. Despite its popularity, the success of this approach depends heavily on how issues such as genetic heterogeneity, gene-gene, and gene-environment interactions are properly handled. If addressed properly, the likelihood of detecting genetic linkage and of efficiently estimating the location of the trait locus would be enhanced, sometimes drastically. Previously, we have proposed an approach to deal with these issues by modeling the genetic effect of the target trait locus as a function of covariates pertained to the sibpairs. Here the genetic effect is simply the probability that a sibpair shares the same allele at the trait locus from their parents. Such modeling helps to divide the sibpairs into more homogeneous subgroups, which in turn helps to enhance the chance to detect linkage. One limitation of this approach is the need to categorize the covariates so that a small and fixed number of genetic effect parameters are introduced. In this report, we take advantage of the fact that nowadays multiple markers are readily available for genotyping simultaneously. This suggests that one could estimate the dependence of the generic effect on the covariates nonparametrically. We present an iterative procedure to estimate (1) the genetic effect nonparametrically and (2) the location of the trait locus through estimating functions developed by Liang et al. ([2001a] Hum Hered 51:67-76). We apply this new method to the linkage study of schizophrenia to illustrate how the onset ages of each sibpair may help to address the issue of genetic heterogeneity. This analysis sheds new light on the dependence of the trait effect on onset ages from affected sibpairs, an observation not revealed previously. In addition, we have carried out some simulation work, which suggests that this method provides accurate inference for estimating the location of quantitative trait loci.     

Detection of parent-of-origin effects for quantitative traits in complete and incomplete nuclear families with multiple children

For a diallelic genetic marker locus, tests like the parental-asymmetry test (PAT) are simple and powerful for detecting parent-of-origin effects. However, these approaches are applicable only to qualitative traits and thus are currently not suitable for quantitative traits. In this paper, the authors propose a novel class of PAT-type parent-of-origin effects tests for quantitative traits in families with both parents and an arbitrary number of children, which is denoted by Q-PAT(c) for some constant c. The authors further develop Q-1-PAT(c) for detection of parent-of-origin effects when information is available on only 1 parent in each family. The authors suggest the Q-C-PAT(c) test for combining families with data on both parental genotypes and families with data on only 1 parental genotype. Simulation studies show that the proposed tests control the empirical type I error rates well under the null hypothesis of no parent-of-origin effects. Power comparison also demonstrates that the proposed methods are more powerful than the existing likelihood ratio test. Although normality is commonly assumed in methods for studying quantitative traits, the tests proposed in this paper do not make any assumption about the distribution of the quantitative trait.     

Ascertainment correction for Markov chain Monte Carlo segregation and linkage analysis of a quantitative trait

Although extended pedigrees are often sampled through probands with extreme levels of a quantitative trait, Markov chain Monte Carlo (MCMC) methods for segregation and linkage analysis have not been able to perform ascertainment corrections. Further, the extent to which ascertainment of pedigrees leads to biases in the estimation of segregation and linkage parameters has not been previously studied for MCMC procedures. In this paper, we studied these issues with a Bayesian MCMC approach for joint segregation and linkage analysis, as implemented in the package Loki. We first simulated pedigrees ascertained through individuals with extreme values of a quantitative trait in spirit of the sequential sampling theory of Cannings and Thompson [Cannings and Thompson [1977] Clin. Genet. 12:208-212]. Using our simulated data, we detected no bias in estimates of the trait locus location. However, in addition to allele frequencies, when the ascertainment threshold was higher than or close to the true value of the highest genotypic mean, bias was also found in the estimation of this parameter. When there were multiple trait loci, this bias destroyed the additivity of the effects of the trait loci, and caused biases in the estimation all genotypic means when a purely additive model was used for analyzing the data. To account for pedigree ascertainment with sequential sampling, we developed a Bayesian ascertainment approach and implemented Metropolis-Hastings updates in the MCMC samplers used in Loki. Ascertainment correction greatly reduced biases in parameter estimates. Our method is designed for multiple, but a fixed number of trait loci.     

Segregation analysis of two-locus models regulating apolipoprotein-A1 levels

For quantitative traits associated with risk to complex diseases, such as heart disease, single major locus models are likely to be too simplistic. Currently, researchers have begun to use oligogenic models of inheritance, but the resolving power of these models remains to be determined. As the major apoprotein of high density lipoprotein (HDL), apolipoprotein A1 (apo-A1) is generally accepted as a protective factor for coronary artery disease. Although familial aggregation of apo-A1 levels has been reported, the mode of inheritance of apo-A1 remains ill defined. In the present study, we conducted a segregation analysis comparing a series of one-locus and two-locus univariate models for apo-A1 levels in a sample of 137 families ascertained through probands undergoing elective, diagnostic coronary angiography. A two-locus Mendelian model fit these data significantly better than any one-locus model. The incorporation of the second major locus into the model of inheritance leads to a significant improvement in the fit, and a significant decrease of the residual heritability. The best-fitting model included two loci with a reciprocal pattern of epistasis generating 4 distinct genotypic distributions. Taken together, these two major loci account for 58% of the variance of adjusted apo-A1 levels. This demonstration of a second major locus controlling apo-A1 levels may explain the equivocal results obtained from previous studies. This two-locus model may be more powerful for linkage analysis to map one or both of these quantitative trait loci. Genet. Epidemiol. 15:73–86,1998. © 1998 Wiley-Liss, Inc.     

Segregation and linkage analysis of the complex trait Q1

Segregation and linkage analysis of GAW9 Problem 2 quantitative trait 1 (Q1) was performed. Eight segregation models comprising all possible combinations of the environmental factor (EF), quantitative trait 2 (Q2), and quantitative trait 3 (Q3) as covariates were considered. Seven of the eight segregation models showed strong evidence for a major gene, the other model was marginal. When all genotypes are known, some evidence for linkage (lod > 2) was found to all three of the markers that affect Q1. Furthermore, four of the eight models each showed some linkage (lod > 2) to two of the three markers that affect Q1 with no false positives. Each of these segregation analysis major genes is a hybrid combination of the true multiple loci that affect Q1. © 1995 Wiley-Liss, Inc.     

Bivariate combined linkage and association mapping of quantitative trait loci

In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models.     

Improving power and robustness for detecting genetic association with extreme-value sampling design

Extreme-value sampling design that samples subjects with extremely large or small quantitative trait values is commonly used in genetic association studies. Samples in such designs are often treated as "cases" and "controls" and analyzed using logistic regression. Such a case-control analysis ignores the potential dose-response relationship between the quantitative trait and the underlying trait locus and thus may lead to loss of power in detecting genetic association. An alternative approach to analyzing such data is to model the dose-response relationship by a linear regression model. However, parameter estimation from this model can be biased, which may lead to inflated type I errors. We propose a robust and efficient approach that takes into consideration of both the biased sampling design and the potential dose-response relationship. Extensive simulations demonstrate that the proposed method is more powerful than the traditional logistic regression analysis and is more robust than the linear regression analysis. We applied our method to the analysis of a candidate gene association study on high-density lipoprotein cholesterol (HDL-C) which includes study subjects with extremely high or low HDL-C levels. Using our method, we identified several SNPs showing a stronger evidence of association with HDL-C than the traditional case-control logistic regression analysis. Our results suggest that it is important to appropriately model the quantitative traits and to adjust for the biased sampling when dose-response relationship exists in extreme-value sampling designs.     

How useful is the fine‐scale mapping of complex trait linkage peaks? Evaluating the impact of additional microsatellite genotyping on the posterior probability of linkage

The two-stage linkage mapping protocol for complex traits (a primary genome scan with low marker density followed by the high-density genotyping around linkage peaks) is a near-universal practice. The behavior (an increase or a decrease) of the peak upon such fine mapping frequently leads to inferences regarding the veracity of the primary scan finding, namely a true, or a false, positive. We examined by simulation, under the null hypothesis of no linkage and the alternative hypothesis of true linkage, the inferences that can be made regarding the posterior probability of linkage given either a peak increase, or alternatively, a peak decrease, following fine mapping. We considered different models of missing genotype data, fine-mapping LOD score thresholds, and prior probabilities of linkage. Our simulations show that evidence for linkage can increase frequently upon fine mapping under both null and alternative hypotheses, although large increases in LOD scores are more common under the alternative hypothesis. Increased LOD scores accompany an increased posterior probability of linkage, and large LOD score changes and the presence of dominance at the trait locus accentuate this effect. We demonstrate that the greatest changes in the posterior probability of linkage occur when the genotyping data are least complete (and especially when parental genotypes are missing), and the LOD score threshold for fine mapping is relaxed.     

On a semiparametric test to detect associations between quantitative traits and candidate genes using unrelated individuals

Although genetic association studies using unrelated individuals may be subject to bias caused by population stratification, alternative methods that are robust to population stratification such as family-based association designs may be less powerful. Recently, various statistical methods robust to population stratification were proposed for association studies, using unrelated individuals to identify associations between candidate markers and traits of interest (both qualitative and quantitative). Here, we propose a semiparametric test for association (SPTA). SPTA controls for population stratification through a set of genomic markers by first deriving a genetic background variable for each sampled individual through his/her genotypes at a series of independent markers, and then modeling the relationship between trait values, genotypic scores at the candidate marker, and genetic background variables through a semiparametric model. We assume that the exact form of relationship between the trait value and the genetic background variable is unknown and estimated through smoothing techniques. We evaluate the performance of SPTA through simulations both with discrete subpopulation models and with continuous admixture population models. The simulation results suggest that our procedure has a correct type I error rate in the presence of population stratification and is more powerful than statistical association tests for family-based association designs in all the cases considered. Moreover, SPTA is more powerful than the Quantitative Similarity-Based Association Test (QSAT) developed by us under continuous admixture populations, and the number of independent markers needed by SPTA to control for population stratification is substantially fewer than that required by QSAT.     

Linkage Analysis of Quantitative Traits in Randomly Ascertained Pedigrees: Comparison of Penetrance‐Based and Variance Component Analysis

Penetrance‐based linkage analysis and variance component linkage analysis are two methods that are widely used to localize genes influencing quantitative traits. Using computer programs PAP and SOLAR as representative software implementations, we have conducted an empirical comparison of both methods' power to map quantitative trait loci in extended, randomly ascertained pedigrees, using simulated data. Two‐point linkage analyses were conducted on several quantitative traits of different genetic and environmental etiology using both programs, and the lod scores were compared. The two methods appear to have similar power when the underlying quantitative trait locus is diallelic, with one or the other method being slightly more powerful depending on the characteristics of the quantitative trait and the quantitative trait locus. In the case of a multiallelic quantitative trait locus, however, the variance component approach has much greater power. These findings suggest that one should give careful thought to the likely allelic architecture of the quantitative trait to be analyzed when choosing between these two analytical approaches. It may be the case in general that linkage methods which explicitly or implicitly rely on the assumption of a diallelic trait locus fare poorly when this assumption is incorrect. © 2001 Wiley‐Liss, Inc.     

The impact of marker allele frequency misspecification in variance components quantitative trait locus analysis using sibship data

In cases where sibship data are collected for a quantitative trait locus (QTL) linkage study without access to parental genotypes, the proportion of genes shared identical by descent must be estimated using the marker allele frequencies. No systematic study has been conducted to date to evaluate the effect of misspecification of these frequencies on a test of quantitative trait linkage. Analysis of both simulated and actual data on quantitative traits was carried out under various sets of allele frequency estimates. While correctly specifying the allele frequency distribution led to a slightly more powerful test and higher lod scores, the differences were small and would not likely alter the conclusion of a study. These results suggest that, at least for QTL analysis, there is a great deal of tolerance for misspecifying marker allele frequencies with little, if any, appreciable effect on the linkage test. However, the observed variations may be sufficiently large to alter the priority on might give to a positive finding for follow up.     

Detecting epistatic interactions contributing to quantitative traits

The restricted partition method (RPM) is a partitioning algorithm for examining multi-locus genotypes as (potentially non-additive) predictors of a quantitative trait. The motivating application was to develop a robust method to examine quantitative phenotypes for epistasis (gene-gene interactions), but the method can be applied without modification to gene-environment interactions. Simulation results indicate that the method provides an efficient way to identify loci contributing epistatically to a quantitative trait, even if the loci have no single locus effects. Statistical significance can be estimated through permutation testing. An example using real data involving the metabolism of a chemotherapy drug is included for illustration. Although the examples in this article involve 2-locus interactions, the RPM is computationally feasible for the analysis of more than two loci or factors.     

A flexible copula-based approach for the analysis of secondary phenotypes in ascertained samples

Data collected for a genome-wide association study of a primary phenotype are often used for additional genome-wide association analyses of secondary phenotypes. However, when the primary and secondary traits are dependent, naïve analyses of secondary phenotypes may induce spurious associations in non-randomly ascertained samples. Previously, retrospective likelihood-based methods have been proposed to correct for sampling biases arising in secondary trait association analyses. However, most methods have been introduced to handle studies featuring a case-control design based on a binary primary phenotype. As such, these methods are not directly applicable to more complicated study designs such as multiple-trait studies, where the sampling mechanism also depends on the secondary phenotype, or extreme-trait studies, where individuals with extreme primary phenotype values are selected. To accommodate these more complicated sampling mechanisms, only a few prospective likelihood approaches have been proposed. These approaches assume a normal distribution for the secondary phenotype (or the latent secondary phenotype) and a bivariate normal distribution for the primary-secondary phenotype dependence. In this paper, we propose a unified copula-based approach to appropriately detect genetic variant/secondary phenotype association in the presence of selected samples. Primary phenotype is either binary or continuous and the secondary phenotype is continuous although not necessary normal. We use both prospective and retrospective likelihoods to account for the sampling mechanism and use a copula model to allow for potentially different dependence structures between the primary and secondary phenotypes. We demonstrate the effectiveness of our approach through simulation studies and by analyzing data from the Avon Longitudinal Study of Parents and Children cohort.     

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.     

Bias correction to secondary trait analysis with case–control design

In genetic association studies with densely typed genetic markers, it is often of substantial interest to examine not only the primary phenotype but also the secondary traits for their association with the genetic markers. For more efficient sample ascertainment of the primary phenotype, a case–control design or its variants, such as the extreme‐value sampling design for a quantitative trait, are often adopted. The secondary trait analysis without correcting for the sample ascertainment may yield a biased association estimator. We propose a new method aiming at correcting the potential bias due to the inadequate adjustment of the sample ascertainment. The method yields explicit correction formulas that can be used to both screen the genetic markers and rapidly evaluate the sensitivity of the results to the assumed baseline case‐prevalence rate in the population. Simulation studies demonstrate good performance of the proposed approach in comparison with the more computationally intensive approaches, such as the compensator approaches and the maximum prospective likelihood approach. We illustrate the application of the approach by analysis of the genetic association of prostate specific antigen in a case–control study of prostate cancer in the African American population. Copyright © 2012 John Wiley & Sons, Ltd.