Variance components/major locus likelihood approximation for quantitative, polychotomous, and multivariate data

Genz and Mendell-Elston Estimation of the High-Dimensional Multivariate Normal Distribution

Statistical analysis of multinomial data in complex datasets often requires estimation of the multivariate normal (mvn) distribution for models in which the dimensionality can easily reach 10–1000 and higher. Few algorithms for estimating the mvn distribution can offer robust and efficient performance over such a range of dimensions. We report a simulation-based comparison of two algorithms for the mvn that are widely used in statistical genetic applications. The venerable Mendell-Elston approximation is fast but execution time increases rapidly with the number of dimensions, estimates are generally biased, and an error bound is lacking. The correlation between variables significantly affects absolute error but not overall execution time. The Monte Carlo-based approach described by Genz returns unbiased and error-bounded estimates, but execution time is more sensitive to the correlation between variables. For ultra-high-dimensional problems, however, the Genz algorithm exhibits better scale characteristics and greater time-weighted efficiency of estimation.

The inheritance of extra-hepatic portosystemic shunts and elevated bile acid concentrations in Maltese dogs

OBJECTIVES

To determine the heritability of extra-hepatic portosystemic shunts and elevated post-prandial serum bile acid concentrations in Maltese dogs.

MATERIALS AND METHODS

Maltese dogs were recruited and investigated by a variable combination of procedures including dynamic bile acid testing, rectal ammonia tolerance testing, ultrasonography, portal venography, surgical inspection or necropsy. In addition, nine test matings were carried out between affected and affected dogs, and affected and unaffected dogs.

RESULTS

In 135 variably related Maltese, shunt status could be confirmed in 113, including 19 with an extra-hepatic portosystemic shunt (17 confirmed at surgery, 2 at necropsy). Rectal ammonia tolerance testing results and post-prandial serum bile acid concentrations were retrievable for 50 and 88 dogs, respectively. Pedigree information was available for these 135 and an additional 164 related dogs. Two consecutive test matings were carried out between two affected animals (whose shunts had been attenuated), with 2 of 8 (25%) of offspring having an extra-hepatic portosystemic shunt. Six test matings were carried out between an affected and an unaffected animal, with 2 of 22 (9%) offspring affected. Heritability of extra-hepatic portosystemic shunt was 0·61 calculated using variance components analysis [95% confidence interval (CI) 0·14 to 1·0, P=0·001]. The best fitting model from segregation analysis was a common, partially penetrant, recessive model (allele frequency 0·34, penetrance 0·99, CI 0·09 to 1·0). The heritability of elevated post-prandial serum bile acid (and thus likely portal vein hypoplasia) was 0·81 (CI 0·43 to 1·0, P=0·2) after logarithmic transformation of post-prandial serum bile acid concentrations.

CLINICAL SIGNIFICANCE

There is strong support for extra-hepatic portosystemic shunts and elevated post-prandial serum bile acid concentrations both being inherited conditions in Maltese.

Family-based designs for genome-wide association studies

Association mapping has successfully identified common SNPs associated with many diseases. However, the inability of this class of variation to account for most of the supposed heritability has led to a renewed interest in methods - primarily linkage analysis - to detect rare variants. Family designs allow for control of population stratification, investigations of questions such as parent-of-origin effects and other applications that are imperfectly or not readily addressed in case-control association studies. This article guides readers through the interface between linkage and association analysis, reviews the new methodologies and provides useful guidelines for applications. Just as effective SNP-genotyping tools helped to realize the potential of association studies, next-generation sequencing tools will benefit genetic studies by improving the power of family-based approaches.

A Variance-Component Framework for Pedigree Analysis of Continuous and Categorical Outcomes

Variance-component methods are popular and flexible analytic tools for elucidating the genetic mechanisms of complex quantitative traits from pedigree data. However, variance-component methods typically assume that the trait of interest follows a multivariate normal distribution within a pedigree. Studies have shown that violation of this normality assumption can lead to biased parameter estimates and inflations in type-I error. This limits the application of variance-component methods to more general trait outcomes, whether continuous or categorical in nature. In this paper, we develop and apply a general variance-component framework for pedigree analysis of continuous and categorical outcomes. We develop appropriate models using generalized-linear mixed model theory and fit such models using approximate maximum-likelihood procedures. Using our proposed method, we demonstrate that one can perform variance-component pedigree analysis on outcomes that follow any exponential-family distribution. Additionally, we also show how one can modify the method to perform pedigree analysis of ordinal outcomes. We also discuss extensions of our variance-component framework to accommodate pedigrees ascertained based on trait outcome. We demonstrate the feasibility of our method using both simulated data and data from a genetic study of ovarian insufficiency.

Major gene effect and additive familial pattern of inheritance of asthma exist among families of probands with sickle cell anemia and asthma

In the United States, sickle cell anemia (SCA) affects approximately 1 in 400 African-American newborns. Acute episodes of pain and acute chest syndrome (ACS) are the two leading causes of hospitalization. A relationship between the diagnosis of asthma and the incidence of pain and ACS has been established. We tested the hypothesis that a familial pattern of inheritance of asthma exists among first degree relatives of probands with SCA and asthma. Segregation analysis was performed in 104 families ascertained through affected probands. Of these, 19.7% (41/208) of the parents and 31.8% (28/88) of siblings of affected probands reported having been told by a doctor he or she had asthma at any age. Modes of inheritance were tested, using the Pedigree Analysis Package parameterized for the discrete trait of asthma affection status. A major effect was present and significant. Further tests were performed to determine whether transmission probabilities of the major effect followed Mendelian expectations. The additive mode of inheritance was the most parsimonious, while the residual heritability was found negligible. Our results support the hypothesis that a familial pattern of inheritance of asthma exists among first degree relatives of probands with SCA and asthma, suggesting that asthma is a co-morbid condition with SCA rather than a lung disease phenotype mimicking asthma.

Model averaging in linkage analysis

Methods for genetic linkage analysis are traditionally divided into "model-dependent" and "model-independent," but there may be a useful place for an intermediate class, in which a broad range of possible models is considered as a parametric family. It is possible to average over model space with an empirical Bayes prior that weights models according to their goodness of fit to epidemiologic data, such as the frequency of the disease in the population and in first-degree relatives (and correlations with other traits in the pleiotropic case). For averaging over high-dimensional spaces, Markov chain Monte Carlo (MCMC) has great appeal, but it has a near-fatal flaw: it is not possible, in most cases, to provide rigorous sufficient conditions to permit the user safely to conclude that the chain has converged. A way of overcoming the convergence problem, if not of solving it, rests on a simple application of the principle of detailed balance. If the starting point of the chain has the equilibrium distribution, so will every subsequent point. The first point is chosen according to the target distribution by rejection sampling, and subsequent points by an MCMC process that has the target distribution as its equilibrium distribution. Model averaging with an empirical Bayes prior requires rapid estimation of likelihoods at many points in parameter space. Symbolic polynomials are constructed before the random walk over parameter space begins, to make the actual likelihood computations at each step of the random walk very fast. Power analysis in an illustrative case is described. (c) 2006 Wiley-Liss, Inc.

A rare variant of the leptin gene has large effects on blood pressure and carotid intima-medial thickness: a study of 1428 individuals in 248 families

BACKGROUND

Rare mutations in the leptin (LEP) gene cause severe obesity. Common polymorphisms of LEP have been associated with obesity, but their association with cardiovascular disease has been little studied. We have examined the impact of both common and rare polymorphisms of the LEP gene on blood pressure (BP), subclinical atherosclerosis as measured by carotid intima-medial thickness (CIMT), and body mass index (BMI) in a large family study.

METHODS

Five polymorphisms spanning LEP were typed in 1428 individuals from 248 nuclear families. BP, CIMT, BMI, and plasma leptin were measured.

RESULTS

The polymorphisms typed captured all common haplotypes present at LEP. There was strong association between a rare polymorphism in the 3' untranslated region of LEP (C538T) and both pulse pressure (p = 0.0001) and CIMT (p = 0.008). C/T heterozygotes had a 22% lower pulse pressure and a 17% lower CIMT than C/C homozygotes. The polymorphism accounted for 3-5% of the population variation in pulse pressure and CIMT. There was no association between any LEP polymorphism and either BMI or plasma leptin level.

CONCLUSIONS

This large family study shows that the rare T allele at the C538T polymorphism of LEP substantially influences pulse pressure and CIMT, but does not appear to exert this effect through actions on plasma leptin level or BMI. This suggests that autocrine or paracrine effects in vascular tissue may be important physiological functions of leptin. This study also provides evidence that rare polymorphisms of particular genes may have substantial effects within the normal range of certain quantitative traits.

Adjusting for treatment effects in studies of quantitative traits: antihypertensive therapy and systolic blood pressure

A population-based study of a quantitative trait may be seriously compromised when the trait is subject to the effects of a treatment. For example, in a typical study of quantitative blood pressure (BP) 15 per cent or more of middle-aged subjects may take antihypertensive treatment. Without appropriate correction, this can lead to substantial shrinkage in the estimated effect of aetiological determinants of scientific interest and a marked reduction in statistical power. Correction relies upon imputation, in treated subjects, of the underlying BP from the observed BP having invoked one or more assumptions about the bioclinical setting. There is a range of different assumptions that may be made, and a number of different analytical models that may be used. In this paper, we motivate an approach based on a censored normal regression model and compare it with a range of other methods that are currently used or advocated. We compare these methods in simulated data sets and assess the estimation bias and the loss of power that ensue when treatment effects are not appropriately addressed. We also apply the same methods to real data and demonstrate a pattern of behaviour that is consistent with that in the simulation studies. Although all approaches to analysis are necessarily approximations, we conclude that two of the adjustment methods appear to perform well across a range of realistic settings. These are: (1) the addition of a sensible constant to the observed BP in treated subjects; and (2) the censored normal regression model. A third, non-parametric, method based on averaging ordered residuals may also be advocated in some settings. On the other hand, three approaches that are used relatively commonly are fundamentally flawed and should not be used at all. These are: (i) ignoring the problem altogether and analysing observed BP in treated subjects as if it was underlying BP; (ii) fitting a conventional regression model with treatment as a binary covariate; and (iii) excluding treated subjects from the analysis. Given that the more effective methods are straightforward to implement, there is no argument for undertaking a flawed analysis that wastes power and results in excessive bias.

Inheritance pattern of Beckwith-Wiedemann syndrome is heterogeneous in 291 families with an affected proband

Beckwith-Wiedemann syndrome (BWS) is congenital disorder whose molecular etiology is related to genetic and epigenetic mutations on 11p15. The majority of cases of BWS are sporadic, but a substantial proportion are familial, with an unknown inheritance pattern, although autosomal dominant and sex-dependent inheritance have been proposed. We tested the hypothesis that in familial BWS, autosomal dominant inheritance is the primary mode of transmission underlying familial instances. Segregation analysis was performed in 291 families ascertained with an affected child. Individuals were considered to have BWS if they had two of five major features: macroglossia, macrosomia, hypoglycemia at birth, abdominal wall defect, and ear pits or creases. Models of inheritance were tested using pedigree analysis package (PAP) parameterized for a discrete trait. A total of 291 families of an affected proband were included in the study. The analysis was based on a revised general model that included a boundary solution. Sporadic and environmental models were rejected. Overall, the results suggested Mendelian inheritance but under recessive or additive mode of inheritance, which fit the data equally well rather than dominant inheritance. However, the presence of families in the cohort consistent with dominant and sex-dependent inheritance suggest familial BWS may be a heterogeneous group comprised of different inheritance patterns. Familial BWS does not appear to be consistent with autosomal dominant transmission, and is likely a complex mixture of different inheritance patterns.

A quantitative trait locus influences coordinated variation in measures of ApoB-containing lipoproteins

Lipoprotein phenotypes are known to be strongly intercorrelated. These intercorrelations are due to genetic and environmental effects on common metabolic pathways. The purpose of this study was to determine if we could localize genes that exert pleiotropic effects on multiple related lipoprotein traits in humans. Using data from the San Antonio Family Heart Study, we extracted principal components from a set of 12 intercorrelated lipoprotein traits that included phenotypes reflecting lipid and protein concentrations and size distributions for LDLs and HDLs. Five principal components were extracted from the data and all were significantly heritable (h(2) = 0.41-0.57). When subjected to linkage analyses, only one, Component 5, returned a LOD score > or = 3 (LOD score was 3.0 at 38cM on chromosome 15; genome-wide P-value = 0.039). LDL median diameter (-0.529), non-HDLC (-0.422), and ApoB (-0.403) concentrations were the only traits with loadings (absolute value) >0.4, suggesting Component 5 is related to LDL size or perhaps more generally to beta-lipoprotein metabolism. Surprisingly, none of the 12 original lipoprotein traits had a LOD >1 in this region of chromosome 15. These data provide evidence for a novel gene, influencing beta-lipoprotein phenotypes, whose effect(s) is detected only when several lipoprotein traits are considered together.

Model-fitting and linkage analysis of sodium–lithium countertransport

Increased sodium-lithium countertransport activity (SLC) associates with hypertension and is highly heritable, yet the underlying genes remain unknown. SLC, measured on 1113 and remeasured 2-3 years later on 675 adult members of 48 Utah pedigrees, was tested for candidate gene association, major locus inheritance, and linkage to genome scan markers using a bivariate model with genotype-specific effects of age, body mass index (BMI), and triglycerides level (TG). No effect of the alpha-adducin Gly460Trp polymorphism on SLC was found. In contrast, SLC increased with age in carriers of apolipoproteinE varepsilon2 (85 individuals; 8.7% of the sample) and decreased in noncarriers. Model-fitting analyses inferred two additional loci with genotype-specific responses to BMI and TG. Using the inferred model, lod scores >2 were obtained for D3S3038, D11S4464, and D10S677 for the BMI-responsive locus, and for D8S1048 for the TG-responsive locus.

Segregation analysis comparing liability and quantitative trait models for hypertension using the Genetic Analysis Workshop 13 simulated data

Discrete (qualitative) data segregation analysis may be performed assuming the liability model, which involves an underlying normally distributed quantitative phenotype. The appropriateness of the liability model for complex traits is unclear. The Genetic Analysis Workshop 13 simulated data provides measures on systolic blood pressure, a highly complex trait, which may be dichotomized into a discrete trait (hypertension). We perform segregation analysis under the liability model of hypertensive status as a qualitative trait and compare this with results using systolic blood pressure as a quantitative trait (without prior knowledge at that stage of the true underlying simulation model) using 1050 pedigrees ascertained from four replicates on the basis of at least one affected member. Both analyses identify models with major genes and polygenic components to explain the family aggregation of systolic blood pressure. Neither of the methods estimates the true parameters well (as the true model is considerably more complicated than those considered for the analysis), but both identified the most complicated model evaluated as the preferred model. Segregation analysis of complex diseases using relatively simple models is unlikely to provide accurate parameter estimates but is able to indicate major gene and/or polygenic components in familial aggregation of complex diseases.

Site and gender specificity of inheritance of bone mineral density

Differences in genetic control of BMD by skeletal sites and genders were examined by complex segregation analysis in 816 members of 147 families with probands with extreme low BMD. Spine BMD correlated more strongly in male-male comparisons and hip BMD in female-female comparisons, consistent with gender- and site-specificity of BMD heritability.

INTRODUCTION

Evidence from studies in animals and humans suggests that the genetic control of bone mineral density (BMD) may differ at different skeletal sites and between genders. This question has important implications for the design and interpretation of genetic studies of osteoporosis.

METHODS

We examined the genetic profile of 147 families with 816 individuals recruited through probands with extreme low BMD (T-score < -2.5, Z-score < -2.0). Complex segregation analysis was performed using the Pedigree Analysis Package. BMD was measured by DXA at both lumbar spine (L1-L4) and femoral neck.

RESULTS

Complex segregation analysis excluded purely monogenic and environmental models of segregation of lumbar spine and femoral neck BMD in these families. Pure polygenic models were excluded at the lumbar spine when menopausal status was considered as a covariate, but not at the femoral neck. Mendelian models with a residual polygenic component were not excluded. These models were consistent with the presence of a rare Mendelian genotype of prevalence 3-19%, causing high BMD at the hip and spine in these families, with additional polygenic effects. Total heritability range at the lumbar spine was 61-67% and at the femoral neck was 44-67%. Significant differences in correlation of femoral neck and lumbar spine BMD were observed between male and female relative pairs, with male-male comparisons exhibiting stronger lumbar spine BMD correlation than femoral neck, and female-female comparisons having greater femoral neck BMD correlation than lumbar spine. These findings remained true for parent-offspring correlations when menopausal status was taken into account. The recurrence risk ratio for siblings of probands of a Z-score < -2.0 was 5.4 at the lumbar spine and 5.9 at the femoral neck.

CONCLUSIONS

These findings support gender- and site-specificity of the inheritance of BMD. These results should be considered in the design and interpretation of genetic studies of osteoporosis.

Localization of genes that control LDL size fractions in baboons

LDL phenotypes are strongly associated with risk of cardiovascular disease and are heritable, although little is known about individual genes that influence them. We investigated genetic control of LDL size-related phenotypes in 634 pedigreed baboons fed three diets contrasting in levels of fat and cholesterol. On a high-cholesterol high-fat diet, we obtained significant evidence for a quantitative trait locus (QTL) for cholesterol concentrations of lipoproteins between 27 and 28 nm (LOD=4.22, genomic P=0.0047) on the baboon homologue of human chromosome 22. For baboons fed a low-cholesterol high-fat diet, we obtained suggestive evidence for a QTL for cholesterol concentrations between 26 and 27 nm (LOD=2.67) on the baboon homologue of human chromosome 5. We speculate that this QTL influences LDL size distributions because LDL median diameters and other LDL fractions also showed peak LOD scores in this same chromosomal region. On a low-cholesterol low-fat basal diet we obtained suggestive evidence for a QTL for cholesterol concentrations of lipoproteins between 26 and 27 nm in diameter (LOD=2.15) on the baboon homologue of human chromosome 16. Thus, we have evidence for three putative QTLs that influence variation in baboon LDL size phenotypes on different diets.

Two loci affect angiotensin I-converting enzyme activity in baboons

Serum LDL cholesterol (LDLC) concentrations and ACE activities are risk factors for the development of cardiovascular disease (CVD). However, the relationship between ACE and CVD susceptibility, and possible mechanisms of action, is controversial. With data on 622 pedigreed baboons, we used statistical genetic methods to determine the mode of inheritance of ACE activities and its relationship to LDLC on different diets. ACE activity was moderately heritable, and quantitative trait linkage analyses detected a quantitative trait locus (QTL) for ACE activity on the baboon homolog of human chromosome 17 (near the ACE structural locus, maximum multipoint lod=7.5, genomic P=0.000003). Bivariate analyses revealed that ACE activity was genetically correlated (rhoG) with LDLC response (LDLCRC) to a high-cholesterol diet (rhoG=0.30+/-0.13, P=0.01) but not to LDLC on a basal diet (rhoG=0.08+/-0.13). Bivariate genetic analyses indicated that a previously detected QTL for LDLCRC had significant (P=0.025) pleiotropic effects on ACE activity levels and accounted for the genetic correlation. Therefore, we have detected 2 putative loci that affect ACE activity in baboons, one of which also affects LDLC dietary response. The existence of at least 2 genes that affect ACE activity, one of which is diet-responsive, may help explain the lack of consistency among studies of the relationship between ACE and CVD.

Locus controlling LDL cholesterol response to dietary cholesterol is on baboon homologue of human chromosome 6

OBJECTIVE

Cholesterolemic responses to dietary lipids are known to be heritable, but the genes that may affect this response have yet to be identified. Using segregation analysis, we previously detected a potential quantitative trait locus (QTL) in baboons that influenced low density lipoprotein cholesterol response to dietary cholesterol. We performed linkage analyses to locate this QTL by using data on the baboon genetic linkage map.

METHODS AND RESULTS

We obtained evidence for linkage of this potential QTL to the same locus (D6S311) on the baboon homologue of human chromosome 6 by using variance components and parametric linkage analysis methods (2-point lod scores 4.17 [genomic probability value 0.008] and 2.81 [genomic P=0.10], respectively). Linkage analyses of serum levels of apolipoprotein B dietary response, a correlated trait, also gave weak suggestive evidence of linkage to this chromosomal region (maximum 2-point lod score 1.91). Although the LPA locus is nearby, we found no evidence of linkage with LPA.

CONCLUSIONS

This report is the first to localize, in any primate species, a potential QTL that influences low density lipoprotein cholesterol response to dietary cholesterol.

Complex segregation analysis of restless legs syndrome provides evidence for an autosomal dominant mode of inheritance in early age at onset families

A strong familial component of restless legs syndrome (RLS) is known. The objective of this study therefore was to investigate the likely mode of inheritance of RLS. RLS patients and their first-degree relatives were investigated and classified in RLS affected and RLS nonaffected subjects. Assessments were based on direct, personal standardized diagnostic interviews. Complex segregation analysis was performed with the families stratified according to the mean age at onset of the disease within the families. Two hundred thirty-eight RLS patients, 537 first-degree relatives, and 133 spouses were interviewed. Two groups of families were stratified: mean age at onset up to 30 years of age (Group A) and older than 30 years (Group B; p < 0.005). In Group A, segregation analysis strongly favored a single major gene acting autosomal dominant with a multifactorial component. Parameter estimates were 0.003 for the allele frequency, 1.0 for the penetrance, and 0.005 for the phenocopy rate. In Group B, no evidence for a major gene could be elucidated. The segregation pattern found in our families argues for an autosomal allele acting dominantly in RLS families with an early age at onset of symptoms and suggests that RLS is a causative heterogeneous disease.

High-resolution genetic mapping of the ACE-linked QTL influencing circulating ACE activity

Fine-mapping of trait loci through combined linkage and association analysis is an important component of strategies designed to identify causative gene variants, particularly in situations where the trait may be influenced by one or more of many polymorphisms within the same gene. Angiotensin-1 converting enzyme (ACE) provides one of the best models for developing and testing such methodologies, as a major fraction of the heritable variation in the activity of the angiotensin-1 converting enzyme (ACE) is tightly linked to the ACE gene. Moreover, ACE contains many frequent polymorphisms that are in strong linkage disequilibrium with each other. Although none of these variants induces a significant amino-acid change, one or more, either singly or in combination, are likely to have a strong effect on the quantitative phenotype. Here, we show that measured-haplotype analysis of SNP data from a large European family cohort can be used to localise the major ACE-linked genetic factors influencing the trait to a 16 kb interval within the gene, thus limiting the number of ACE variants that need to be considered in future studies designed to elucidate their biological effects. The approaches developed will be applicable to the fine-mapping of other quantitative trait loci in humans.

Genetic determination of HDL variation and response to diet in baboons

We fed 634 baboons three diets to assess the separate effects of increasing dietary fat and cholesterol intakes on three independent measures of HDL phenotype: concentrations of HDL cholesterol and apoAI, and size distributions of HDL cholesterol. Increasing dietary fat significantly increased concentrations of HDL cholesterol and apoAI (both, P<0.0001), but did not affect HDL particle sizes, whereas increasing dietary cholesterol increased HDL cholesterol (P<0.0001) concentrations and HDL particle sizes (P=0.08), but did not affect apoAI concentrations. A substantial proportion of variation in each of the HDL traits was influenced by genes (heritabilities ranged from 25 to 61%) and a common set of genes influenced HDL variation on each of the diets (genetic correlations ranged from 0.64 to 1.0). However, genes exerted a smaller effect on HDL response to changes of dietary fat and of dietary cholesterol. Therefore, dietary fat and cholesterol alter HDL levels and characteristics, but the dietary responses are not strongly mediated by additive genetic effects.

Is disease severity in ankylosing spondylitis genetically determined?

OBJECTIVE

To assess the role of genes and the environment in determining the severity of ankylosing spondylitis.

METHODS

One hundred seventy-three families with >1 case of ankylosing spondylitis were recruited (120 affected sibling pairs, 26 affected parent-child pairs, 20 families with both first- and second-degree relatives affected, and 7 families with only second-degree relatives affected), comprising a total of 384 affected individuals. Disease severity was assessed by the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) and functional impairment was determined using the Bath Ankylosing Spondylitis Functional Index (BASFI). Disease duration and age at onset were also studied. Variance-components modeling was used to determine the genetic and environmental components contributing to familiality of the traits examined, and complex segregation analysis was performed to assess different disease models.

RESULTS

Both the disease activity and functional capacity as assessed by the BASDAI and the BASFI, respectively, were found to be highly familial (BASDAI familiality 0.51 [P = 10(-4)], BASFI familiality 0.68 [P = 3 x 10(-7)]). No significant shared environmental component was demonstrated to be associated with either the BASDAI or the BASFI. Including age at disease onset and duration of disease as covariates made no difference in the heritability assessments. A strong correlation was noted between the BASDAI and the BASFI (genetic correlation 0.9), suggesting the presence of shared determinants of these 2 measures. However, there was significant residual heritability for each measure independent of the other (BASFI residual heritability 0.48, BASDAI 0.36), perhaps indicating that not all genes influencing disease activity influence chronicity. No significant heritability of age at disease onset was found (heritability 0.18; P = 0.2). Segregation studies suggested the presence of a single major gene influencing the BASDAI and the BASFI.

CONCLUSION

This study demonstrates a major genetic contribution to disease severity in ankylosing spondylitis. As with susceptibility to ankylosing spondylitis, shared environmental factors play little role in determining the disease severity.

Genome-wide linkage analysis of blood pressure in Mexican Americans

The genetic mechanisms that control variation in blood pressure level are largely unknown. One of the first steps in understanding those mechanisms is the localization of the genes that have a significant effect on blood pressure. We performed genome scans of systolic (SBP) and diastolic blood pressure (DBP) on a population-based sample of families in the San Antonio Family Heart Study. A likelihood-based Mendelian model incorporating genotype-specific effects of sex, age, age(2), BMI, and blood pressure (SBP or DBP, as appropriate) as covariates was used to perform two-point lodscore (Z) linkage on 399 polymorphic markers. Results showed that the genotype-specific covariate effects were highly significant for both SBP and DBP. Linkage results showed that a quantitative trait locus (QTL) influencing DBP was significantly linked to D2S1790 (Z = 3.92, theta = 0.00) and showed suggestive linkage to D8S373 (Z = 1.92, theta = 0.00). A QTL influencing SBP showed suggestive linkage to D21S1440 (Z = 2.82, theta = 0.00) and D18S844 (Z = 2.09, theta = 0.11). Without the genotype-specific effects in the model, the linkage to D2S1790 was not even suggestive (Z = 1.33, theta = 0.09); thus genotype-specific modeling was crucial in detecting this linkage. A comparison with linkage studies based in other populations showed that the significant linkage to D2S1790 has been replicated at the same marker in the Quebec Family Study. The replicated significant linkage at D2S1790 may begin to establish the locations of the genes that significantly affect blood pressure across several human ethnic groups.

Pedigree analysis package (PAP) vs. MORGAN: model selection and hypothesis testing on a large pedigree

The MORGAN package of programs is compared to a commonly used package, PAP, with respect to model selection in segregation analysis of a quantitative trait. MORGAN uses Monte Carlo Markov chain (MCMC) methods to estimate the likelihood, whereas both versions of PAP used employ an approximation to the likelihood for the mixed model. Comparisons are done by using results obtained from simulated data. All simulations were done on the same 232-member pedigree using data generated under each of several variations of models, which included different combinations of environmental, polygenic, and major gene components. PAP, version 4.0, and MORGAN gave similar results with respect to model selection for the majority of situations, suggesting that MCMC methods provide a computationally tractable approach for analysis of more complex models that cannot be analyzed by more direct computational methods. PAP, version 3.0, gave somewhat more disparate results compared with either PAP version 4.0 or MORGAN. Both MORGAN and the two versions of PAP confirmed that the major gene component is much easier to detect in the presence of some dominance. All three packages frequently falsely accepted the polygenic model when there was high residual heritability.

QTL influencing blood pressure maps to the region of PPH1 on chromosome 2q31-34 in Old Order Amish

BACKGROUND

Hypertension is a major risk factor for coronary heart disease, stroke, congestive heart failure, renal insufficiency, and peripheral vascular disease. Although the genetic contribution to variation in blood pressure is well recognized, the specific genes involved are mostly unknown. We carried out a genome-wide scan to identify loci influencing blood pressure in the Old Order Amish population of Lancaster County, Pennsylvania.

METHODS AND RESULTS

Blood pressures were measured in 694 adult participants from families recruited without regard to blood pressure. We performed a quantitative linkage analysis by using 357 microsatellite markers. In multipoint analysis, strong evidence for linkage was observed with both diastolic (lod=3.36; P=0.00004) and to a lesser extent systolic (lod=1.64; P=0.003) blood pressure in the region of chromosome 2q31-34. Peak evidence for linkage occurred at map positions 217 and 221 cM from pter for diastolic and systolic blood pressure, respectively.

CONCLUSIONS

A gene linked to familial primary pulmonary hypertension has recently been mapped to this same region, suggesting the intriguing hypothesis that other (attenuated) mutations in this same gene may influence variation in systolic and diastolic blood pressure in this population.

Evidence that multiple genes influence baseline concentrations and diet response of Lp(a) in baboons

We investigated the response of lipoprotein(a) [Lp(a)] levels to dietary fat and cholesterol in 633 baboons fed a series of 3 diets: a basal diet low in cholesterol and fat, a high-fat diet, and a diet high in fat and cholesterol. Measurement of serum concentrations in samples taken while the baboons were sequentially fed the 3 diets allowed us to analyze 3 Lp(a) variables: Lp(a)(Basal), Lp(a)(RF) (response to increased dietary fat), and Lp(a)(RC) (response to increased dietary cholesterol in the high-fat environment). On average, Lp(a) concentrations significantly increased 6% and 28%, respectively, when dietary fat and cholesterol were increased (P<0.001). As expected, most of the variation in Lp(a)(Basal) was influenced by genes (h(2)=0.881). However, less than half of the variation in Lp(a)(RC) was influenced by genes (h(2)=0.347, P<0. 0001), whereas the increase due to dietary fat alone was not significantly heritable (h(2)=0.043, P=0.28). To determine whether Lp(a) phenotypic variation was due to variation in LPA, the locus encoding the apolipoprotein(a) [apo(a)] protein, we conducted linkage analyses by using LPA genotypes inferred from the apo(a) isoform phenotypes. All of the genetic variance in Lp(a)(Basal) concentration was linked to the LPA locus (log of the odds [LOD] score was 30.5). In contrast, linkage analyses revealed that genetic variance in Lp(a)(RC) was not linked to the LPA locus (LOD score was 0.036, P>0.5). To begin identifying the non-LPA genes that influence the Lp(a) response to dietary cholesterol, we tested, in bivariate quantitative genetic analyses, for correlation with low density lipoprotein cholesterol [LDLC; ie, non-high density lipoprotein cholesterol less the cholesterol contribution from Lp(a)]. LDLC(Basal) was weakly correlated with Lp(a)(Basal) (rho(P)=0.018). However, LDLC(RC) and Lp(a)(RC) were strongly correlated (rho(P)=0. 382), and partitioning the correlations revealed significant genetic and environmental correlations (rho(G)=0.587 and rho(E)=0.251, respectively). The results suggest that increasing both dietary fat and dietary cholesterol caused significant increases in Lp(a) concentrations and that the response to dietary cholesterol was mediated by a gene or suite of genes that appears to exert pleiotropic effects on LDLC levels as well. The gene(s) influencing Lp(a) response to dietary cholesterol is not linked to the LPA locus.

Joint multipoint linkage analysis of multivariate qualitative and quantitative traits. I. Likelihood formulation and simulation results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.

Heritability of cellular radiosensitivity: a marker of low-penetrance predisposition genes in breast cancer?

Many inherited cancer-prone conditions show an elevated sensitivity to the induction of chromosome damage in cells exposed to ionizing radiation, indicative of defects in the processing of DNA damage. We earlier found that 40% of patients with breast cancer and 5%-10% of controls showed evidence of enhanced chromosomal radiosensitivity and that this sensitivity was not age related. We suggested that this could be a marker of cancer-predisposing genes of low penetrance. To further test this hypothesis, we have studied the heritability of radiosensitivity in families of patients with breast cancer. Of 37 first-degree relatives of 16 sensitive patients, 23 (62%) were themselves sensitive, compared with 1 (7%) of 15 first-degree relatives of four patients with normal responses. The distribution of radiosensitivities among the family members showed a trimodal distribution, suggesting the presence of a limited number of major genes determining radiosensitivity. Segregation analysis of 95 family members showed clear evidence of heritability of radiosensitivity, with a single major gene accounting for 82% of the variance between family members. The two alleles combine in an additive (codominant) manner, giving complete heterozygote expression. A better fit was obtained to a model that includes a second, rarer gene with a similar, additive effect on radiosensitivity, but the data are clearly consistent with a range of models. Novel genes involved in predisposition to breast cancer can now be sought through linkage studies using this quantitative trait.

Measured haplotype analysis of the angiotensin-I converting enzyme gene

Linkage and segregation analysis have shown that circulating angiotensin-I converting enzyme (ACE) levels are influenced by a major quantitative trait locus that maps within or close to the ACE gene. The D variant of a 287 bp insertion/deletion (I/D) polymorphism in intron 16 of the gene is associated with high ACE levels and may also be related to increased risk of cardiovascular disease. Multiple variants that are in linkage disequilibrium with the I/D polymorphism have been described, but it is unknown if any of these are directly implicated, alone or in combination with as yet undiscovered variants, in the determination of ACE levels. An analysis of 10 polymorphisms spanning 26 kb of the ACE gene revealed a limited number of haplotypes in Caucasian British families due to strong linkage disequilibrium operating over this small chromosomal region. A haplotype tree (cladogram) was constructed with three main branches (clades A-C) which account for 90% of the observed haplotypes. Clade C is most likely derived from clades A and B following an ancestral recombination event. This evolutionary information was then used to direct a series of nested, measured haplotype analyses that excluded upstream sequences, including the ACE promoter, from harbouring the major ACE-linked variant that explains 36% of the total trait variability. Residual familial correlations were highly significant, suggesting the influence of additional unlinked genes. Our results demonstrate that a combined cladistic/measured haplotype analysis of polymorphisms within a gene provides a powerful means to localize variants that directly influence a quantitative trait.

Linkage analysis, kinship, and the short-term evolution of chromosomes

Although all meiotic (or linkage) mapping strategies ultimately rely on Mendel's laws, the precise manner in which these laws are exploited in relevant statistical models determines the utility of each strategy for different traits and diseases. In this paper we review the motivation and principles behind each of the three most often used statistical strategies for mapping loci that influence complex, multifactorial traits and diseases (such as diabetes and hypertension), namely: pedigree-based parametric linkage, relative pair allele sharing analysis, and association or linkage disequilibrium analysis. It is our hope to show how Mendel's laws are exploited in each through use of two basic concepts: the short-term evolution of chromosomes, and kinship. Problems inherent in each strategy are described. We then consider how extensions, modifications, or novel derivatives of these three strategies might be fashioned that make better use of the concepts of kinship and short-term chromosome evolution. Two strategies receive emphasis: a haplotype sharing method, which considers the kinship of groups of individuals, and extended variance component models, which make use of genotype information in novel ways.

An unknown genetic defect increases venous thrombosis risk, through interaction with protein C deficiency

We used two-locus segregation analysis to test whether an unknown genetic defect interacts with protein C deficiency to increase susceptibility to venous thromboembolic disease in a single large pedigree. Sixty-seven pedigree members carry a His107Pro mutation in the protein C gene, which reduces protein C levels to a mean of 46% of normal. Twenty-one carriers of the mutation and five other pedigree members had verified thromboembolic disease. We inferred the presence in this pedigree of a thrombosis-susceptibility gene interacting with protein C deficiency, by rejecting the hypothesis that the cases of thromboembolic disease resulted from protein C deficiency alone and by not rejecting Mendelian transmission of the interacting gene. When coinherited with protein C deficiency, the interacting gene conferred a probability of a thrombotic episode of approximately 79% for men and approximately 99% for women, before age 60 years.

Two major loci control variation in beta-lipoprotein cholesterol and response to dietary fat and cholesterol in baboons

We explored the genetic control of cholesterolemic responses to dietary cholesterol and fat in 575 pedigreed baboons. We measured cholesterol in beta-lipoproteins (low density lipoprotein cholesterol [LDLC]) in blood drawn from baboons while they were consuming a baseline (low in cholesterol and fat) diet, a high-saturated fat (lard) diet, and a high-cholesterol, high-saturated fat diet. In addition to baseline levels (LDLC(Base)), we analyzed two variables for diet response: LDLC(RF), which represents the LDLC response to increasing dietary fat (ie, high-fat diet minus baseline), and LDLC(RC), which represents the LDLC response to increasing dietary cholesterol level (ie, high-cholesterol, high-fat diet minus high-fat diet). Heritabilities (h2) of the 3 traits were 0.59 for LDLC(Base), 0.14 for LDLC(RF), and 0.59 for LDLC(RC). In addition, LDLC(Base) and LDLC(RC) had a significant genetic correlation (ie, rhoG=0.54), suggesting that 1 or more genes exert pleiotropic effects on the 2 traits. Segregation analyses detected a single major locus that accounted for nearly all genetic variation in LDLC(RC) and some genetic variation in LDLC(Base) and LDLC(RF) and confirmed the presence of a different major locus that influences LDLC(Base) alone. Preliminary linkage analyses indicated that neither locus was linked to the LDL receptor gene, a likely candidate locus for LDLC. Detection of these major loci with large effects on the LDLC response to dietary cholesterol in a nonhuman primate offers hope of detecting and ultimately identifying similar loci that determine LDLC variation in human populations.

Recessive inheritance of obesity in familial non-insulin-dependent diabetes mellitus, and lack of linkage to nine candidate genes

Segregation analysis of body-mass index (BMI) supported recessive inheritance of obesity, in pedigrees ascertained through siblings with non-insulin dependent diabetes mellitus (NIDDM). BMI was estimated as 39 kg/m2 for those subjects homozygous at the inferred locus. Two-locus segregation analysis provided weak support for a second recessive locus, with BMI estimated as 32 kg/m2 for homozygotes. NIDDM prevalence was increased among those subjects presumed to be homozygous at either locus. Using both parametric and nonparametric methods, we found no evidence of linkage of obesity to any of nine candidate genes/regions, including the Prader-Willi chromosomal region (PWS), the human homologue of the mouse agouti gene (ASP), and the genes for leptin (OB), the leptin receptor (OBR/DB), the beta3-adrenergic receptor (ADRB3), lipoprotein lipase (LPL), hepatic lipase (LIPC), glycogen synthase (GYS), and tumor necrosis factor alpha (TNFA).

Mixture distributions in human genetics research

The use of mixture distributions in genetics research dates back to at least the late 1800s when Karl Pearson applied them in an analysis of crab morphometry. Pearson's use of normal mixture distributions to model the mixing of different species of crab (or 'families' of crab as he referred to them) within a defined geographic area motivated further use of mixture distributions in genetics research settings, and ultimately led to their development and recognition as intuitive modelling devices for the effects of underlying genes on quantitative phenotypic (i.e. trait) expression. In addition, mixture distributions are now used routinely to model or accommodate the genetic heterogeneity thought to underlie many human diseases. Specific applications of mixture distribution models in contemporary human genetics research are, in fact, too numerous to count. Despite this long, consistent and arguably illustrious history of use, little mention of mixture distributions in genetics research is made in many recent reviews on mixture models. This review attempts to rectify this by providing insight into the role that mixture distributions play in contemporary human genetics research. Tables providing examples from the literature that describe applications of mixture models in human genetics research are offered as a way of acquainting the interested reader with relevant studies. In addition, some of the more problematic aspects of the use of mixture models in genetics research are outlined and addressed.

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.

Evidence for multiple genes determining sodium transport

Sodium transport comprises a set of interacting systems. Consequently, a defective sodium transport gene affects multiple sodium transport systems, and a sodium transport variable measured on a sample of individuals reflects genetic variation from a number of different genes, complicating the task of identifying the effect of a single gene. To test for genes which affect sodium transport, we first applied principal components analysis to 14 variables related to sodium transport, thereby defining uncorrelated sources of variation in the variables. The sample consisted of 1,218 members of 68 pedigrees ascertained through probands with early-onset stroke, hypertension, or coronary heart disease. Segregation analysis of the 14 principal components scores provided evidence for 8 genetic variants which alter sodium transport. One of the 8 variants is recessive, has homozygous genotype frequency estimated as 8.8% of the population, and increases sodium-lithium countertransport, the passive sodium leak, body mass index, and triglyceride; the genetic variant may coincide with an insulin resistance gene. A second of the 8 variants is also recessive, has homozygous genotype frequency estimated as 7.4% of the population, and increases intraerythrocytic sodium and the passive sodium leak while decreasing sodium pump number; the genetic variant may reduce pump number. Two of the 8 variants substantially increase sodium-lithium countertransport; frequency estimates for heterozygotes for the dominant variant and homozygotes for the recessive variant equal 1.8% and 3.1%, respectively. Another of the 8 variants is recessive, has homozygous genotype frequency estimated as 1.9%, and increases body mass index. Each of the 3 remaining variants is rare and expressed in less than 1% of the sample.