Genetic analysis of simulated oligogenic traits in nuclear and extended pedigrees: Summary of GAW10 contributions

Participants of GAW10 had available simulated data on phenotypic and marker data for 200 replicates of each of two different collections of pedigrees. The simulated phenotype was multivariate and oligogenic, and included a number of complexities. Participants took widely different approaches to analysis. We compare their results to identify analysis approaches and use of the data that had the greatest impact on the conclusions, accuracy of estimates, and power to identify genetic factors. © 1997 Wiley-Liss, Inc.     

Gibbs sampling-based segregation analysis of asthma-associated quantitative traits in a population-based sample of nuclear families

Asthma is a common, complex human disease. Elevated serum immunoglobulin E (IgE) levels, elevated blood eosinophil counts, and increased airway responsiveness are physiological traits that are characteristic of asthma. Few studies have investigated major gene effects for these traits in a population-based sample. Further, it is not known if any putative major genes may be common to two or more of these traits. We investigated the existence and nature of major genes modulating asthma-associated quantitative traits in an Australian population-based sample of 210 Caucasian nuclear families. The sharing of these major genes was also investigated. Segregation analysis was based upon a Markov Chain Monte Carlo (Gibbs sampling) approach as implemented in the program BUGS v0.6. All models included adjustment for age, height, tobacco smoke exposure, and gender. The segregation of total IgE levels, blood eosinophil counts, and dose-response slope (DRS) of methacholine challenge were all consistent with major loci at which a recessive allele acted to increase or decrease the phenotype. The respective estimated frequencies of the recessive alleles were 68% (total IgE), 10% (blood eosinophil count), and 27% (DRS). Extensive modelling suggested that the major loci controlling total serum IgE levels, blood eosinophil counts, and airway responsiveness represent different genes. These data provide evidence, for the first time, of the existence of at least 3 distinct genetic pathways involving major gene effects on physiological traits closely associated with asthma. These results have implications for gene discovery programs.     

Effect of ignoring genotype-environment interaction on segregation analysis of quantitative traits

Thirty replicates of 200 nuclear families (6 members each) were generated under three GxE interaction models. Segregation analyses of these data were performed using a regressive model taking into account an interaction effect or not. Results showed that ignoring the GxE interaction markedly decreased the power for accepting a major gene and led to serious bias in parameter estimates. © 1993 Wiley-Liss, Inc.     

Numerical comparisons of two formulations of the logistic regressive models with the mixed model in segregation analysis of discrete traits.

Segregation analysis of discrete traits can be conducted by the classical mixed model and the recently introduced regressive models. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affected persons have a liability exceeding a threshold. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype effects, the phenotypes of older relatives, and other covariates. A formulation of the regressive models, based on an underlying liability model, has been recently proposed. The regression coefficients on antecedents are expressed in terms of the relevant familial correlations and a one-to-one correspondence with the parameters of the mixed model can thus be established. Computer simulations are conducted to evaluate the fit of the two formulations of the regressive models to the mixed model on nuclear families. The two forms of the class D regressive model provide a good fit to a generated mixed model, in terms of both hypothesis testing and parameter estimation. The simpler class A regressive model, which assumes that the outcomes of children depend solely on the outcomes of parents, is not robust against a sib-sib correlation exceeding that specified by the model, emphasizing testing class A against class D. The studies reported here show that if the true state of nature is that described by the mixed model, then a regressive model will do just as well. Moreover, the regressive models, allowing for more patterns of family dependence, provide a flexible framework to understand gene-environment interactions in complex diseases.     

Search for faster methods of fitting the regressive models to quantitative traits

The regressive models describe familial patterns of dependence of quantitative measures by specifying regression relationships among a person's phenotype and genotype and the phenotypes and genotypes of antecedents. When the number of sibs in the pattern of dependence increases, as in the class D regressive model, computation of the likelihood becomes time consuming, since the Elston-Stewart algorithm cannot be used generally. On the other hand, the simpler class A regressive model, which imposes a restriction on the sib-sib correlation, may lead to inference of a spurious major gene, as already observed in some instances. A simulation study is performed to explore the robustness of class A model with respect to false inference of a major gene and to search for faster methods of computing the likelihood under class D model. The class A model is not robust against the presence of a sib-sib correlation exceeding that specified by the model, unless tests on transmission probabilities are performed carefully: false detection of a major gene is reduced from a number of 26-30 to between 0 and 4 data sets out of 30 replicates after testing both the Mendelian transmission and the absence of transmission of a major effect against the general transmission model. Among various approximations of the likelihood formulation of the class D model, approximations 6 and 8 are found to work appropriately in terms of both the estimation of all parameters and hypothesis testing, for each generating model. These approximations lessen the computer time by allowing use of the Elston-Stewart algorithm.     

Segregation analysis of breast cancer: A comparison of type-dependent age-at-onset versus type-dependent susceptibility models

Most segregation analyses of breast cancer susceptibility have modeled the effect of the major gene on the age-at-onset distribution. However, in families linked to BRCA1 or BRCA2, there is wide variation in the age-at-onset among gene carriers. We performed a segregation analysis of 544 Minnesota breast cancer families using models which parameterized the putative major gene effect in two ways: earlier age-at-onset, with a common level of susceptibility (model I), and greater susceptibility, with a common mean age-at-onset (model II). Five hypothetical modes of transmission and an unrestricted general hypothesis were fitted to the data. Twice the difference between the log_e likelihood for the data under the specified hypothesis (recessive, no major gene, etc.) and the log_e likelihood under the general hypothesis is distributed asymptotically as a chi-square statistic with the degrees of freedom equal to the difference in the number of parameters estimated. This difference was compared to the critical value for the chi-square distribution to assess goodness-of-fit. Under model I, both Mendelian and non-Mendelian hypotheses were rejected. When model II was used, the non-Mendelian hypotheses were rejected whereas all Mendelian hypotheses were not. Mendelian recessive inheritance of a common allele (q_A = 0.11) with a high penetrance (87%) provided the best fit to the data. We then stratified the families into two subsets based on the age at diagnosis of the proband [≤55 years (n = 265) versus >55 years (n = 279)]; there was no evidence of heterogeneity under either model (I or II). These data suggest that, in some breast cancer families, the effect of the putative susceptibility gene is better represented as increasing overall susceptibility to breast cancer rather than as a shift in the age-at-onset distribution. © 1996 Wiley-Liss, Inc.     

Power and robustness of a score test for linkage analysis of quantitative traits using identity by descent data on sib pairs

Identification of genes involved in complex traits by traditional (lod score) linkage analysis is difficult due to many complicating factors. An unfortunate drawback of non-parametric procedures in general, though, is their low power to detect genetic effects. Recently, Dudoit and Speed [2000] proposed using a (likelihood-based) score test for detecting linkage with IBD data on sib pairs. This method uses the likelihood for theta, the recombination fraction between a trait locus and a marker locus, conditional on the phenotypes of the two sibs to test the null hypothesis of no linkage (theta = (1/2)). Although a genetic model must be specified, the approach offers several advantages. This paper presents results of simulation studies characterizing the power and robustness properties of this score test for linkage, and compares the power of the test to the Haseman-Elston and modified Haseman-Elston tests. The score test is seen to have impressively high power across a broad range of true and assumed models, particularly under multiple ascertainment. Assuming an additive model with a moderate allele frequency, in the range of p = 0.2 to 0.5, along with heritability H = 0.3 and a moderate residual correlation rho = 0.2 resulted in a very good overall performance across a wide range of trait-generating models. Generally, our results indicate that this score test for linkage offers a high degree of protection against wrong assumptions due to its strong robustness when used with the recommended additive model.     

The resolution of genotype x environment interaction in segregation analysis of nuclear families

A model is presented for the effects of one or two loci, a measured index of the environment and genotype x environment (G x E) interaction of risk for a discontinuous trait. Initial properties of the model are explored for the single locus case, with and without the effects of environment and G x E interaction. Seven data sets were simulated, each comprising 500 nuclear families on whom an environmental index has been measured. Maximum-likelihood estimation procedures were used to obtain parameter estimates under seven models for each data set. Likelihood ratio tests were constructed, and in all cases it was possible to identify the "correct" model for the simulated data. The matrices of information realized showed that the parameters could be estimated with acceptable precision and that the effects of genes, environment, and G x E interaction could be resolved in the simulated populations. The effects on conventional segregation analysis of ignoring the environment and G x E are considered.     

Human malaria: Segregation analysis of blood infection levels in a suburban area and a rural area in Burkina Faso

The genetic control of blood infection levels in human malaria remains unclear. Case control studies have not demonstrated a strong association between candidate genes and blood parasite densities as opposed to surveys that have focused on severe malaria. As an alternative approach, we used segregation analyses to determine the genetic control of blood parasitemia. We surveyed 509 residents (53 pedigrees) in a rural area and 389 residents (41 pedigrees) in an urban area during 18 months. Each family was visited 20 times and 28 times in the urban area and in the rural area; the mean number of parasitemia measurements per subject was 12.1 in the town and 14.9 in the village. The intensity of transmission of Plasmodium falciparum was 8-fold higher in the rural area than in the urban area. Using the class D regressive model for both populations, we found that blood parasite densities were correlated between sibs. We obtained strong evidence for a major effect, but we found that the transmission of this major effect was not compatible with a simple Mendelian model, suggesting a more complex mode of inheritance. Moreover, there was a strong interaction between major effect and age, suggesting that the influence of the putative major gene may be more prominent in children than in adults. Further nonparametric linkage studies, such as sib pair analysis, that focus on children would help us better understand the genetic control of blood infection levels. Genet. Epidemiol. 15:435–450,1998. © 1998 Wiley-Liss, Inc.     

Ordered subset analysis in genetic linkage mapping of complex traits

Etiologic heterogeneity is a fundamental feature of complex disease etiology; genetic linkage analysis methods to map genes for complex traits that acknowledge the presence of genetic heterogeneity are likely to have greater power to identify subtle changes in complex biologic systems. We investigate the use of trait-related covariates to examine evidence for linkage in the presence of heterogeneity. Ordered-subset analysis (OSA) identifies subsets of families defined by the level of a trait-related covariate that provide maximal evidence for linkage, without requiring a priori specification of the subset. We propose that examining evidence for linkage in the subset directly may result in a more etiologically homogeneous sample. In turn, the reduced impact of heterogeneity will result in increased overall evidence for linkage to a specific region and a more distinct lod score peak. In addition, identification of a subset defined by a specific trait-related covariate showing increased evidence for linkage may help refine the list of candidate genes in a given region and suggest a useful sample in which to begin searching for trait-associated polymorphisms. This method provides a means to begin to bridge the gap between initial identification of linkage and identification of the disease predisposing variant(s) within a region when mapping genes for complex diseases. We illustrate this method by analyzing data on breast cancer age of onset and chromosome 17q [Hall et al., 1990, Science 250:1684-1689]. We evaluate OSA using simulation studies under a variety of genetic models.     

Equivalence of the mixed and regressive models for genetic analysis. I. Continuous traits

The mixed model of segregation analysis specifies major gene effects and partitions the residual variance into polygenic and environmental components. The model explains familial correlations essentially in terms of genetic causation. The regressive model, on the other hand, is constructed by successively conditioning on ancestral phenotypes and major genes. Familial patterns of dependence are described in terms of correlations without necessarily introducing a particular scheme of causal relationship. These two approaches are compared both theoretically and numerically through computer simulations for the case of continuous traits on nuclear families. The class D regressive model, which is characterized by equal sib-sib correlations, is mathematically and numerically equivalent to the mixed model. The simpler class A regressive model, which is also characterized by equal sib-sib correlations determined in this case by the common parentage, provides good estimates of the mixed model parameters: major gene parameters and residual polygenic heritability, derived from the parent-offspring correlation. However, in the absence of a major gene, the restriction imposed by the class A model on the sibling correlation can affect the conclusions of segregation analysis: False inference of a major gene was observed in two out of ten replicates. Our simulations also indicate that the mixed model allowing for different heritabilities in adults and children leads to correct estimates of the major gene parameters and residual familial correlations (parent-offspring and sib-sib) as specified by the class A model. For all the models studied, major gene effects, when present, are correctly detected and estimated.     

Efficient computation of patterned covariance matrix mixed models in quantitative segregation analysis

The use of patterned covariance matrices in forming pedigree-based mixed models for quantitative traits is discussed. It is suggested that patterned covariance matrix models provide intuitive, theoretically appealing, and flexible genetic modeling devices for pedigree data. It is suggested further that the very great computational burden assumed in the implementation of covariance matrix-dependent mixed models can be overcome through the use of recent architectural breakthroughs in computing machinery. A brief and nontechnical overview of these architectures is offered, as are numerical and timing studies on various aspects of their use in evaluating mixed models. As the kinds of computers discussed in this paper are becoming more prevalent and easier to access and use, it is emphasized that it behooves geneticists to consider their use to combat needless approximation and time constraints necessitated by smaller, scalar computation oriented, machines.     

Mapping quantitative traits in unselected families: algorithms and examples

Linkage analysis has been widely used to identify from family data genetic variants influencing quantitative traits. Common approaches have both strengths and limitations. Likelihood ratio tests typically computed in variance component analysis can accommodate large families but are highly sensitive to departure from normality assumptions. Regression‐based approaches are more robust but their use has primarily been restricted to nuclear families. In this paper, we develop methods for mapping quantitative traits in moderately large pedigrees. Our methods are based on the score statistic, which in contrast to the likelihood ratio statistic can use nonparametric estimators of variability to achieve robustness of the false‐positive rate against departures from the hypothesized phenotypic model. Because the score statistic is easier to calculate than the likelihood ratio statistic, our basic mapping methods utilize relatively simple computer code that performs statistical analysis on output from any program that computes estimates of identity by descent. This simplicity also permits development and evaluation of methods to deal with multivariate and ordinal phenotypes, and with gene‐gene and gene‐environment interaction. We demonstrate our methods on simulated data and on fasting insulin, a quantitative trait measured in the Framingham Heart Study. Genet. Epidemiol. 33:617–627, 2009. © 2009 Wiley‐Liss, Inc.     

Use of the regressive models in linkage analysis of quantitative traits

Use of the regressive models to account for residual familial correlations in linkage analysis of complex quantitative traits can increase the power to detect linkage. This is especially observed when the effect of the gene to be mapped is small or when the residual correlations are substantial. © 1993 Wiley-Liss, Inc.     

Trade-off between false positives and false negatives in the linkage analysis of complex traits

This study examines the issue of false positives in genomic scans for detecting complex trait loci using sibpair linkage methods and investigates the trade-off between the rate of false positives and the rate of false negatives. It highlights the tremendous cost in terms of power brought about by an excessive control of type I error and, at the same time, confirms that a larger number of false positives can occur otherwise in the course of a genomic scan. Finally, it compares the power and rate of false positives obtained in preplanned replicated studies conducted using a liberal significance level to those for single-step studies that use the same total sample size but stricter levels of significance. For the models considered here, replicate studies were found more attractive as long as one is willing to accept a trade-off, exchanging a much lower rate of false negatives for a slight increase in the rate of false positives. Genet. Epidemiol. 14:453–464,1997. © 1997 Wiley-Liss, Inc.     

Determining trait locus position from multipoint analysis: accuracy and power of three different statistics.

Previous work using two-point linkage analysis showed that performing a lod score (LOD) analysis twice, once assuming dominant and once assuming recessive inheritance, and then taking the larger of the two values (designated MMLS) usually has more power to detect linkage than any other method tested. Using computer simulation for a variety of complex inheritance models, we demonstrated power for the MMLS comparable with analysis assuming the true model. However, reports in the literature suggested that the MMLS approach might fail to detect linkage using multipoint analysis due to genetic model misspecification. Here, we tested the robustness of the MMLS approach under multipoint analysis. We simulated data under complex inheritance models, including heterogeneity, epistatic, and additive models. We examined the expected maximum LOD, LOD assuming heterogeneity (HLOD), and nonparametric linkage statistics and the corresponding estimated position in a chromosomal interval of 10 markers with 10% recombination between markers. The mean estimates of position were generally good for all three statistics except when heterogeneity existed, where the LOD and the NPL did not perform as well as the HLOD. The MMLS approach was as robust using multipoint as using two-point linkage analysis. LOD and/or the HLOD generally had more power to detect linkage than NPL across a variety of generating models, even after correcting for the multiple tests. For finding linkage to one locus of several contributing to disease expression, assuming the dominant and recessive models with reduced penetrance is a good approximation of the mode of inheritance at that locus.     

Sib-pair linkage analyses of nuclear family data: Quantitative versus dichotomous disease classification

Model-free sib-pair linkage analysis was used to screen 367 highly polymorphic markers for evidence of linkage to a disease, defined either quantitatively (Q1) or dichotomously (AF). Five individual replicates, plus a case family data set containing all families in these replicates with at least one individual with AF, were analyzed. Sib-pair linkage results for Q1 and AF varied considerably among the five replicates and did not consistently detect any of the three underlying major loci, MG1, MG2, and MG3. For the pooled case families, linkage analyses of Q1, but not AF, detected the flanking markers for MG1 and MG2 at the 0.05 and 0.01 levels, respectively. Overall, type 1 error rates were not elevated. The ability to analyze the disease quantitatively (Q1) and construct a data set more appropriate for linkage analysis (case families) enhanced the power to detect at least some of the major loci underlying the disease. © 1997 Wiley-Liss, Inc.     

Regressive logistic modeling of familial aggregation for asthma in 7,394 population-based nuclear families

The aim of this population-based study was to determine whether asthma aggregates in families, and if so, whether aggregation was consistent with environmental and/or genetic etiologies. Data were from 7,394 nuclear families (41,506 individuals) from the 1968 Tasmanian Asthma Survey, in which all Tasmanian schoolchildren born in 1961 were surveyed by respiratory questionnaire completed by their parents. Similar data were obtained for parents and siblings of probands. For a child, having ever had asthma was predicted by a parent or sibling having ever had asthma; odds ratio (OR) = 3.13 (95% confidence interval [CI] 2.82–3.48) for mother, 2.99 (2.69–3.32) for father, and 3.47 (3.23–3.72) for a sibling. Regressive logistic modeling showed that, in addition to parent-offspring effects, the data were consistent with the existence of an unmeasured factor shared by siblings, evident in 15% (SE 2%) of families and associated with a conditional OR of 9.68 (8.27–11.32). Familial aggregation was best described by a general oligogenic model with non-Mendelian transmission probabilities. Of the Mendelian models, a codominant model with an allele frequency of 16% (SE 0.3%) was preferred. Under a dominant model there was evidence for additional parent-offspring and sibling effects of similar magnitude. It is unlikely that there is one major loci influencing asthma susceptibility; the overall effects of asthma genes in the population are more likely to be inherited codominantly, at least for the majority of loci of major etiological importance. The role of environmental factors in explaining part of familial aggregation for asthma cannot be ruled out, as major triggers of asthma attacks are familial. Genet. Epidemiol. 14:317–332,1997. © 1997 Wiley-Liss, Inc.     

Segregation analysis of dopamine-beta-hydroxylase (DBH) and catechol-o-methyltransferase (COMT): Identification of major locus and polygenic components

Enzymes of catecholamine metabolism, plasma dopamine-beta-hydroxylase (DBH), and erythrocyte catechol-O-methyltransferase (COMT) were each previously shown to be transmitted as single codominant loci in a sample of approximately 30 multigenerational families that were analyzed with the single major locus model. Here, both major locus and polygenic hypotheses are tested by applying the mixed model of analysis to the identical samples, after breaking the families into two-generation units. For plasma DBH, the most parsimonious model is a dominant major locus (ie, high values dominant to low values) accounting for 41% of the variance and a polygenic component accounting for 25% of the variance. For erythrocyte COMT, the most parsimonious model is a dominant major locus accounting for 56% of the variance and a polygenic component accounting for 27% of the variance. The major locus for COMT has been supported by previous biochemical studies. The major locus for DBH is supported by the finding from our previous study of possible linkage to the ABO locus. Further biochemical and molecular genetic investigations are needed to better define the genetic loci determining the activity of these enzymes.