In family studies, phenotypic similarities between relatives yield information on the overall contribution of genes to trait variation. Large samples are important for these family studies, especially when comparing heritability between subgroups such as young and old, or males and females. We recruited a cohort of 6,148 participants, aged 14–102 y, from four clustered towns in Sardinia. The cohort includes 34,469 relative pairs. To extract genetic information, we implemented software for variance components heritability analysis, designed to handle large pedigrees, analyze multiple traits simultaneously, and model heterogeneity. Here, we report heritability analyses for 98 quantitative traits, focusing on facets of personality and cardiovascular function. We also summarize results of bivariate analyses for all pairs of traits and of heterogeneity analyses for each trait. We found a significant genetic component for every trait. On average, genetic effects explained 40% of the variance for 38 blood tests, 51% for five anthropometric measures, 25% for 20 measures of cardiovascular function, and 19% for 35 personality traits. Four traits showed significant evidence for an X-linked component. Bivariate analyses suggested overlapping genetic determinants for many traits, including multiple personality facets and several traits related to the metabolic syndrome; but we found no evidence for shared genetic determinants that might underlie the reported association of some personality traits and cardiovascular risk factors. Models allowing for heterogeneity suggested that, in this cohort, the genetic variance was typically larger in females and in younger individuals, but interesting exceptions were observed. For example, narrow heritability of blood pressure was approximately 26% in individuals more than 42 y old, but only approximately 8% in younger individuals. Despite the heterogeneity in effect sizes, the same loci appear to contribute to variance in young and old, and in males and females. In summary, we find significant evidence for heritability of many medically important traits, including cardiovascular function and personality. Evidence for heterogeneity by age and sex suggests that models allowing for these differences will be important in mapping quantitative traits. Genetic analysis of complex traits, which are influenced by many different variables, is difficult because different genes and environmental factors can affect each individual. To simplify analysis, the authors turned to Sardinia, one of the rare, relatively isolated populations. They recruited 6,148 participants, aged 14–102 y, from four neighboring towns. Their sample includes many related individuals, including, for example, approximately 5,000 pairs of brothers and sisters. The authors measured 98 traits in each individual, including different aspects of blood composition and several cardiovascular and personality measures.Here, the authors evaluate the overall impact of genes and environment on each trait and show that genes can explain many of the differences and similarities between individuals. Genetic influences were typically larger in females and in younger individuals, but interesting exceptions were observed. For example, genetic factors accounted for approximately 26% of the variation in blood pressure for those more than 42 y old, but only for approximately 8% in younger individuals. Their analysis also showed that the same genetic factor could influence multiple traits, for example by affecting multiple features of personality or of cardiovascular function. DNA analyses of this cohort will eventually allow researchers to identify genes that affect each of the traits studied, including important risk factors for cardiovascular disease. Complex traits, including aging-associated conditions, can be influenced by a multiplicity of genetic and environmental factors. Because each factor is expected to make only a small contribution to trait variability, and this contribution may itself be influenced by interactions with other susceptibility factors, identifying the genetic basis of complex traits is challenging and requires large sample sizes . IsolateSardinia is the second largest island in the Mediterranean. Its modern population numbers approximately 1.65 million and constitutes a genetically isolated founder population , which hHere, we use a large cohort of 6,148 Sardinians to study the heritability of a spectrum of 98 quantitative traits. Studying broad groups of traits, we could assess the generality of any trends, such as changes in heritability with aging. To increase the potential clinical utility of the results, we focused on traits that affect major domains of clinical interest. For example, in addition to anthropometric features, we quantified levels of plasma and serum markers, including total cholesterol, high-density lipoprotein (HDL), and low-density lipoprotein (LDL) levels, and measured subclinical vascular alterations  that areOur study uses the full range of phenotypic variation in the population to dissect the genetic contribution and provide a quantitative assessment of the impact of inherited variation on each trait. In addition, we report evidence for heterogeneity in the genetic and environmental contributions to variation, by comparing variances and covariances between males and females and between the younger and older individuals in our cohort. Finally, we examine evidence for an overlap in the genetic determinants of multiple traits, identifying clusters of traits that appear to be influenced by the same genes. The joint study of cardiovascular and personality traits afforded us an opportunity to look for a genetic factor that might contribute to the association of certain personality traits and cardiovascular problems . OverallWe recruited and phenotyped 6,148 individuals, male and female, age 14 y and above A from a Nearly all subjects were born in Sardinia  and, specifically, in the Ogliastra region  together with detailed results for all our analysis. To examine the effect of age and sex on each trait, we first generated and reviewed summary plots for each trait. The complete set of plots is available online (p < 0.0005) for differences in trait means between the sexes (75 of 98 traits) and across age bands (91 of 98 traits).We next calculated the mean and standard deviation for all traits, both in the entire cohort and after stratifying the sample by sex and age. When stratifying the sample by age, we considered four age bands , each including approximately 25% of sampled individuals. The results are summarized in 2, and the terms for the interaction of sex with age and age2) , each of which is a composite of six facets of personality, are measured. The NEO-PI-R provides a comprehensive and detailed assessment of normal adult personality in terms of emotional, interpersonal, experiential, attitudinal, and motivational styles. The inventory has a robust factor structure that has been replicated in Italy [Personality phenotypes were assessed with the Revised NEO Personality Inventory (NEO-PI-R ), a quesin Italy  and in min Italy . Scales in Italy . Two tra1C), and ESR were also measured. C-reactive protein (CRP) was assessed using the standard low-sensitivity assay [From each participant screened, 25 ml of blood was drawn and fractionated to provide serum, EDTA-plasma, heparin-plasma, white blood cells, and red blood cells. Clinical laboratories in Sardinia provided blood cell counts and applied a standard battery of blood tests for the measurement of electrolytes, renal function, liver function, thyroid function, and iron metabolism. Given our interest in cardiovascular risk factors, fasting lipid profiles, markers of insulin resistance  was calculated as (PP = SBP − DBP) and mean blood pressure (MBP) as (MBP = DBP + PP/3). Standard 12-lead electrocardiography was performed on all participants, from which the PR interval and the QT interval corrected for heart rate (QTC) were measured.Participants also underwent non-invasive assessments of arterial structure and function that are increasingly recognized as potent predictors of adverse cardiovascular outcomes ,57,58. CDuring the sonographic evaluation of the common carotid artery, Doppler studies allowed the measurement of PSV, end-diastolic velocity (EDV), pulsatility index (IP), systolic–diastolic ratio (SD_ratio), and acceleration time (AT).2). For conciseness, additional details of how individual phenotypes, including cardiovascular measures, were collected are supplied as In addition to personality traits, cardiovascular measures, and blood composition, we also considered four anthropometric traits recorded during physical examination of each subject  and one derived quantity  scripts. These tools allowed us to check that pedigrees were self-consistent, and to identify univariate and multivariate outliers. Outliers and other unusual trait values were inspected against the original records whenever possible.Quality assessment of the data was carried out using PEDSTATS , and in-2, sex, and the two corresponding interaction terms as covariates in all analyses. We considered a series of models for each trait, and these are detailed below, together with details of transformations we applied to each trait to guard against the possibility of statistical artifacts induced by outliers or non-normal marginal distributions.To utilize fully the information in our cohort, and to accommodate covariate effects, we estimated heritabilities using a variance components model ,24. Thisz-score from the standard normal distribution. When ties were present, percentiles were averaged across all ties.Variance components analyses are sensitive to outliers, kurtosis, and skewness in the trait distribution. Quantile normalization provides a practical way to deal with these problems in the context of gene mapping and, specifically, variance component analyses –63. For g2 and an environmental component σe2. As usual, the environmental component is unique to each individual, whereas the polygenic component is shared between individuals in proportion to their kinship coefficient. Thus, if iY is the observed trait measurement for individual i, we define its variance as i) =Var =Cov, based on their reported relationship  =Var =CovI be an indicator variable with value 1 when individuals i and j are full sibs, and value 0 otherwise. Then we leti) =Var =CovI σs2. In most datasets, including our own, the two models cannot be distinguished statistically [ij = 0.25Δ and sib = 1I when i and j are full siblings, and ijΔ = sib=I 0 for nearly all other pairs of individuals, it is simple to show that the two models lead to identical predictions of variances and covariances when we set σd2 = 4 σs2 and adjust σe2 appropriately. Although our dataset does not allow us to distinguish between models with only genetic dominance , models with only shared environment , and other intermediate models , comparisons of parameter estimates from these models are informative. In the model with genetic dominance, the quantity H2 = (σd2 + σg2)/(σd2 + σg2 + σe2) provides a liberal estimate of the overall impact of genes on the phenotype at hand, whereas in the model attributing any excess similarity between siblings to shared environment, the quantity h2 = σg2/(σs2 + σg2 + σe2) provides a very conservative estimate of the overall impact of genes. Whenever there was significant evidence (p < 0.001) for shared sibling environment or genetic dominance, genetic dominance was included in the heterogeneity analyses described below.After fitting this base model, we considered refined models including additional variance components to model genetic dominance, σficients ). Then wstically . In factg,male2 and σe,male2, and females, σg,female2 and σe,female2. The variances for each trait measurement and the covariances for trait-measurements between individuals of the same sex follow naturally from the formulae given in the section describing the Base Polygenic Model (above). When individuals i and j were of opposite sexes, we set the covariance to i, Yj) =Cov, only for genetic effects  or where variability increased uniformly for both genetic and environmental factors .To model heterogeneity, we evaluated models in which separate variance components were fitted for males, σi, Yj) =Cov =Cov(Y 2 ij ρsexϕsex < 1−1 < ρ) resulted in a significant improvement in the likelihood. Thus, our data provide no evidence that different genes contribute to genetic variation in males and females, but rather that the same genes make different contributions in each sex.Setting x2, and to models with a mitochondrial genetic variance component, σm2. In models with an X-linked variance component, i) =Var(Y σg2 + σe2 + 2 ii(X)ϕ σx2 and i, Yj) =Cov(Y 2 ijϕ σg2 + 2 ij(X)ϕ σx2, in which calculation of the kinship coefficient for X-linked genes is detailed at the end of the i) =Var =Cov σm2. The indicator function M takes a value = 1 if individuals i and j are related through their maternal lineages, and 0 otherwise.We also considered the possibility of X-linked or mitochondrial inheritance. X-linked inheritance can produce differences in the total variance between males and females, and either of these phenomena can generate sex-dependent covariances between relatives . We compared models with heterogeneity to models with an X-linked variance component, σg,old2 and σe,old2, and for individuals whose age was below the sample median, σg,young2 and σe,young2. When there was evidence for heterogeneity, we considered intermediate models in which heterogeneity was allowed only for environmental effects , or only for genetic effects , or in which the total variance for both genetic and environmental factors changed by a shared factor .Similarly to our analysis with heterogeneity by sex, we defined separate variance components for individuals whose age was greater or equal than the sample median (42 y of age), σY and Z, we portioned the bivariate correlation into an environmental correlation, e,ρ and a genetic correlation, g,ρ for each pair of traits. To do this, we fitted the base polygenic model to each pair of traits simultaneously, and set the cross-trait correlation to i,Zi) = ρeCovρi,Zj) =Covϕ. To summarize the results, we defined |1 − g|ρ as the distance between each pair of traits, and implemented a simple hierarchical clustering analysis [To investigate the origin of correlations between each pair of traits analysis , which s2, and sex) and a model for variances and covariances. Likelihoods were maximized using a computationally efficient scoring method [http://www.sph.umich.edu/csg/chen/poly). The program uses Generalized Estimating Equations estimates (GEE) [All models were fitted by maximizing the standard multivariate normal likelihood , which dg method  implemenes (GEE)  to seleces (GEE)  and QTDTes (GEE) , with ides (GEE) .i and j, i > j implies that i is not an ancestor of j (any ordering where ancestors precede their descendants is suitable).Recall that the kinship coefficient is the probability that two identical alleles will be sampled from a pair of individuals when we select one allele at random from each. The self-kinship coefficient is the probability that two alleles sampled from one individual, with replacement, are identical. We used a recursive formulation to estimate kinship coefficients for X-linked genes, analogous to the conventional approach described in Lange  for autoij(X),ϕ as follows:Then, we defined the kinship coefficient for X-linked genes, i ≥ j, it can be used to estimate any kinship coefficient because ij(X)ϕ = ji(X)ϕ. The definition reflects the fact that males carry only one allele for X-linked genes, inherited from their mother. Females carry two alleles, one inherited from each parent. The functions mother(i) and father(i) return indexes for the parents of i.Although this definition only covers the situation in which Protocol S1This section provides a detailed protocol for the assessment of cardiovascular traits.(18 KB PDF)Click here for additional data file.Table S1This table includes trait means and variances. Trait means are stratified by sex and into four age bands.(37 KB PDF)Click here for additional data file.Table S2Highlights subsets of traits identified in the clustering analysis, for which the genetic correlation exceeds 0.5.(7 KB PDF)Click here for additional data file.Table S3The table presents Procrustes-rotated principal components from the genetic correlations among the 30 facets of the NEO-PI-R, targeted to the American normative factor structure. (11 KB PDF)Click here for additional data file.


Biomarkers of carotid atherosclerosis range from those that are widely available and relatively simple to measure such as serum cholesterol levels, and B-mode Ultrasound measurement of intima media thickness (IMT) to those that are more complex and technologically demanding but perhaps potentially more sensitive and specific to disease such as total plaque volume and total plaque area measured from 3-dimensional ultrasound images. In this study we measured and compared intima media thickness (IMT), total plaque volume (TPV) and total plaque area (TPA) in two separate populations, both vulnerable to carotid atherosclerosis.In total, 88 subjects (mean age 72.8) with carotid stenosis of at least 60%, based on a peak Doppler flow, and 82 subjects (mean age 60.9) with diabetic nephropathy were assessed in a cross-sectional study. Conventional atherosclerotic risk factors were examined and the associations and correlations between these and carotid ultrasound phenotypes measured from B-mode and 3-dimensional ultrasound images were assessed.IMT and TPV were only modestly correlated in the two separate populations . ANOVA analyses indicated that both IMT and TPV were significantly associated with age (p < .001) and Framingham score (p < .05), but only TPV was associated with diabetes (p < .001) and presence of plaque ulcerations (p < .01)IMT and TPV were modestly correlated in a diabetic patient population and only TPV was associated with diabetes and the presence of plaque ulcerations in a diabetic population and carotid stenosis group. The 3-dimensional information provided by TPV can be critically important in unmasking association with risk factors not observed with less complex single-dimension assessments of carotid atherosclerosis such as those provided by IMT. Measurements of atherosclerosis range from clinical events such as myocardial infarction and stroke, and biomarkers such as blood pressure, serum cholesterol and triglycerides levels, to measurements acquired with non-invasive imaging modalities such as computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound (US). Non-invasive imaging measurements can be considered as physical characteristics or phenotypes that can be measured in specific subjects and populations. Such physical characteristics or phenotypes that are shown to correlate with disease activity can be considered to be disease biomarkers, and those biomarkers that can be shown to correlate with clinical outcomes are considered as surrogate endpoints. Non-invasive imaging phenotypes are also of particular interest as they may reflect different stages of or different underlying mechanisms that contribute to atherogenesis; some of these phenotypes directly reflect changes in plaque and atherosclerotic vessel architecture providing a distinct advantage over biochemical biomarkers from blood samples. Quantitative assessment of different non-invasive imaging phenotypes in different vulnerable patient populations is an important approach to understanding natural disease progression and treatment-related disease regression.An emerging imaging phenotype of atherosclerosis is carotid total plaque volume (TPV), measured with three-dimensional ultrasound and specialized image processing software . The curIn this study we aimed to measure and compare total plaque volume (TPV), total plaque area (TPA) and intima-media thickness (IMT) in the carotid arteries, as well as previously established biomarkers, in two special and vulnerable populations: middle-aged patients with diabetic nephropathy and elderly patients with asymptomatic carotid stenosis of at least 60%. Imaging measurements of atherosclerosis that we continue to develop and validate are assessed in these populations to better understand the associations of these with one another and with risk factors related to atherosclerosis progression.One study population consisted of 88 subjects with internal carotid artery stenosis (carotid stenosis population) of at least 60%, based on a peak Doppler flow velocity cut-off established by the North American Carotid Endarterectomy Trial (NASCET) [Clinical data collected and used in the analysis of both populations were age, sex, body mass index (BMI), plasma cholesterol, low-density lipoproteins (LDL), high-density lipoproteins (HDL) and triglycerides, blood pressure (BP), number of plaque ulcerations, diabetes status and smoking history. Age, sex, height and weight were self-reported. For both cohorts, blood pressure was measured once in one arm (the one arm previously determined to have the highest pressure), as many as three times. The average of multiple measurements was used. Subjects with physician-diagnosed diabetes were considered to be diabetic. Smokers were defined as those who currently smoked or those who had stopped smoking less than one year prior to the ultrasound scan. Blood for biochemical determinations was collected after a 12-hour fast. Plasma measurements included triglycerides, total cholesterol, HDL and LDL. Framingham risk scores , definedUltrasound (US) images were acquired with an HDI 5000 duplex machine and an L12-5 transducer . A single experienced sonographer acquired images suitable for determination of IMT, TPA and TPV.Ultrasound images were acquired from an anterolateral longitudinal view and saved to S-VHS tapes. The sonographer used the minimum gain necessary to clearly visualize lumen-intima and media-adventitia echoes, which are of best quality when the image plane is parallel to the carotid artery axis. These views were reviewed using an image processing board and a specialized recorder with digital memory permitting digitization of a full video frame in "still" mode. The resultant digitized ultrasound images, captured at end-diastole, were analyzed using Prowin  edge-detPlaque area measurements were made by a trained sonographer on magnified, longitudinal views of the common carotid arteries in real time. The patient was scanned until the largest extent of a plaque could be seen, and the image was used to outline plaque with the use of a trackball and the area was immediately calculated by the microprocessor in the scanner. Plaque was defined as a local thickening of the intima layer of greater than 1 mm . This wa3D US images were viewed and analyzed using 3D Quantify software . The proPlaque ulcerations in the common and internal carotid arteries were scored by a single observer. Plaque ulcerations were identified as focal defects in plaque surface of at least 0.5 mm in depth, length and width that were visible from multiple angles. Subjects were scored as positive if at least a single ulceration was observed in the 3D US image.Data analysis was conducted with statistical software SPSS version 12.0 . Associations between the different ultrasound measures of atherosclerosis were determined using the Pearson product-moment correlation. For the asymptomatic stenosis population, the correlation was determined between TPA and TPV. For the diabetic nephropathy population, correlations were determined between IMT, TPA and TPV. Distributions were significantly non-normally distributed and therefore, IMT TPA and TPV variables were transformed and subjected to analysis of normality. After transformation, the inverse of IMT, and cubed root of both TPV and TPA were normally distributed. The transformed variables were used for the analyses. Simple linear regressions were performed predicting the inverse of IMT, the TPV and TPA transformed by cube root, using a number of dichotomous and continuous predictors: age, sex, BMI, BP, number of ulcerations, diabetes and smoking history, and Framingham score. This analysis was conducted for the populations as a whole, as well as for subpopulations characterized by sex and, in the diabetic cohort, diabetes type. A significant result indicates that there is a significant difference between the categories from the dichotomous and continuous variables with respect to the phenotypes measured.Clinical attributes for the two subject populations, as a whole and by sex, are provided in Table Figure IMT data are provided in Table Pearson correlation coefficients between transformed IMT, TPA and TPV are shown in Table 2 and 187 ± 170 mm3, respectively) were significantly greater than for type 1 diabetics (TPA 0.74 ± 0.83 cm2 and TPV 47.2 ± 55.6 mm3). The two subgroups, however, did not significantly differ in mean IMT. As this and previous work shows that age is predictive of TPA and TPV in younger populations, TPA and TPV were reassessed for correlations with of diabetes type while controlling for the mean age difference between type 1 and type 2 diabetics. In this analysis we found that TPV was not significant (p < 0.088) and neither was TPA (p < 0.959). As the TPV result approached significance, a sample size calculation was performed to determine how many individuals would be required to achieve significant differences  and this indicated that 216 subjects across diabetes types would be required to detect group differences when controlling for age.As shown in Table IMT measurements has been used for many years in the assessment of carotid atherosclerosis; IMT image acquisition and analysis is relatively straightforward and provides a one-dimensional measure of carotid artery wall changes. However, different multi-dimensional methods of measuring atherosclerosis may potentially provide biologically distinct and perhaps more sensitive and specific measures of carotid atherosclerosis . For exaHegele and collaborators first showed that different atherosclerosis phenotypes associate with different risk factors in a closed aboriginal population . In theiOverall these results suggest that in different subject populations, both vulnerable to vascular disease, carotid ultrasound phenotypes associate differently with various risk factors. Differences were observed as well in that TPA and TPV in both populations were associated with ulcerations, whereas IMT was not associated with plaque ulcerations for the diabetic population where IMT was measured. Moreover, for the diabetic population, only TPA and TPV were significantly associated with diabetes type, and not IMT. This suggests that advanced plaque development that is reflected in measurements of TPA and TPV is associated with type 2 diabetes and that the presence of type 2 diabetes may play a role in mechanisms contributing to plaque burden, but not contributing specifically to IMT.Here we extend the first reported comparisons of imaging phenotypes of atherosclerosis by Hegele and collaborators ,17-20 anWhile the mean age of the carotid stenosis cohort was nearly 12 years older, mean TPA and TPV were 2.5 and 4.2 fold greater than in the younger diabetic cohort and over half the older cohort showed 3D US evidence of at least one ulcer. In the older stenosis population only, females had statistically significantly lower mean TPA and TPV compared to males. Although the diabetic nephropathy cohort was much younger, Framingham scores were greater than two-fold overall risk as compared to the older stenosis cohort.Hegele and collaborators showed that for a middle-aged aboriginal population (Sandy Lake Canada) carotid IMT was associated with age and hypertension, whereas TPV was associated with age and the presence of diabetes. In our analysis, IMT was significantly associated with age, diastolic BP and Framingham score, but not diabetes. TPV and TPA were significantly associated with age and diabetes and with the presence of ulcerations and Framingham score. For the elderly population with significant carotid stenosis, both TPA and TPV were significantly associated with sex and presence of ulcerations. Such differences in risk factor and ultrasound phenotypes in different populations create a framework for understanding risk factor relationships in middle age and elderly populationsBecause different phenotypes may be related to different biological and genetic factors, the use of these phenotypes as measurement tools may provide for a wide range of sensitivities and specificities to disease progression and regression that is population-dependent. While our sample sizes are small, our results suggest that while imaging measures themselves correlate similarly across diverse populations, a given imaging measures associates with different risk factors in different populations. We suggest that clinical studies that aim to use imaging measures as surrogate endpoints should measure specific biomarkers that are dependent on the treatment and specific population being studied. It may be necessary for specific new interventions to be targeted to specific study populations that are well characterized with respect to genotype, phenotype or other underlying characteristics. Study populations may need to be targeted based on the likelihood of well-characterized treatment effects that can be predicted in advance using the approaches we have taken here. While all of these issues require clarification in the future, it is clear that individual imaging measures such as IMT, TPA and TPV will require rigorous testing and validation in specific target populations before they can be used as surrogate endpoints in treatment studies.The author(s) declare that they have no competing interests.SAR measured all carotid US phenotypes and performed some of the statistical analyses. AAH trained the IMT observer, supervised the analysis of IMT, assisted in the final analysis of the data and helped draft the manuscript. AF participated in the analysis of the imaging data and assisted in the supervision of the imaging phenotype measurements. JDS participated in the design and analyses of the study. GP conceived the study, participated in its design and statistical analyses, analysed the statistical and some imaging data and drafted the manuscript. All authors read and approved the final manuscript.


One implicit assumption in most linkage analysis is that live-born siblings unselected for a phenotype do not share alleles greater than the Mendelian expectation at any particular locus. However, since most families are recruited for genetic studies because of the presence of disease, there is little data available to confirm that this is the case. We hypothesized that loci that behave in a non-Mendelian fashion could be identified using genotype data from the Framingham Heart Study families. We tested the hypothesis that live-born sibs, either stratified by or irrespective of gender, demonstrate excess sharing of alleles on the autosomes, i.e., transmission ratio distortion. Multipoint linkage analysis of siblings either according to gender or not was performed using an allele-sharing method. Such observations may have implications for the mapping of loci for complex disease and quantitative traits in human pedigrees.p < 0.002 when sibships were stratified by gender-three of which were present in males. Of note, a female-specific locus co-localized with region that is linked to mean systolic blood pressure in the same families. In addition, three other regions demonstrated excess sharing of alleles in sibships irrespective of gender, including a region on chromosome 10p14-p15 (p = 7.5 × 10-4).No results that reached genome-wide significance were observed. However, four regions demonstrated excess sharing of alleles at Although no loci meeting genome-wide significance were detected to demonstrate transmission ratio distortion, loci with suggestive evidence for linkage were detected. These may have implications for the mapping of susceptibility loci for complex disease in human pedigrees. The twoTransmission ratio distortion (TRD) has been defined as "a statistically significant departure from the Mendelian inheritance ratio expected regardless of the cause" . There aAt certain TRD loci, the effect may be sex-specific -5, and tThe Framingham families represent a valuable resource for the study of TRD because they are relatively ethnically homogeneous (predominantly White), and were not recruited for the presence of disease or trait value. The only reasons that families were included in the genetic studies was based on their age being 28-62 years for the original cohort and 12-58 years for the offspring cohort at recruitment, being alive when DNA was obtained (in the late 1980s and early 1990s), and their relatively large size . Results from these families will help to determine whether concerns about TRD are of general concern for the mapping of susceptibility loci for complex diseases.Our primary interest is to identify autosomal TRD loci in the Framingham Heart Study families. We hypothesized that such loci could act either in a sex-specific or nonspecific fashion. Ethics approval was obtained from the Hospital for Sick Children Research Ethics Board (#2002/116). Genotype data from 398 autosomal microsatellite markers in 1702 individuals from 330 pedigrees were used. To test for sex-specific TRD, families were divided into nuclear families containing two or more genotyped same-sex siblings. There were 222 sibships with ≥2 genotyped female sibs and 201 such male sibships . In the female families, female siblings were coded as affected. Similarly, in the male families, male siblings were coded as affected. Siblings of the opposite sex, when present, were kept in the family to improve estimates of allele sharing between siblings, but were coded as unaffected. Marker allele frequencies were counted from the founders in the male and female families separately.all scoring function, and the recommended family weighting scheme of power: 0.5. p-Values were obtained using normal approximation.To investigate TRD that is not sex-specific, nuclear families with two or more genotyped siblings were generated irrespective of gender. There were 459 such families. Any genotyped sib was coded as affected. For both the sex-specific and nonspecific data, multipoint nonparametric linkage analysis was performed using ALLEGRO v. 1.1b  using thp < 0.002 for the sex-specific analysis. The results for the male and female families are provided for comparison. No results reached the criteria for suggestive linkage [In Table  linkage . Of notep < 0.002 (Table p = 7.4 × 10-4), but was close. Note that the information content at this region is only 0.36, indicating that from this region only about one-third of the possible meiotic information has been extracted. Additional markers in this region would assist in increasing the meiotic information and making the estimates of allele sharing between siblings more accurate and less dependent upon the specification of marker allele frequencies.When we tested for the hypothesis that TRD would act in non-sex-specific fashion we identified three regions with 02 Table . None ofNo results for TRD reach either suggestive or significant linkage in the context of genome-wide studies . This imp = 0.0017, Table Despite the relatively weakly significant results from this study, there are some observations worthy of comment. First, of the published genome-wide linkage studies of disease-related traits in the Framingham Heart Study families, the only trait-locus pair to produce significant linkage was mean systolic blood pressure to chromosome 17 at markers GATA25A04 and ATC6A06 . In thatp < 0.002. This means that the current observation is certainly not a confirmation of our previous results. However, the mechanism(s) of TRD at any locus are generally unknown. Complex modes of inheritance for TRD have been described that at some loci depend upon the grandparental and parental origins of alleles in addition to the gender of the offspring [The region on chromosome 10 also deserves some mention Table . Using dffspring ,5. Such Finally, families selected for large sibship size may actually bias against the detection of TRD loci. The reason for this is that families with large sibships will typically have fewer spontaneous abortions due to any TRD loci than families with small sibships. Therefore the parents of large sibships are expected to have a lower frequency of TRD-causing alleles than parents of families with fewer offspring. One implication of this could be that there is lower power to detect TRD loci in families with large sibships compared to those with smaller sibships. This concern applies to the CEPH reference families that have been used in some TRD studies -5 becausIn summary, we provide some evidence for TRD loci in families from the Framingham Heart Study. Although the effects observed are not significant, they could potentially complicate the mapping of complex disease loci.


Genotype information generated by individual and international efforts carries the promise of revolutionizing disease studies and the association of phenotypes with alleles and haplotypes. Given the enormous amounts of public genotype data, tools for analyzing, interpreting and visualizing these data sets are of critical importance to researchers. In past works we have developed algorithms for genotypes phasing and tag SNP selection, which were shown to be quick and accurate. Both algorithms were available until now only as batch executables.Here we present GEVALT , a software package designed to simplify and expedite the process of genotype analysis, by providing a common interface to several tasks relating to such analysis. GEVALT combines the strong visual abilities of Haploview with our quick and powerful algorithms for genotypes phasing (GERBIL), tag SNP selection (STAMPA) and permutation testing for evaluating significance of association. All of the above are provided in a visually appealing and interactive interface.GEVALT is an integrated viewer that uses state of the art phasing and tag SNP selection algorithms. By streamlining the application of GERBIL and STAMPA together with strong visualization for assessment of the results, GEVALT makes the algorithms accessible to the broad community of researchers in genetics. Genotype information generated by individual and international efforts carries the promise of revolutionizing disease studies and the association of phenotypes with alleles and haplotypes. Given the enormous amounts of public genotype data, tools for analyzing, interpreting and visualizing these data sets are of critical importance to researchers.In past works we have developed the following analysis algorithms:1. GERBIL [. GERBIL  – an alg2. STAMPA [. STAMPA  – an alg. STAMPA .Both GERBIL and STAMPA were available until now only as batch executables. In this work we introduce GEVALT . GEVALT (Version 1.1) is an integrated software providing easy access to the GERBIL and STAMPA algorithms as well as to some other tools for genotype analysis. GEVALT is based on Haploview version 3.2  and it mGEVALT is implemented in JAVA based on the open source code of Haploview version 3.2. The analysis algorithms  are implemented in C++. Both Linux and Windows versions of GEVALT are available for download, as well as the JAVA source code.GEVALT accepts input in a variety of formats. Genotype data can be loaded as unphased genotypes in the standard linkage format, or as either partially or fully phased chromosomes. Genotype data dumps from the HapMap website  can alsoAfter phasing is completed, GEVALT generates several displays and option menus including the following:Phased genotypes: The phased genotypes of each individual are displayed. Different colors are used to indicate alleles phased by GERBIL, missing data and Mendelian errors . All other operations, such as parameter adjustments and display changes, are done with no noticeable delay even for data sets with hundreds of markers and hundreds of individuals. Gerbil can currently handle up to 300 markers, while Stampa can handle thousands of markers. Both algorithms can handle thousands of individuals.To the best of our knowledge, only two extant programs offer both algorithmic and visualization tools for genotype analysis: Haploview  and HapSWe intend to continue the development of GEVALT. In particular, we shall extend Gerbil to handle more SNPs, and improve Stampa so that it incorporates into its solution predefined tag SNPs. We also intend to incorporate a new algorithm for evaluating the significance of disease association, which is dramatically faster than the standard permutation test .GEVALT is an integrated viewer that uses state of the art phasing and tag SNP selection algorithms. It streamlines the application of GERBIL and STAMPA, which were available until now only as batch executables, and allows using them together with the strong visualizations of Haploview for assessment of the results. Both running the algorithms and visualizing the results are done within the graphical user interface, unlike, e.g., the HapScope software , which oProject name: GEVALT• Project home page: • Operating systems: Windows and Linux.• Programming language: Java and C++• Other requirements: Java 1.3 or higher.• License: free non-commercial research use license.• Any restrictions to use by non-academics: license needed for commercial use.• OD and GK contributed to the design of GEVALT. OD implemented GEVALT and GK implemented the analysis algorithms. RS supervised the project. All authors participated in the drafting and revising of the manuscript, and read and approved the final manuscript.


In our studies of genetically isolated populations in a remote mountain area in the center of Sardinia , we found that 80–85% of the inhabitants of each village belong to a single huge pedigree with families strictly connected to each other through hundreds of loops. Moreover, intermarriages between villages join pedigrees of different villages through links that make family trees even more complicated. Unfortunately, none of the commonly used pedigree drawing tools are able to draw the complete pedigree, whereas it is commonly accepted that the visual representation of families is very important as it helps researchers in identifying clusters of inherited traits and genotypes. We had a representation issue that compels researchers to work with subsets extracted from the overall genealogy, causing a serious loss of information on familiar relationships.To visually explore such complex pedigrees, we developed PedNavigator, a browser for genealogical databases properly suited for genetic studies.The PedNavigator is useful for genealogical research due to its capacity to represent family relations between persons and to make a visual verification of the links during family history reconstruction. As for genetic studies, it is helpful to follow propagation of a specific set of genetic markers (haplotype), or to select people for linkage analysis, showing relations between various branch of a family tree of affected subjects.PedNavigator is an application integrated into a Framework designed to handle data for human genetic studies based on the Oracle platform. To allow the use of PedNavigator also to people not owning the same required informatics infrastructure or systems, we developed PedNavigator Lite with mainly the same features of the integrated one, based on MySQL database server. This version is free for academic users, and it is available for download from our site  Acquiring, storing and manipulating genealogical information is an important issue in human genetic research. In our studies of genetically isolated populations in a remote mountain area in the center of Sardinia  called Ogliastra , we had When the descent of so many people is being investigated, the problem of how to handle huge pedigrees arises, as genealogies taken into account can be composed of up to thousands of individuals and typically include loops, multiple mates and several related families. The problem is how to give a clear picture of family relationships by means of a graphical representation in order to highlight internal organization of pedigrees that is also easy to understand. To address this point, researchers usually deal with pedigrees using software like: Cyrillic, Cherwell Scientific, 2000; Progeny, Progeny Corp, 2000; GAP, Epicenter Software, 2000; CoPE, GIS Infobiogen, 1999 . These pIn order to give researchers a suitable support for navigating complex genealogical relations, we implemented a web-based application called PedNavigator (from a contraction of "Pedigree Navigator") -designed "ad hoc" to facilitate such a difficult task. With PedNavigator a user can easily navigate pedigrees by simply clicking on the desired person to expand branches of her/his pedigree. In this way, navigation becomes an easy task also with extensive pedigrees. The application is integrated with our Oracle database, giving researchers the opportunity of enriching each person's pedigree with the corresponding demographic, genetic, clinical and phenotypic data. A previous version of PedNavigator is depicted in , whereasPedNavigator can be installed on a web server (like Apache Tomcat) and can be consulted through Internet browsers supporting DHTML. The main page of PedNavigator is divided into two parts: (i) the upper side contains a browsable graphical representation of a pedigree , entrusted with actually drawing the pedigree. Both sub-systems are illustrated below in greater detail.From an architectural perspective, the application is composed by two sub-systems: the Query Sub-System, devised to query the genealogical database, together with the Layout Sub-System  Snowflake (SF)(2) Snowflake with Sibs (SFWS)(3) Direct Ancestors (DA)(4) Full Descendant Tree (FDT)(5) Direct Paternal Descendants (DPD)(6) Direct Maternal Descendants (DMD)(7) Minimum Common Ancestor (MCA)(8) Minimum Common Ancestor Paternal Lineage (MCAPL)(9) Minimum Common Ancestor Maternal Lineage (MCAML)The SF visit mode recursively includes all persons directly related with the person being investigated, by following downward and upward relationships until a given depth is reached, like a snowflake where the centre is the selected person. The SFWF is similar but with the addition of sibs of the extracted persons. The DA mode acts according to the classic pedigree representation, in which the ancestors of an individual are shown. The FDT mode supplies the descendants of an individual, including mates of everyone, if present. The DPD and DMD modes follow descendants according to paternal or maternal lineage, and is often used in genealogical studies to inquire on the spread of the surname or to support the Y-chromosome and mitochondrial DNA studies. The MCA builds a pedigree showing the minimum path linking two selected individuals, where founders are their minimum common ancestors. The MCAPL and MCAML are variants of MCA and follow paths containing only maternal or paternal lineages. It is worth pointing out that, for each visit mode, a search depth can be specified -in order to limit the number of persons included in a pedigree's representation and to increase its graphical clarity. As depicted in Figure The layout sub-system is devoted to graphically represent pedigrees extracted by the previous sub-system. As shown in Figure A pedigree is internally represented by a directed graph: an abstract data type defined by a set of nodes and arcs, useful for modelling hierarchical networks. In particular, nodes (vertices) represent individuals, whereas arcs (edges) represent family ties. Provided that arc orientations are suitably chosen, any graph obtained from a pedigree is acyclic; thus, pedigrees can be suitably represented by hierarchical directed acyclic graphs (DAGs) and we can use algorithms taken from graph theory for handling pedigrees.et al. [In the literature, different algorithms have been proposed to draw hierarchical DAGs. The underlying heuristics is usually devoted (i) to minimize the intersections between arcs, and (ii) to distribute nodes homogeneously. The complexity of the problem being NP-hard, we implemented a layout algorithm according to Sugiyama et al. . This alAs for the first step, the natural order of nodes between genealogical generations promotes an efficient separation of vertices in separate ranks. In this case, some additional constraints hold: e.g., a daughter / son must belong to a generation inferior than the one of her / his parents and the siblings must belong to the same generation. As a result, every node is assigned to a non-ambiguous Y position within the virtual grid.et al. [O(n), that applies scale factors to regulate total dimensions of the image, minimizing superimpositions of the text associated to each node. The resulting bitmap can now be inserted in the HTML page that represents the PedNavigator user interface.The second step highly affects the quality of a pedigree layout. Due to its intrinsic complexity the second step yields sub-optimal solutions, as suitable heuristics must be adopted to reduce the computational effort and time. In order to do that, we implemented some procedures described by Gansner et al. ,8. Origiet al. . Before We implemented PedNavigator according to the client / server model; i.e., clients carry out requests to the web application server where the PedNavigator is installed, which in turn interrogates the database server. Following the principle of maximum portability, we wrote PedNavigator entirely in Java, also taking advantage of the Servlet technology, widely acknowledged as the "state of art" for dynamic web page generation. The Apache Tomcat Application Server, available under the GPL license for most operating systems, has been adopted as the web application server. To access the genealogical database, we adopted the standard JDBC Java package, which is an abstraction layer devised to perform SQL queries independently from the database vendor. On the other hand, while remaining compatible with the most widely used web browsers, the client side of the user interface takes advantage of small JavaScript scripts aimed at improving the quality of the user interface.Our research is focused on the isolated population of several villages of Ogliastra because they present extremely advantageous characteristics for complex-trait studies. Our approach is family-based and the person is the key, but we must confront some daunting problems in our effort to fully use the data. The existence and accessibility of both ancient and recent archives  lets us reconstruct, in principle, the complete genealogy of the entire population of each village. This is an important prerequisite to build large genealogies which connect many selected individuals, chosen according to their phenotypes.We needed something intuitive yet powerful to allow us to fully use this unprecedented wealth of genealogical data. Thus, we created PedNavigator to easily represent deep-rooted complex pedigrees with which the researcher can interact and better explore links between individuals to find even distant relationships. This intuitive informatics tool allows us to reconstruct, with an excellent degree of accuracy, genealogies of the villages since the early 1600's. What's more, our genealogies have been cross-validated with the study of mitochondrial DNA and the Y chromosome, identifying also ancient founders and their progeny . Thanks PedNavigator has been used in the first phase of the genealogical data collection, to perform a visual verification of existing ties between individuals. In this way, the data entry activity has been greatly facilitated, with particular reference to the activity of checking whether the family ties between individuals have been correctly entered or not. In a subsequent phase, it has been used to follow the propagation of a selected haplotype throughout parenthood ties, so that possible genotypic mistakes can be easily located. Currently, thanks to further visualization options , PedNavigator has the capacity to select individuals for linkage analysis, showing relations (within various branches of a family tree) among affected subjects.


We introduce a method for the analysis of multilocus, multitrait genetic data that provides an intuitive and precise characterization of genetic architecture. We show that it is possible to infer the magnitude and direction of causal relationships among multiple correlated phenotypes and illustrate the technique using body composition and bone density data from mouse intercross populations. Using these techniques we are able to distinguish genetic loci that affect adiposity from those that affect overall body size and thus reveal a shortcoming of standardized measures such as body mass index that are widely used in obesity research. The identification of causal networks sheds light on the nature of genetic heterogeneity and pleiotropy in complex genetic systems. Disease states are often associated with multiple, correlated traits that may result from shared genetic and nongenetic factors. Genetic analysis of multiple traits can reveal a network of effects in which each trait is influenced by more than one genetic locus (heterogeneity) and different traits share one or more loci in common (pleiotropy). Physiological interactions independent of genetic factors may also contribute to the observed correlations. Structural equation modeling is proposed as a statistical method to characterize the architecture of multiple trait genetic systems. Application of structural equation modeling to body size, adiposity, and bone geometry traits illustrates how the effects of a genetic locus can be decomposed along direct and indirect paths that may be mediated through interactions with other traits. Using this technique the authors identify adiposity loci that act independently of loci affecting overall body size. The most common and pervasive human health problems, including heart disease, osteoporosis, diabetes, and cancer, result from the complex interaction of multiple genetic and environmental factors. Disease states are often associated with multiple, correlated traits, referred to as subphenotypes. The ability to assay subphenotypes of a disease state presents a unique opportunity to investigate the mechanisms underlying disease susceptibility and progression . ObserveThe genetic analysis of complex traits is facilitated by the study of inbred line crosses using animal models, typically rodents. The genetically varied progeny from a cross can be reared in a controlled environment, and multiple quantitative phenotypes that are relevant to a disease outcome can be measured in individual animals . GeneticMultivariate analysis of quantitative traits can be used to investigate the structure of a genetic system that includes allelic variation at multiple loci, intermediate phenotypes, and disease states . Jiang aStructural equation models (SEMs), also known as path models , are relHerein, we propose a SEM approach to analyze complex genetic systems using mouse inbred crosses. SEM methodology has been applied in several studies of human inheritance with the aim of improving QTL detection –19. The The SM × NZB intercross population of 260 female and 253 male mice was raised on an atherogenic diet for 16 wk starting at 8 wk of age. At 24 wk we obtained total body weight and weights of the inguinal, gonadal, peritoneal, and mesenteric fat pads. Lean body weight was computed by subtracting the total of the fat pad weights from the body weight. In the analyses described here, all traits were square-root transformed to obtain the best linear relationships. Additional information on husbandry, phenotyping, and genotyping of this cross can be found in Stylianou et al. .The NZB × RF intercross population consists of 661 female mice raised on standard (4% fat) diet. At 10 wk of age, femurs were isolated and their geometric properties were determined by peripheral quantitative computed tomography. We consider body weight and two bone geometry traits, femur length and the periosteal circumference of the femur (PCIR). All traits were log transformed to obtain the best linear relationships. Additional information on this cross can be found in Wergedal et al. .http://www.jax.org/staff/churchill/labsite/datasets/qtl/qtlarchive.The Institutional Animal Care and Use Committee of The Jackson Laboratory approved all experimental protocols. All data used in this study are available at structural equations, that define the interactions among the variables. In the graphical representation of a SEM, a variable with an arrow pointing to it is termed an endogenous variable, which is similar to a response or dependent variable in regression terminology. An endogenous variable is causally affected by the state of at least one other variable in the model. A variable without an arrow pointing to it is termed an exogenous variable, which is similar to an independent variable or predictor in regression terminology. Exogenous variables are upstream of all causal effects in the model. Variables that are connected through a single edge in the graphical model are said to have direct path. An effect that is mediated through other measured variables is represented by an indirect path with more than one edge. Variables may be connected by more than one path. The sign and magnitude of the direct effects in the graphical model are represented by path coefficients in the structural equations.In structural equation modeling, variables are standardized by centering on sample means. Thus the variances and covariances are the parameters of interest. The key idea behind SEM is that causal relationships among the variables determine the expected pattern of correlations . A SEM rθ is a vector of model parameters that includes path coefficients, variances of all exogenous variables, and covariances for all pairs of exogenous variables; p is the number of variables included in the model; Σ is the predicted covariance matrix and is implicitly a function of the model parameters; S is the observed covariance matrix; and |X| denotes the determinant of a matrix X. The number of unique elements in a covariance matrix is p(p + 1)/2 due to symmetry, and the number of model parameters is denoted by q. Intuitively, the parameter values are chosen to give a predicted covariance matrix that is as similar as possible to the observed covariance matrix, subject to the constraints imposed by the structural equations. A critical quantity in determining our ability to fit and assess a model is the residual degrees of freedom (df), where df = p(p + 1)/2 − q. If the residual df are less than 1, the model has as many or more parameters than data points and thus the goodness-of-fit cannot be assessed.The endogenous variables in a SEM are assumed to follow a multivariate normal distribution, while exogenous variables can be either continuous or categorical. The maximized log likelihood function takes the form ,26:wherTo illustrate causal inference in the context of QTL mapping, consider the possible relationships between a genetic locus, Q, and two correlated traits, A and B, as in Causal effects from a QTL to a phenotype have a defined direction. The causal inference follows as a consequence of meiotic randomization of genetic factors in the inbred line cross. The causal inference can be extended to include the relationships among phenotypes by considering both the unadjusted and partial correlation relationships among the variables. For example, in model M7, Q and A are unconditionally independent. However, conditioning on B will result in a nonzero partial correlation. By contrast, in M8, Q and A will be unconditionally correlated. Conditioning on B breaks the causal chain from Q to A, and their partial correlation will be zero. When all three variables are causally connected, as in models M1–M3, the raw and partial correlations will all be nonzero, but they will change in magnitude depending on the signs of the path coefficients. The relationships among the various raw and partial correlations are subject to statistical fluctuations but they can be captured in the log of odds ratio (LOD) scores, as described below, and these form the basis for constructing multilocus SEMs.The process of developing a SEM for genetic mapping data is described in five steps, below. Steps 1 and 2 involve QTL detection and they employ standard QTL detection methods and serve the purpose of identifying the variables that will be used in the structural modeling. Once the QTL have been identified, their genotypes are imputed  and the Y is a vector of trait values, β0 is the population mean, Q is a vector of QTL genotypes, β1 is the QTL effect, and ɛ is the residual vector. The location of the QTL is scanned over the entire genome and a LOD score  is used to determine if a QTL is present. If covariates, such as sex, are important predictors of the trait values, these should be included in the linear model underlying the genome scans [We use genome scans to identify the genetic loci that will be included in the SEM . A singlme scans . In addime scans .X is the conditioning variable and β2 is the effect of X on the response Y, adjusted for the Q effect.In this step we perform conditional genome scans using one trait as a covariate in the analysis of another trait. The choice of which trait(s) to use as covariates may be dictated by the known biological relationships among the traits, or it may be carried out systematically. In this setting, factors that are believed to be upstream in causal pathways should be employed as conditioning variables. The linear model used in the conditional genome scans isX is causally connected to Q and to Y. We use a critical value of 2.0 as a guideline, corresponding to a 0.05 type I error rate based on simulations in which the conditioning variable is unrelated to the response. The significance of these edges will be evaluated further in subsequent steps.Comparison of the unconditioned and conditioned scans may reveal a substantial change in the LOD score at a locus. If the change (ΔLOD) is large in absolute value, this suggests that the variable The direction of change in the LOD score upon adjustment for a covariate depends on the signs of QTL effects on the trait and on the covariate, as well as the sign of the path coefficient connecting the trait and the covariate. When both the direct and indirect paths share the same sign, the LOD score in the conditional scan will be smaller than the unconditional LOD score. When the direct path and the indirect path have opposite effects, the conditional LOD score will be greater than the unconditional LOD score. In this case, the direct and indirect effects cancel one another and the QTL effect is reduced in the unconditional scan. It follows that changes in the LOD upon conditioning can be used to infer the sign of QTL effects along different paths.In the graphical SEM, each measured trait is represented as a node; QTLs identified in steps 1 and 2 are also included as nodes. Edges should be directed from the QTL nodes to the corresponding traits. When a significant ΔLOD value is observed, edges should be directed from the QTL to each of the traits, and an edge from the conditioning trait to the response should also be added. The significance and causal direction of these edges should be examined in model refinement (step 5).In many instances, a SEM that includes only measured variables will be sufficient. However, latent variables  represenN − 1)F(θ), where N is the sample size and F(θ) is defined in Equation 1. It follows a χ2 distribution with df p(p + 1)/2 − q. Significant values (p < 0.05) indicate that the model does not provide a good fit to the data. Each path coefficient should be individually significant (p < 0.05) using a t-test . The maximum standardized residual difference between the observed and predicted covariance matrices should be small. The root mean square error of approximation measures the lack of fit of the model to the theoretic population covariance matrix and values of 0.05 or less indicate an acceptable fit. A model that does not provide an accurate prediction of the observed covariance should be refined.This step involves a comparison of the predicted and observed covariance matrices, t-tests for individual path coefficients, and consideration of other model diagnostics. The goodness-of-fit test statistic is  , providep-value associated with the goodness-of-fit test should be greater than 0.05; (3) the largest standardized residual should not exceed 2.0 in absolute value; (4) individual path coefficients should be significantly different from zero based on the t-test; (5) standardized path coefficients should not be trivial ; and (6) a substantial proportion of phenotypic variance of the endogenous variables should be explained by the model. If all of these standards are met, we may conclude that the model provides a reasonable description of the data.Model refinement and assessment (steps 4 and 5) are often carried out iteratively. A final model should meet several standards : (1) it In the context of an intercross (F2) population, each QTL has three possible genotypic states. We can assume intralocus additivity by encoding genotypes as 0, 1, or 2, and treating these scores as a continuous variable in the SEM. Alternatively, the genetic effect is represented as a pair of 0,1 (dummy) variables. The most widely used parameterization, following Cockerham , partitiOne important feature of SEM is that direct and indirect effects of a QTL on a trait can be distinguished, and the relative strengths of effects along different paths can be calculated and compared ,21. The We note that the sign of a path coefficient from a QTL to a trait is determined by the choice of the reference genotype (encoded as zero). If the effect of an allelic substitution away from the reference is to increase the mean trait value, the sign of the path coefficient is positive. If allelic substitution away from the reference causes the trait value to decrease, the sign is negative. In the examples below, the homozygous NZB genotype is our reference. The same interpretation applies to path coefficients for categorical covariates such as sex. In the models below we have used female as the reference.Genome scans were carried out in the MATLAB software environment  using the pseudomarker package (v2.02) . Scans wWe first consider the problem of defining a measure of adiposity. Fat pad weights and lean body weight are positively correlated in the SM × NZB cross population. Fat pad weight by itself is inadequate as a measure of obesity. Two animals with similar fat pad weights may have different body size such that one animal is considered obese and the other not. Thus it is important to consider the fat pad weight relative to the size of the animal. In our analysis we used the lean body weight as surrogate for size. The lean body weight is computed by subtracting the weights of the four major fat pads from the total body weight and thus will include a small contribution from other adipose tissues.adiposity index as the ratio of fat pad weight to lean body weight. Second, one could regress fat pad weight on lean body weight and consider the deviation from the regression line  as a measure of adiposity. Although the regression approach is clearly preferred, ratio standardization is still widely used [(y = bx) between the variables, which implies that the regression line relating these traits should pass through the origin. One might argue that a hypothetical animal with zero lean body mass should also have a fat pad mass of zero. However, the argument is fallacious, as it extrapolates beyond the range of the data over which the linear approximation is valid. Regression standardization allows one additional df in the form of an intercept term (y = a + bx). The relationship of mesenteric fat pad weight to lean body weight is shown graphically in There are two common approaches to defining a relative measure. First, one could compute an ely used ,35. To sA genome scan of the mesenteric fat pad weight (with sex as an additive covariate) reveals significant QTLs on Chromosomes 1, 17, and 19 A. A secoWe note here that a genome scan of the adiposity index (unpublished data) reveals only two significant QTLs, one on Chromosome 19 and the other on Chromosome 1, and there are no suggestive QTLs. As indicated below, these two loci primarily affect the overall body size and are not specifically impacting adiposity. Genome scans for all four fat pad traits are provided in p < 0.05, genome-wide adjusted) in at least one of the genome scans and any suggestive QTLs that have significant ΔLOD values. Directed edges from each QTL to the corresponding trait are included in the graphical SEM. QTLs with a ΔLOD exceeding 2 in absolute value are connected with directed edge to both traits. In addition, a directed edge is tentatively connected from lean body weight to the fat pad weight. We used an additive model of the genetic effects. This initial model is assessed and refined, using the steps described in Materials and Methods, to arrive at the model shown in As a starting point for the development of a SEM we consider all of the QTLs that are significant (t = 1.48) indicates that the path coefficient from mesenteric fat pad weight to lean body weight is nonsignificant. M1 also has the smallest CAIC value . In addition, M1 has the smallest CAIC value relative to other models. We conclude that model M1 provides the best description of these data.Body weight and bone geometry phenotypes are known to be associated but the causal relationships among them are largely unknown . Here weThe graphical SEM is shown in In experimental crosses, meiosis serves as a randomization mechanism that distributes naturally occurring genetic variation in a combinatorial fashion among a set of cross progeny. Genetically randomized populations share the properties of statistically designed experiments that provide a basis for causal inference. This is consistent with the notion that causation flows from genes to phenotypes. We propose that the inference of causal direction can be extended to include relationships among phenotypes and demonstrate that causal hypotheses can be tested. When models are nested, likelihood ratio tests can be applied. For non-nested sets of models, penalized likelihood methods such as AIC or CAIC can be used to identify good models. However, the credibility of any causal hypothesis must be judged by biological standards and not solely on statistical evidence. From this perspective, we view SEM as a device for generating causal hypotheses to be tested by subsequent experimentation.As descriptive models, SEMs are useful for identifying the nature of pleiotropic QTL effects. The phenotypes that we choose to measure and the QTLs that we detect will rarely, if ever, occur in one-to-one correspondence. Allelic variation at a locus will often impact multiple traits, and these effects may be mediated through multiple physiological pathways. SEMs provide a quantitative description of the entire system of QTLs and phenotypes. In our analysis of the SM × NZB fat pad data we identified distinct classes of QTLs that affect body size and adiposity. The SEM analysis reveals a shortcoming of standardized variables, such body mass index and adiposity index, that are widely used in obesity research. This suggests that a reexamination of obesity QTLs in the literature may be worthwhile. The SEM is able to distinguish QTLs that affect adiposity from those that affect body size, whereas standardized measures could confound these two distinct types of effects.Specification of a good initial model is perhaps the most important step in structural equation modeling of genetic data. We have developed a strategy to specify the initial model based on genome-wide QTL scans with conditioning on intermediate phenotypes. For the data examined here, these initial models fit reasonably well and final models were obtained with minor or no refinements. Our model development strategy incorporates elements of both exploratory and confirmatory SEM, because the initial model structure has been shaped by considering the same data that are used to assess and refine the SEM. Goodness-of-fit criteria are most informative regarding a lack of fit, and are subject to the error of overfitting. In the models presented here, most of the residual df derive from the known structure of linkage among QTLs. We used additive genetic models, but also described approaches to include dominance and epistasis . AlthougSample size is an important consideration for both QTL mapping and for structural modeling. We recommend using at least 200 mice in an intercross mapping design to ensure that all large to moderate effect QTL are detected. Structural modeling relies on estimated variances and covariances and sample size will determine the precision of these estimates. Guidelines developed for SEM suggest that the sample size should be at least five, and preferably ten times the number of variables in the model . RealistAwareness of the limitations of any model is essential to its proper interpretation. Genetic mapping in line crosses provides only coarse resolution, and any apparently singular QTL may represent the composite effects of several tightly linked polymorphic loci. Tight linkage may be misinterpreted as pleiotropy. Important QTLs or epistatic interactions may not be detected and critical physiological parameters may not have been measured. When important components of a system are missing, correlations or spurious effects may be induced that would otherwise not be inferred. For example, significant covariances among residual errors for all of the fat pad traits suggest that nongenetic factors may be involved. Food intake is a plausible source of the correlated variation. Latent variables are useful when multiple traits are highly correlated and are presumed to share a common causal factor that is not directly measured, or one that is not measurable.Structural equation modeling provides a powerful descriptive approach to the genetic analysis of multiple traits. SEMs allow characterization of pleiotropic and heterogeneous genetic effects of multiple loci on multiple traits as well as the physiological interactions among traits. With both graphical and algebraic representations, SEMs provide an intuitive and precise description of the genetic architecture of a complex system.Figure S1Genome-wide scans for inguinal (A), gonadal (B), peritoneal (C), and mesenteric (D) fat pad traits, based on a single QTL model. Through (A) to (D), the top scan is unconditioned for lean body weight; the middle scan is conditioned for lean body weight; and the bottom scan is the difference in LOD scores between conditioning and unconditioning. ING, inguinal fat pad weight; GON, gonadal fat pad weight; LBWT, lean body weight; MES, mesenteric fat pad weight and PERI, peritoneal fat pad weight. Phenotypes are square root transformed.(585 KB PDF)Click here for additional data file.Figure S2Structural equation models for inguinal (A), gonadal (B), peritoneal (C), and mesenteric (D) fat pad traits. See (521 KB PDF)Click here for additional data file.Table S1(29 KB DOC)Click here for additional data file.Table S2(28 KB DOC)Click here for additional data file.Table S3(28 KB DOC)Click here for additional data file.Table S4(29 KB DOC)Click here for additional data file.


We used genotype and phenotype data from the Framingham Heart Study to perform a full-genome scan for quantitative trait loci underlying the metabolic syndrome.Because high blood pressure, altered lipid levels, obesity, and diabetes so frequently occur together, they are sometimes collectively referred to as the metabolic syndrome. While there have been many studies of each metabolic syndrome trait separately, few studies have attempted to analyze them Heritability estimates for all of the covariate-adjusted and age- and gender-standardized individual traits, and the composite metabolic syndrome trait, were all fairly high (0.39–0.62), and the composite trait was among the highest at 0.61. The composite trait yielded no regions with suggestive linkage by Lander and Kruglyak's criteria, although there were several noteworthy regions for individual traits, some of which were also observed for the composite variable.Despite its high heritability, the composite metabolic syndrome trait variable did not increase the power to detect or localize linkage peaks in this sample. However, this strategy and related methods of combining correlated individual traits deserve further investigation, particularly in settings with complex causal pathways. Coronary artery disease (CAD) and related cardiovascular diseases are genetically complex and heterogeneous. Several identified risk factors for CAD, including diabetes mellitus, arterial hypertension, hypercholesterolemia, and obesity also show strong and at least partially independent genetic components . To dateA particular complication to the identification of novel CAD genes is the high correlation among cardiovascular risk factors. In fact, because high blood pressure, altered lipid levels, obesity, and diabetes so frequently occur together, they are sometimes collectively referred to as the metabolic syndrome or syndrome X (MSX ). BecausOur study utilizes genotype and phenotype data from the Framingham Heart Study, made available for the Genetic Analysis Workshop 13 (GAW13), to search for quantitative trait loci (QTL) underlying MSX in this large, carefully followed sample. Specifically, we defined five MSX-related quantitative traits across the life-span (systolic blood pressure (SBP), triglycerides (TGL), high-density lipoprotein cholesterol (HDL), blood sugar (BS), and body mass index (BMI), calculated their heritabilities, and performed whole-genome scans on each. We then combined the individual quantitative traits into a composite quantitative trait, the metabolic syndrome score (MSS), and calculated its heritability and scanned the genome for linkage.complete observations available for each subject varied from one (n = 116) to five (n = 524), with a mean of 3.7 observations per subject. Of these 1617 individuals, 1313 also had genotype data available.From the data provided for Problem 1 in the GAW13 data set (Framingham Heart Study), we selected the 1617 individuals between the ages of 30 and 69 with at least one examination cycle in which there was complete data for all five component measures . These age limits were chosen because our preliminary analyses, consistent with the cardiovascular literature, suggested that heritability was greatest in this interval, and because the data tended to be sparse at lower and higher ages. We used all available complete observations  from age 30 to 69 for each individual, and developed a life-span measure for each trait, as described below. The number of 2 (m)] were approximately normally distributed, so we used the raw values. TGL was log-transformed to better approximate a normal distribution. BS was markedly skewed and leptokurtotic, so we followed the procedure used by Meigs et al. . HDL was subtracted from the score because it is protective against CAD, and tends to be inversely correlated with the other component traits; thus, lower HDL values correspond to a higher MSS. These resulting sums were then averaged to create a lifespan MSS. The MSS as calculated yields a lifetime score for each individual that is an indication of how his or her MSS deviates from the age and gender mean.To generate an MSS for each of the subjects' available observations, we combined the standardized residuals for each component trait Heritability estimates were calculated, controlling for average age and gender at which subjects contributed data, for each of the component traits, and for the MSS composite trait, using the variance-components methods implemented in SOLAR . We thenDescriptive statistics for raw values of each of the component traits, prior to covariate adjustment and standardization procedures, are provided in Table p < 0.00001).Heritability estimates for the individual component traits were all fairly high, ranging from 0.39 to 0.62, and MSS was at the high end of this range at 0.61 . How. How16])Despite its high heritability, the relatively crude estimate of a composite metabolic syndrome variable (MSS) did not increase our ability to detect or localize linkage peaks in this sample. Not surprisingly, the only two noteworthy signals for MSS appear to be driven by linkages to its component traits . Nonetheless, we feel that similar strategies, bucking the current trend toward disaggregation of complex phenotypes, may merit further exploration in this and other settings with complex causal pathways marked by extensive correlation among intermediate causes. If this approach is to succeed, it will be critical to develop weighting schemes that more accurately represent the contribution of each trait to the overall syndrome.


Rough set theory and decision trees are data mining methods used for dealing with vagueness and uncertainty. They have been utilized to unearth hidden patterns in complicated datasets collected for industrial processes. The Genetic Analysis Workshop 14 simulated data were generated using a system that implemented multiple correlations among four consequential layers of genetic data . When information of one layer was blocked and uncertainty was created in the correlations among these layers, the correlation between the first and last layers (susceptibility genes and the disease trait in this case), was not easily directly detected. In this study, we proposed a two-stage process that applied rough set theory and decision trees to identify genes susceptible to the disease trait. During the first stage, based on phenotypes of subjects and their parents, decision trees were built to predict trait values. Phenotypes retained in the decision trees were then advanced to the second stage, where rough set theory was applied to discover the minimal subsets of genes associated with the disease trait. For comparison, decision trees were also constructed to map susceptible genes during the second stage. Our results showed that the decision trees of the first stage had accuracy rates of about 99% in predicting the disease trait. The decision trees and rough set theory failed to identify the true disease-related loci. Data mining approaches have been applied to different areas to derive useful and comprehensive knowledge. Methods focusing on functionalities of data mining, such as classification, prediction, association, and clustering, have been developed . Varianta, b, c, ...,l, were given for each subject. A total of 917 SNP markers, spaced 3 cM apart, were provided on 10 chromosomes. In addition, a genome screen of 416 microsatellite markers, spaced 7 cM apart, was also given. In this study, only the SNP datasets of the first 10 replicates were analyzed. Simulated data answers were revealed after the analysis was done.The GAW14 simulated data was generated to represent diseased families sampled from four geographically diverse sites, Aipotu, Karangar, Danacaa, and New York City, with varied criteria for diagnosis of KPD. Subjects from these four sites had different living environments and ethnic backgrounds. One hundred replicates were generated. In each replicate, 100 nuclear families were collected from each of the first three sites and 50 extended families from the fourth site. In addition to the KPD affected status, 12 KPD-related phenotypes, labeling as  was used to build the decision tree. The choice of pruning confidence affects how the error rates were estimated and hence the severity of pruning; values smaller than the default (25%) cause more of the initial tree to be pruned, while larger values resulted in less pruning. In this study, the pruning confidence level was set at 25%. The GAW14 simulated data was transformed into an appropriate format for the software. The KPD affected status and the 12 phenotypes were coded as 0 and 1 for unaffected and affected; SNP genotypes 11, 12, and 22 were coded as 1, 2, and 3, respectively.A decision tree is often constructed based on some attributes to divide a group of subjects into more homogenous subgroups with respect to the target outcome variable. Briefly, a decision tree is built using a recursive partitioning process and a pruning process. Initially, a root node is built to represent the entire group. Then two leaf nodes are constructed, each representing a subgroup with a specific character of a selected attribute. At each level of tree construction, entropy was employed to calculate the information gain of each attribute. The attribute with the maximal information gain was chosen as a node at that level. The process continued until we got to the end of the branch. Then, each branch was defined as the leaf of the selected attribute. A route stemmed from the root to the leaf is defined as a rule. The attribute closer to the tree root is the most important decision factor for the rule. The pruning process for a decision tree was to replace a whole sub-tree with a leaf node. The replacement took place if a decision rule was established such that the expected error rate in the sub-tree was greater than in the single leaf. With this approach, the final decision tree was built. In this study, the C4.5 Release 8 software 1, X4, X6, X7} for D = 1 and Class 2 = {X2, X3, X5, X8} for D = 2. The set of attributes that discerns the elementary set {X1, X2} contains attribute a2 and a4, which will be put into the discernibility matrix (Table Rough set theory (RST), introduced by Pawlak , has beefA (D) =  (a2)=  a2 = a1a2+a2a4f(A) is a Boolean function, constructed as follows: a1a2 represented as a1 ∧ a2, i.e., a1 and a2, and  represented as (a1 + a2) or it can be represented as (a1 or a2). The functions a1a2 found from the above calculation can represent the original information system. Using a1a2 as an example, (deleted attributes a3 and a4), we represent our system in Table The so-called discernibility function For the second stage of this study, the KPD affected status and the 12 phenotypes were treated as decision variables. SNP genotypes 11, 12, and 22 were coded as 1, 2, and 3 respectively. The significant conditional attributes retained in the decision rules could be seen as the genes susceptible to the corresponding trait.At the first stage, based on the phenotypes of subjects and their parents, classification trees were built to predict trait values. Phenotypes retained in the decision trees were then advanced to the second stage where RST was applied to discover the minimal subsets of genes associated with the disease trait. For comparison, decision trees were also constructed to map susceptible genes at the second stage. In addition, phenotypes not significantly associated with the KPD affected status were also analyzed at the second stage. Analysis was done for each of the four groups as well as for the pooled data of the four groups. SNPs on a same chromosome were analyzed at the same time. Genome scans were performed by analyzing the pooled set of the significant SNPs across the 10 chromosomes.b and h were the most common effects shown in the decision trees across groups . More nodes were needed to construct decision trees in the NYC group than in the other three groups  for identifying SNPs with various levels of penetrance rates.Our results showed that the decision trees at the first stage had accuracy rates about 99% in predicting the disease trait. The application of the decision trees and RST failed to identify some disease-related loci.GAW14: Genetic Analysis Workshop 14KPD: Kofendrerd Personality DisorderRST: Rough set theoryL-YW participated in the study design, carried out the analysis, and drafted the manuscript. C-LH participated in the study design, developed the algorithms, and helped to draft the manuscript. C-HC participated in study design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.