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.     

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.     

Multilevel modeling for the analysis of longitudinal blood pressure data in the Framingham Heart Study pedigrees

Background

The data arising from a longitudinal familial study have a complex correlation structure that cannot be modeled using classical methods for the analysis of familial data at a single time point.

Methods

To fit the longitudinal systolic blood pressure (SBP) pedigree data arising from the Framingham Heart Study, we proposed to use multilevel modeling. That approach was used to distinguish multiple levels of information with individual repeated measurements (Level 1) being made within individuals (Level 2), and individuals clustered within pedigrees (Level 3). Residuals from the subject-specific and pedigree-specific regression models were summed both for the mean SBP and slope of SBP change over time, in order to define two new outcomes that were then used in a genome-wide linkage analysis.

Results

Evidence for linkage for the two outcomes (mean SBP and slope) was found in several chromosomal regions with a maximum LOD score of 3.6 on chromosome 8 and 3.5 on chromosome 17 for the mean SBP, and 2.5 on chromosome 1 for SBP slope. However, the linkage on chromosome 8 was only detected when the sample was restricted to subjects between age 25 and 75 and with at least four exams (Cohort 1) or 3 exams (Cohort 2).

Discussion

Multilevel modeling is a powerful approach to detect genes involved in complex traits when longitudinal data are available. It allows for complex hierarchical data structure to be taken into account and therefore, a better partitioning of random within-individual variation from other sources of variability (genetic or nongenetic).

     

Longitudinal variance components models for systolic blood pressure, fitted using Gibbs sampling

This paper describes an analysis of systolic blood pressure (SBP) in the Genetic Analysis Workshop 13 (GAW13) simulated data. The main aim was to assess evidence for both general and specific genetic effects on the baseline blood pressure and on the rate of change (slope) of blood pressure with time. Generalized linear mixed models were fitted using Gibbs sampling in WinBUGS, and the additive polygenic random effects estimated using these models were then used as continuous phenotypes in a variance components linkage analysis. The first-stage analysis provided evidence for general genetic effects on both the baseline and slope of blood pressure, and the linkage analysis found evidence of several genes, again for both baseline and slope.     

Variance components linkage analysis for adjusted systolic blood pressure in the Framingham Heart Study

We performed variance components linkage analysis in nuclear families from the Framingham Heart Study on nine phenotypes derived from systolic blood pressure (SBP). The phenotypes were the maximum and mean SBP, and SBP at age 40, each analyzed either uncorrected, or corrected using two subsets of epidemiological/clinical factors. Evidence for linkage to chromosome 8p was detected with all phenotypes except the uncorrected maximum SBP, suggesting this region harbors a gene contributing to variation in SBP.     

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.     

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.     

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.     

Blood pressure levels of the Suruí and Zoró Indians of the Brazilian Amazon: group- and sex-specific effects resulting from body composition, health status, and age

Two related Tupí-Mondê-speaking tribes of the Aripuan? Indian Park of western Brazil are compared in terms of their recent contact with Western culture, subsistence patterns, general health, and blood pressure levels. Age, weight, height, sex, and tribal affiliation for Suruí and Zoró adults over age 18 are included in an analysis of covariance to test regression models of both diastolic and systolic blood pressure. Because of significant interaction effects between sex and other covariates, sex-specific models were developed. The relationship between body mass and blood pressure level in males conforms with Western data, but the direction and magnitude of effects for the age and body mass covariates in both sexes conflict with data from other modernizing societies. With age, weight/height ratio, and sex differences controlled for, Suruí males show a lower mean systolic blood pressure (SBP) level and diastolic blood pressure (DBP) level than Zoró males. Intertribal differences were smaller among females: Suruí females SBP and DBP differences were similar but did not reach significance. Other sex-specific differences include a greater inverse relationship between age and SBP level among the 104 male subjects than among the 98 female subjects (with similar trends in DBP) and a small but significant effect of the weight/height ratio on both SBP and DBP in males but not in females. Health status data for these groups suggest that hypothesized increases in mean blood pressure levels following the Suruí's acceptance of a Western diet and social stratification may be modified by their health status, particularly prevalent infectious disease.     

Evidence of a rare gene for low systolic blood pressure in the Framingham Heart Study

A major risk factor for coronary heart disease in both men and women is elevated systolic blood pressure (SBP). We performed segregation analysis on age, sex-adjusted, and transformed systolic blood pressure data on 1,141 families from the Framingham cohort-offspring study using the segregation analysis program POINTER. The results of hypothesis testing revealed: (1) these data are consistent with familial transmission; (2) there is evidence for the transmission of a rare, major gene for low SBP with a gene frequency of q = 0.02; and (3) most of the transmissible component to SBP can be attributed to the polygenic background with H = 0.31.     

Genetic epidemiological study of blood pressure in a sedentary rural agricultural population of West Bengal, India

To study the genetic epidemiology of blood pressure (BP), data on 78 families were collected from a sedentary agricultural population of eastern India. The general levels of both systolic (SBP) and diastolic (DBP) blood pressures are found to be low (mean SBP = 106.41 mm Hg; mean DBP = 63.94 mm Hg). Trends of blood pressures with age are similar to those reported earlier (e.g., in the Framingham study). Environmental variables--e.g., occupation and tobacco use--do not have any direct significant effect on blood pressure variability in this population. Path analysis of family data shows a highly significant familial aggregation and yields a genetic heritability (maximum) estimate of 0.3 for both SBP and DBP. Sib-sib and mother-child correlation estimates are, respectively, 0.3 and 0.25. Father-child correlation estimates are 0.13 for SBP and near zero for DBP. A pseudopolygenic model yields the best fit to the data on SBP, while for DBP a proper resolution of various models considered could not be obtained.     

Multivariate variance-components analysis of longitudinal blood pressure measurements from the Framingham Heart Study

Multivariate variance-components analysis provides several advantages over univariate analysis when studying correlated traits. It can test for pleiotropy or (in the longitudinal context) gene x age interaction. It can also have more power than univariate analyses to detect a quantitative trait locus influencing several traits. We apply multivariate variance components to longitudinal systolic blood pressure data from the Framingham Heart Study. We find evidence for a polygenic influence on blood pressure (heritabilities at different ages range from 27% to 38%). Tests based on a factor-analytic parameterization of the polygenic variance find significant (p < 2 x 10(-3)) evidence that different genes affect blood pressure at different ages. Still, estimates for the proportion of polygenic variance due to shared genes ran as high as 85% for some trait pairs. Univariate and multivariate linkage analyses replicate previous linkage results on chromosome 17 (maximum LOD scores of 2.2 and 2.4, respectively). In this study, multivariate analysis provides no increase in power; this is likely due to the strong positive correlation in systolic blood pressure measured at different ages.     

Pleiotropic effects on cardiovascular risk factors within and between the fourth and sixth decades of life: implications for genotype x age interactions

We used an approach for detecting genotype x environment interactions to detect and characterize genotype x age interaction in longitudinal measures of three well known cardiovascular risk factors: total plasma cholesterol (TC), systolic blood pressure (SBP), and body weight (Wgt). Our objectives were to determine if the same gene or suite of genes influences quantitative variation in each of these phenotypes in the 4th and 6th decades of life, to assess the impact of additive gene effects in these two decades, and to evaluate the stability of pleiotropic relationships among these phenotypes. Using the Framingham Heart Study data, we constructed two cross-sectional samples comprising individuals on whom these phenotypes were measured at ages 30-39 years (Original Cohort: exam 1, Offspring Cohort: exam 2) and at ages 50-59 years (Original Cohort: exam 11, Offspring Cohort: exam 5). We also constructed a longitudinal sample from the cross-sectional sample members for whom measures on these traits were available at both ages (i.e., 4th and 6th decades of life). Patterns of pleiotropy, inferred from genetic correlations between traits, differ between the two age classes. Further, additive genetic variance in SBP during the 4th decade of life is attributable to a different gene or suite of genes than during the 6th. The magnitude of the effect increases for SBP. Variation in TC and Wgt appear to be influenced by the same gene or genes in both decades. The magnitude of the effect is stable for TC, but increases dramatically with age for Wgt.     

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.     

Association of birth weight and current body size to blood pressure in female twins.

It has been proposed that low birth weight is associated with high levels of blood pressure in later life. The aim of this study was to assess the relationship of blood pressure to birth weight and current body size during growth and adulthood. A total of 711 female multiple births, with one group of 244 in their growth phase mean age 12.0 (2.3)(SD) years and the other of 467 adults (mean age 35.2 (12.6) years), had height, weight and both systolic (SBP) and diastolic (DBP) blood pressures measured, and self-reported their birth weight. Regression analyses were performed to assess the cross-sectional and within-pair associations of blood pressure to birth weight, with and without adjustments for current body size. Within-pair analysis was based on 296 twin pairs. Cross-sectionally, a reduction in birth weight of 1 kg was associated with 2 to 3 mm Hg higher age-adjusted SBP, which was of marginal significance and explained about 2% of the population variance. Adjustment for body mass index did not significantly change this association. Within-pair analyses found no association between birth weight and SBP or DBP,even after adjusting for current body size. After age, current body size was the strongest predictor of systolic BP. The weak association of blood pressure to birth weight cross-sectionally is of interest, but any within-pair effect of birth weight on blood pressure must be minimal compared with the effect of current body size.     

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.     

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.     

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.     

Life course trajectories of systolic blood pressure using longitudinal data from eight UK cohorts

Background

Much of our understanding of the age-related progression of systolic blood pressure (SBP) comes from cross-sectional data, which do not directly capture within-individual change. We estimated life course trajectories of SBP using longitudinal data from seven population-based cohorts and one predominantly white collar occupational cohort, each from the United Kingdom and with data covering different but overlapping age periods.

Methods and Findings

Data are from 30,372 individuals and comprise 102,583 SBP observations spanning from age 7 to 80+y. Multilevel models were fitted to each cohort. Four life course phases were evident in both sexes: a rapid increase in SBP coinciding with peak adolescent growth, a more gentle increase in early adulthood, a midlife acceleration beginning in the fourth decade, and a period of deceleration in late adulthood where increases in SBP slowed and SBP eventually declined. These phases were still present, although at lower levels, after adjusting for increases in body mass index though adulthood. The deceleration and decline in old age was less evident after excluding individuals who had taken antihypertensive medication. Compared to the population-based cohorts, the occupational cohort had a lower mean SBP, a shallower annual increase in midlife, and a later midlife acceleration. The maximum sex difference was found at age 26 (+8.2 mm Hg higher in men, 95% CI: 6.7, 9.8); women then experienced steeper rises and caught up by the seventh decade.

Conclusions

Our investigation shows a general pattern of SBP progression from childhood in the UK, and suggests possible differences in this pattern during adulthood between a general population and an occupational population. Please see later in the article for the Editors'' Summary