Comparison of Haseman-Elston regression analyses using single, summary, and longitudinal measures of systolic blood pressure

To compare different strategies for linkage analyses of longitudinal quantitative trait measures, we applied the "revisited" Haseman-Elston (RHE) regression model (the cross product of centered sib-pair trait values is regressed on expected identical-by-descent allele sharing) to cross-sectional, summary, and repeated measurements of systolic blood pressure (SBP) values in replicate 34, randomly selected from the Genetic Analysis Workshop 13 simulated data. RHE linkage scans were performed without knowledge of the generating model using the following phenotypes derived from untreated SBP measurements: the first, the last, the mean, the ratio of the change between the first and last over time, and the estimated linear regression slope coefficient. Estimates of allele sharing in sibling pairs were obtained from the complete genotype data of Cohorts 1 and 2, but linkage analyses were restricted to the five visits of Cohort 2 siblings. Evidence for linkage was suggestive (p < 0.001) at markers neighboring SBP genes Gb35, Gs10, and Gs12, but weaker signals (p < 0.01) were obtained at markers mapping close to Gb34 and Gs11. Linkage to baseline genes Gb34 and Gb35 was best detected using the first SBP measurement, whereas linkage to slope genes Gs10-12 was best detected using the last or mean SBP value. At markers on chromosomes 13 and 21 displaying strongest linkage signals, marginal RHE-type models including repeated SBP measures were fit to test for overall and time-dependent genetic effects. These analyses assumed independent sib pairs and employed generalized estimating equations (GEE) with a first-order autoregressive working correlation structure to adjust for serial correlation present among repeated observations from the same sibling pair.     

Segregation and linkage analysis for longitudinal measurements of a quantitative trait

We present a method for using slopes and intercepts from a linear regression of a quantitative trait as outcomes in segregation and linkage analyses. We apply the method to the analysis of longitudinal systolic blood pressure (SBP) data from the Framingham Heart Study. A first-stage linear model was fit to each subject's SBP measurements to estimate both their slope over time and an intercept, the latter scaled to represent the mean SBP at the average observed age (53.7 years). The subject-specific intercepts and slopes were then analyzed using segregation and linkage analysis. We describe a method for using the standard errors of the first-stage intercepts and slopes as weights in the genetic analyses. For the intercepts, we found significant evidence of a Mendelian gene in segregation analysis and suggestive linkage results (with LOD scores >or= 1.5) for specific markers on chromosomes 1, 3, 5, 9, 10, and 17. For the slopes, however, the data did not support a Mendelian model, and thus no formal linkage analyses were conducted.     

Increasing genotype-phenotype model determinism: application to bivariate reading/language traits and epistatic interactions in language-impaired families

While advances in network and pathway analysis have flourished in the era of genome-wide association analysis, understanding the genetic mechanism of individual loci on phenotypes is still readily accomplished using genetic modeling approaches. Here, we demonstrate two novel genotype-phenotype models implemented in a flexible genetic modeling platform. The examples come from analysis of families with specific language impairment (SLI), a failure to develop normal language without explanatory factors such as low IQ or inadequate environment. In previous genome-wide studies, we observed strong evidence for linkage to 13q21 with a reading phenotype in language-impaired families. First, we elucidate the genetic architecture of reading impairment and quantitative language variation in our samples using a bivariate analysis of reading impairment in affected individuals jointly with language quantitative phenotypes in unaffected individuals. This analysis largely recapitulates the baseline analysis using the categorical trait data (posterior probability of linkage (PPL) = 80%), indicating that our reading impairment phenotype captured poor readers who also have low language ability. Second, we performed epistasis analysis using a functional coding variant in the brain-derived neurotrophic factor (BDNF) gene previously associated with reduced performance on working memory tasks. Modeling epistasis doubled the evidence on 13q21 and raised the PPL to 99.9%, indicating that BDNF and 13q21 susceptibility alleles are jointly part of the genetic architecture of SLI. These analyses provide possible mechanistic insights for further cognitive neuroscience studies based on the models developed herein.     

Genome-wide linkage scan for genes affecting longitudinal trends in systolic blood pressure

Only one genome scan to date has attempted to make use of the longitudinal data available in the Framingham Heart Study, and this attempt yielded evidence of linkage to a gene for mean systolic blood pressure. We show how the additional information available in these longitudinal data can be utilized to examine linkages for not only mean systolic blood pressure (SBP), but also for its trend with age and its variability. Prior to linkage analysis, individuals treated for hypertension were adjusted to account for right-censoring of SBP. Regressions on age were fitted to obtain orthogonal measures of slope, curvature, and residual variance of SBP that were then used as dependent variables in the model-free linkage program SIBPAL. We included mean age, gender, and cohort as covariates in the analysis. To improve power, sibling pairs were weighted for informativity using weights derived from both the marker and trait. The most significant results from our analyses were found on chromosomes 12, 15, and 17 for mean SBP, and chromosome 20 for both SBP slope and curvature.     

Genome-wide linkage analysis of systolic blood pressure slope using the Genetic Analysis Workshop 13 data sets

Systolic blood pressure (SBP) is an age-dependent complex trait for which both environmental and genetic factors may play a role in explaining variability among individuals. We performed a genome-wide scan of the rate of change in SBP over time on the Framingham Heart Study data and one randomly selected replicate of the simulated data from the Genetic Analysis Workshop 13. We used a variance-component model to carry out linkage analysis and a Markov chain Monte Carlo-based multiple imputation approach to recover missing information. Furthermore, we adopted two selection strategies along with the multiple imputation to deal with subjects taking antihypertensive treatment. The simulated data were used to compare these two strategies, to explore the effectiveness of the multiple imputation in recovering varying degrees of missing information, and its impact on linkage analysis results. For the Framingham data, the marker with the highest LOD score for SBP slope was found on chromosome 7. Interestingly, we found that SBP slopes were not heritable in males but were for females; the marker with the highest LOD score was found on chromosome 18. Using the simulated data, we found that handling treated subjects using the multiple imputation improved the linkage results. We conclude that multiple imputation is a promising approach in recovering missing information in longitudinal genetic studies and hence in improving subsequent linkage analyses.     

Extension of the Haseman-Elston regression model to longitudinal data

We propose an extension to longitudinal data of the Haseman and Elston regression method for linkage analysis. The proposed model is a mixed model having several random effects. As response variable, we investigate the sibship sample mean corrected cross-product (smHE) and the BLUP-mean corrected cross product (pmHE), comparing them with the original squared difference (oHE), the overall mean corrected cross-product (rHE), and the weighted average of the squared difference and the squared mean-corrected sum (wHE). The proposed model allows for the correlation structure of longitudinal data. Also, the model can test for gene x time interaction to discover genetic variation over time. The model was applied in an analysis of the Genetic Analysis Workshop 13 (GAW13) simulated dataset for a quantitative trait simulating systolic blood pressure. Independence models did not preserve the test sizes, while the mixed models with both family and sibpair random effects tended to preserve size well.     

Genome scan linkage results for longitudinal systolic blood pressure phenotypes in subjects from the Framingham Heart Study

The relationship between elevated blood pressure and cardiovascular and cerebrovascular disease risk is well accepted. Both systolic and diastolic hypertension are associated with this risk increase, but systolic blood pressure appears to be a more important determinant of cardiovascular risk than diastolic blood pressure. Subjects for this study are derived from the Framingham Heart Study data set. Each subject had five records of clinical data of which systolic blood pressure, age, height, gender, weight, and hypertension treatment were selected to characterize the phenotype in this analysis. We modeled systolic blood pressure as a function of age using a mixed modeling methodology that enabled us to characterize the phenotype for each individual as the individual's deviation from the population average rate of change in systolic blood pressure for each year of age while controlling for gender, body mass index, and hypertension treatment. Significant (p = 0.00002) evidence for linkage was found between this normalized phenotype and a region on chromosome 1. Similar linkage results were obtained when we estimated the phenotype while excluding values obtained during hypertension treatment. The use of linear mixed models to define phenotypes is a methodology that allows for the adjustment of the main factor by covariates. Future work should be done in the area of combining this phenotype estimation directly with the linkage analysis so that the error in estimating the phenotype can be properly incorporated into the genetic analysis, which, at present, assumes that the phenotype is measured (or estimated) without error.     

Quantitative trait linkage analysis of longitudinal change in body weight

One of the great strengths of the Framingham Heart Study data, provided for the Genetic Analysis Workshop 13, is the long-term survey of phenotypic data. We used this unique data to create new phenotypes representing the pattern of longitudinal change of the provided phenotypes, especially systolic blood pressure and body weight. We performed a linear regression of body weight and systolic blood pressure on age and took the slopes as new phenotypes for quantitative trait linkage analysis using the SOLAR package. There was no evidence for heritability of systolic blood pressure change. Heritability was estimated as 0.15 for adult life "body weight change", measured as the regression slope, and "body weight gain" (including only individuals with a positive regression slope), and as 0.22 for body weight "change up to 50" (regression slope of weight on age up to an age of 50). With multipoint analysis, two regions on the long arm of chromosome 8 showed the highest LOD scores of 1.6 at 152 cM for "body weight change" and of >1.9 around location 102 cM for "body weight gain" and "change up to 50". The latter two LOD scores almost reach the threshold for suggestive linkage. We conclude that the chromosome 8 region may harbor a gene acting on long-term body weight regulation, thereby contributing to the development of the metabolic syndrome.     

Evidence for Three Novel QTLs for Adiposity on Chromosome 2 With Epistatic Interactions: The NHLBI Family Heart Study

We sought to identify quantitative trait loci (QTLs) by genome‐wide linkage analysis for BMI and waist circumference (WC) exploring various strategies to address heterogeneity including covariate adjustments and complex models based on epistatic components of variance. Because cholesterol‐lowering drugs and diabetes medications may affect adiposity and risk of coronary heart disease, we excluded subjects medicated for hypercholesterolemia and hyperglycemia. The evidence of linkage increased on 2p25 (BMI: lod = 1.59 vs. 2.43, WC: lod = 1.32 vs. 2.26). Because environmental and/or genetic components could mask the effect of a specific locus, we investigated further whether a QTL could influence adiposity independently of lipid pathway and dietary habits. Strong evidence of linkage on 2p25 (BMI: lod = 4.31; WC: lod = 4.23) was found using Willet's dietary factors and lipid profile together with age and sex in adjustment. It suggests that lipid profile and dietary habits are confounding factors for detecting a 2p25 QTL for adiposity. Because evidence of linkage has been previously detected for BMI on 7q34 and 13q14 in National Heart, Lung, and Blood Institute Family Heart Study (NHLBI FHS), and for diabetes on 15q13, we investigated epistasis between chromosome 2 and these loci. Significant epistatic interactions were found between QTLs 2p25 and 7q34, 2q37 and 7q34, 2q31 and 13q14, and 2q31–q36 and 15q13. These results suggest multiple pathways and factors involving genetic and environmental effects influencing adiposity. By taking some of these known factors into account, we clarified our linkage evidence of a QTL on 2p25 influencing BMI and WC. The 2p25, 2q24–q31, and 2q36–q37 showed evidence of epistatic interaction with 7q34, 13q14, and 15q13.     

Use of the robust sib-pair method to screen for single-locus, multiple-locus, and pleiotropic effects: application to traits related to hypertension.

Robust sib-pair linkage analysis can be used as a screening tool in the search for the potential involvement of single-loci, multiple-loci, and pleiotropic effects of single loci underlying phenotypic variation. Four large families were each ascertained through one adult white male with essential hypertension. The robust sib-pair method was used to screen these families for evidence of linkage between 39 quantitative traits related to hypertension and 25 genetic marker loci. All traits were analyzed on the untransformed, square-root and log-transformed scales. Among other findings, there is a suggestion of linkage between the 6-phosphogluconate dehydrogenase locus on chromosome 1p36 and mean fifth-phase diastolic blood pressure. There may also be linkage between the following markers and traits: the adenylate kinase-1 marker and/or the Lewis blood group marker and the traits height, weight, and biacromial breadth; the glyoxylase I marker and the traits upper-arm circumference and suprailiac skinfold thickness; the ABO blood group and adenylate kinase-1 markers on chromosome 9q34 and the third component of complement marker on chromosome 19p13 and dopamine-beta-hydroxylase; and the P1 blood group and the traits weight and 1-h postload serum glucose level.     

Genome‐wide Linkage Analysis of Multiple Metabolic Factors: Evidence of Genetic Heterogeneity

The metabolic syndrome is a highly complex disease and has become one of the major public‐health challenges worldwide. We sought to identify genetic loci with potential influence on multiple metabolic factors in a white population in Beaver Dam, Wisconsin, and to explore the possibility of genetic heterogeneity by family history of diabetes (FHD). Three metabolic factors were generated using principal‐component factor analysis, and they represented: (i) glycemia, (ii) blood pressure, and (iii) combined (BMI, high‐density lipoprotein (HDL) cholesterol, and serum uric acid) factors. Multipoint model‐free linkage analysis of these factors with 385 microsatellite markers was performed on 1,055 sib‐pairs, using Haseman–Elston regression. Genome‐wide suggestive evidence of linkage was found at 30 cM on chromosome 22q (empirical P (P_e) = 0.0002) for the glycemia factor, at 188–191 cM on chromosome 1q (P_e = 0.0007) for the blood pressure factor, and at 82 cM on chromosome 17q (P_e = 0.0007) for the combined factor. Subset analyses of the families by FHD showed evidence of genetic heterogeneity, with divergent linkage signals in the subsets on at least four chromosomes. We found evidence of genetic heterogeneity by FHD for the three metabolic factors. The results also confirmed findings of previous studies that mapped components of the metabolic syndrome to a chromosome 1q region.     

Heterogeneity of genetic control of blood pressure in ethnically different populations.

We review the literature on statistical genetic analyses of blood pressure in samples from various ethnic backgrounds using different statistical methods and packages. We then provide the results of a complex segregation analysis performed on familial data on systolic and diastolic blood pressure in 2 ethnically different populations, Chuvashans and Turkmenians. Two types of major gene models were tested in the segregation analysis: Model type 1 tests for a Mendelian mode of transmission and estimates genotype-specific averages regardless of age and sex effect, and model type 2 estimates age and sex effects on each of 3 genotypes within the putative major genotype. In both total samples, by both types of segregation analysis, familial aggregation of both systolic and diastolic blood pressure was inconsistent with the Mendelian mode of inheritance. In the next step of analysis the pedigrees in both samples were sorted into 2 groups on the basis of 2 likelihoods as obtained under Mendelian and nontransmission models for each entire sample. This procedure resulted in the appearance of 2 subsamples (large and small) in each ethnic sample. The segregation analysis that was carried out then on the larger subsample provided consistent evidence to support the major gene effect on systolic and diastolic blood pressure in 2 ethnic groups. Interestingly, model type 2 showed that in both ethnically different large subsamples, for each sex the genotype predisposing to a larger mean value of systolic (or diastolic) blood pressure also displayed the highest rate of blood pressure increase with age. We discuss in detail possible sources of heterogeneity in familial transmission of blood pressure observed in our 2 samples, and we suggest a method to improve the analysis of heterogeneity for trait inheritance.     

Use of a random coefficient regression (RCR) model to estimate growth parameters

We used a random coefficient regression (RCR) model to estimate growth parameters for the time series of observed serum glucose levels in the Replicate 1 of the Genetic Analysis Workshop 13 simulated data. For comparison, a two time-point interval was also selected and the slope between these two observations was calculated. This process yielded four phenotypes: the RCR growth phenotype, a two time-point slope phenotype, and Time 1 and Time 2 serum glucose level phenotypes. These four phenotypes were used for linkage analyses on simulated chromosomes 5, 7, 9, and 21, those chromosomes that contained loci affecting the growth course for serum glucose levels. The linkage analysis of the RCR-derived phenotype showed overwhelming evidence for linkage at one locus (LOD 65.78 on chromosome 5), while showing elevated but nonsignificant LOD scores for two other loci (LOD 1.25 on chromosome 7, LOD 1.10 on chromosome 9), and no evidence of linkage for the final locus. The two time-point slope phenotype showed evidence for linkage at one locus (LOD 4.16 on chromosome 5) but no evidence for linkage at any of the other loci. A parallel cross-sectional approach, using as input phenotypes the endpoints of the two-point slope phenotype, gave strong linkage results for the major locus on chromosome 5 (maximal LOD scores of 17.90 and 27.24 for Time 1 and Time 2, respectively) while showing elevated but nonsignificant linkage results on chromosome 7 (maximal LOD scores of 1.71 and 1.48) and no evidence for linkage at the two remaining loci. The RCR growth parameter showed more power to detect linkage to the major locus than either the cross-sectional or two-point slope approach, but the cross-sectional approach gave a higher maximal LOD score for one of the minor loci.     

Genome-wide linkage analysis of longitudinal phenotypes using σ<Superscript>2</Superscript><Subscript>A</Subscript> random effects (SSARs) fitted by Gibbs sampling

The study of change in intermediate phenotypes over time is important in genetics. In this paper we explore a new approach to phenotype definition in the genetic analysis of longitudinal phenotypes. We utilized data from the longitudinal Framingham Heart Study Family Cohort to investigate the familial aggregation and evidence for linkage to change in systolic blood pressure (SBP) over time. We used Gibbs sampling to derive sigma-squared-A-random-effects (SSARs) for the longitudinal phenotype, and then used these as a new phenotype in subsequent genome-wide linkage analyses. Additive genetic effects (sigma2A.time) were estimated to account for approximately 9.2% of the variance in the rate of change of SBP with age, while additive genetic effects (sigma2A) were estimated to account for approximately 43.9% of the variance in SBP at the mean age. The linkage results suggested that one or more major loci regulating change in SBP over time may localize to chromosomes 2, 3, 4, 6, 10, 11, 17, and 19. The results also suggested that one or more major loci regulating level of SBP may localize to chromosomes 3, 8, and 14. Our results support a genetic component to both SBP and change in SBP with age, and are consistent with a complex, multifactorial susceptibility to the development of hypertension. The use of SSARs derived from quantitative traits as input to a conventional linkage analysis appears to be valuable in the linkage analysis of genetically complex traits. We have now demonstrated in this paper the use of SSARs in the context of longitudinal family data.     

Evidence that a single gene with gender- and age-dependent effects influences systolic blood pressure determination in a population-based sample.

A biometrical study was carried out to evaluate the role of genetic variation in determining interindividual differences in systolic blood pressure (SBP) in the population at large. SBP was measured in 1,266 Caucasian individuals in 278 pedigrees ascertained through children enrolled in the Rochester, MN, school system. The sample included 646 males and 620 females 550 years of age and not taking antihypertensive medication or oral contraceptives. Complex segregation analysis was first applied to these data by using a regression model for age, in which the intercept was gender and ousiotype specific but in which the slope was only gender specific. When the slope was independent of ousiotype, neither variation at a single gene combined with polygenic effects (mixed genetic model) nor variation in a single environmental factor combined with polygenetic effects (mixed environmental model) explained the distribution of SBP in this sample. However, when the regression model for age allowed both the intercept and slope to be gender and ousiotype specific, the mixed environmental model was rejected whereas the mixed genetic model was not. These results suggest that variability in SBP may be influenced by major effects of allelic variation at a single gene that are both gender and age dependent. This study (1) suggests that particular genotypes determined by a single gene are associated with a steeper increase of SBP with age among males and females 550 years of age in the general population and (2) illustrates the need to consider models that more realistically represent the relationship between genotypic variability and phenotypic variability, to understand the genetics of human quantitative traits.     

Principal component for metabolic syndrome risk maps to chromosome 4p in Mexican Americans: the San Antonio Family Heart Study

Metabolic syndrome refers to the clustering of disease conditions such as insulin resistance, hyperinsulinemia, dyslipidemia, hypertension, and obesity. To explore the genetic predispositions of this complex syndrome, we conducted a principal components analysis using data on 14 phenotypes related to the risk of developing metabolic syndrome. The subjects were 566 nondiabetic Mexican Americans, distributed in 41 extended families from the San Antonio Family Heart Study. The factor scores obtained from these 14 phenotypes were used in multipoint linkage analysis using SOLAR. Factors were identified that accounted for 73% of the total variance of the original variables: body size-adiposity, insulin-glucose, blood pressure, and lipid levels. Each factor exhibited evidence for either significant or suggestive linkage involving four factor-specific chromosomal regions relating to chromosomes 1, 3, 4, and 6. Significant evidence for linkage of the lipid factor was found on chromosome 4 near marker D4S403 (LOD = 3.52), where the cholecystokinin A receptor (CCKAR) and ADP-ribosyl cyclase 1 (CD38) genes are located. Suggestive evidence for linkage of the body size-adiposity factor to chromosome 1 near marker D1S1597 (LOD = 2.53) in the region containing the nuclear receptor subfamily 0, group B, member 2 gene (NROB2) also was observed. The insulin-glucose and blood pressure factors were linked suggestively to regions on chromosome 3 near marker D3S1595 (LOD = 2.20) and on chromosome 6 near marker D6S 1031 (LOD = 2.08), respectively. In summary, our findings suggest that the factor structures for the risk of metabolic syndrome are influenced by multiple distinct genes across the genome.     

Interval mapping and congenic strains for a blood pressure QTL on rat Chromosome 13

The renin locus (Ren) on rat Chromosome (Chr) 13 had previously been shown to cosegregate with blood pressure in crosses involving Dahl salt-sensitive (S) and Dahl salt-resistant (R) rats. In the present work, interval mapping of blood pressure on Chr 13 with a large F₂ (S × R), n = 233, population yielded a maximum LOD = 4.2 for linkage to blood pressure, but the quantitative trait locus (QTL) was only poorly localized to a large 35-centiMorgan (cM) segment of Chr 13. In the linkage analysis, the S-rat QTL allele (S) was associated with higher, and the R-rat QTL allele (R) with lower blood pressure, the difference between homozygotes being about 20 mm Hg. A congenic strain was made by introgressing the R-rat Ren allele into the recipient S strain. This congenic strain showed a 24 mm Hg reduction (P = 0.004) in blood pressure compared with S rats for rats fed 2% NaCl diet for 24 days; this difference was confirmed by two other independent tests. Two congenic substrains were derived from the first congenic strain with shorter R Chr 13 segments on the S background. Comparisons among these congenic strains showed that a blood pressure QTL was in the 24-cM chromosomal segment between Syt2 and D13M1Mit108. This segment does not include the renin locus, which is thus excluded from being the gene on rat Chr 13 responsible for genetic differences in blood pressure detected by linkage analysis. Received: 20 December 1996 / Accepted: 7 April 1997     

Genome-wide linkage scan for the metabolic syndrome: the GENNID study

In the United States, the metabolic syndrome (MetS) constitutes a major public health problem with over 47 million persons meeting clinical criteria for MetS. Numerous studies have suggested genetic susceptibility to MetS. The goals of this study were (i) to identify susceptibility loci for MetS in well-characterized families with type 2 diabetes (T2D) in four ethnic groups and (ii) to determine whether evidence for linkage varies across the four groups. The GENNID study (Genetics of NIDDM) is a multicenter study established by the American Diabetes Association in 1993 and comprises a comprehensive, well-characterized resource of T2D families from four ethnic groups (whites, Mexican Americans, African Americans, and Japanese Americans). Principal component factor analysis (PCFA) was used to define quantitative phenotypes of the MetS. Variance components linkage analysis was conducted using microsatellite markers from a 10-cM genome-wide linkage scan, separately in each of the four ethnic groups. Three quantitative MetS factors were identified by PCFA and used as phenotypes for MetS: (i) a weight/waist factor, (ii) a blood pressure factor, and (iii) a lipid factor. Evidence for linkage to each of these factors was observed. For each ethnic group, our results suggest that several regions harbor susceptibility genes for the MetS. The strongest evidence for linkage for MetS phenotypes was observed on chromosome 2 (2q12.1-2q13) in the white sample and on chromosome 3 (3q26.1-3q29) in the Mexican-American sample. In conclusion, the results suggest that several regions harbor MetS susceptibility genes and that heterogeneity may exist across groups.