Abstract
Background
The genetic regulation of variation in intraindividual fluctuations in systolic blood pressure over time is poorly understood. Analysis of the magnitude of the average fluctuation of a person's systolic blood pressure around his or her ageadjusted trend line, however, shows moderate, albeit significant, family resemblance in Cohort 1 of the Framingham Heart Study. To determine whether genomic regions affecting this phenotype could be identified, we pursued a "modelfree" multipoint quantitative linkage analysis.
Results
Two different linkage methods revealed multiple nominally significant signals, two to four of which are "replicated" in Cohort 2. When both cohorts are assembled into extended pedigrees, three linkage signals remain nominally significant by one or both methods.
Conclusion
Any or all of the genomic regions in the vicinity of D5S1456, D11S2359, and D20S470 may contain elements that regulate systolic blood pressure homeostasis.
Background
We used the rich longitudinal Framingham Heart Study data to explore the hypothesis that there is a heritable component to intraindividual
 variation
We are particularly interested in assessing variation in the context of homeostatic regulation. It has been shown that a locus influencing ageadjusted SBP maps to chromosome 17q in these data [1]. We hypothesize that there is, additionally, familial resemblance for the
 magnitude
Methods
Familial resemblance in Cohort 1
First we evaluated the distribution of AVGRES and found it to be significantly skewed and leptokurtotic in both males and females. A logarithmic (base 10) transformation rendered AVGRES normally distributed in both genders (for males, p = 0.35, and for females, p = 0.46). All subsequent analyses were carried out on the transformed values of AVGRES.
To assess family resemblance for AVGRES we used the FCOR program from the S.A.G.E. computer package [3]. Table 1 reports the genderspecific sibpair correlations and their respective sample sizes. Modest, albeit significant, correlations in the range of 0.2 to 0.3 were obtained, and all are substantially higher than the spousal correlation of 0.045.
Table 1. Family resemblance for log AVGRES in cohort
Linkage analysis
Our plan was to analyze all available sib pairs from Cohort 1 for linkage with the objective of developing hypotheses that could be tested in Cohort 2. Unfortunately, only a small subset of the Cohort 1 subjects (that were used to assess family resemblance) were genotyped. The distribution of genotyped sibs is as follows: 38 pairs, 6 trios, and 1 quintet.
To perform multipoint quantitative linkage analysis for log AVGRES, we chose two methods implemented in the GENEHUNTER linkage program: nonparametric (NP) and expectation maximization HasemanElston (EMHE). The NP method performs a Wilcoxon ranksum test by first summing the ranks of absolute trait difference from sib pairs, multiplied by a simple weight based on the number of alleles shared identically by descent (IBD). Z scores are then obtained by the usual method [4].
The EMHE procedure is based on the traditional HasemanElston method of regressing the squared sibpair trait difference on the proportion of alleles shared IBD. In addition, when genotype information is missing, the EM algorithm infers the probability of alleles shared IBD by taking into account the allele sharing distribution as well as the regression parameters estimated from the real data points [5]. Similar to the NP score, the EMHE test statistic for the regression coefficient is asymptotically normally distributed with mean 0 and unit variance. The GENEHUNTER 'pairs used' option was set to 3, which corresponds to 'all pairs of affected/phenotyped sibs.' This option weighs a sibship's contribution according to the number of independent pairs it contains, and guards against the possibility of large sibships dominating the results [69].
Results
Cohort 1
Table 2 reports all markers that attained nominal significance at the 5% level (i.e., score ≥ 1.645). Linkage signals at four markers were detected with just the NP statistic, 25 with just the EMHE statistic; 11 signals were detected with both statistics.
Table 2. Significant NP and EMHasemanElston scores from Cohort 1 and the "replication" scores from Cohort 2
Cohort 2
The members of Cohort 2 have a maximum of only five SBP assessments (taken over a period of about 20 years). We felt that performing the regression analysis on subjects with fewer than five measurements could not adequately capture the sort of variation we are interested in. Indeed, the relative paucity of Cohort 2 measures may render it fundamentally different from Cohort 1. Restricting the analysis to genotyped sibs who were older than age 20 and had all five SBP assessments, however, yielded a much larger sample size compared to Cohort 1: 151 pairs, 84 trios, 35 quartets, 7 quintets, 4 sextets, and 2 septets.
Table 2 reports the NP and EMHE linkage scores for those markers that attained nominal significance in Cohort 1. As expected, few of the original signals could be validated. If we count as a "replication," markers with a pvalue < 0.05 obtained under the same weighting and statistical methodology, then there are two replications: D5S1456 for the NP approach and D11S2359 for the EMHE approach. Two additional markers (D1S1653 and D20S470) revealed a "reversal". Both of these markers gave a nominally significant signal in Cohort 1 with the EMHE statistic, but in Cohort 2 it was the NP statistic that achieved nominal "replication".
Extended pedigrees
Combining available individuals from both cohorts results in 17 new families that were not analyzed in either cohort. Specifically, there are two halfsib pair families, two sibpair families (that straddle the cohorts), and 13 families with additional avuncular or cousin members. Five large pedigrees were disassembled at a marriage node into smaller units. A total of 305 families were used for the combined analyses.
Table 3 reports the results of the multipoint linkage analysis in the extended pedigrees for the four "replicated" markers (and their closest neighbors). Compared to the NP and EMHE scores obtained from the sibpair analysis of Cohort 2, the scores for the extended families reflect some degradation, although all but D1S1653 remain nominally significant by one or the other method.
Table 3. Linkage analysis of extended families for markers with significant evidence in Cohorts 1 and 2^{A}
Discussion
Physiological homeostasis is the process whereby a narrow range of phenotypes develops in the presence of wide variation in genotypes and environments. A classic example is the ability of homeothermic mammals to maintain a constant body temperature despite substantial genetic variation and fluctuating ambient air temperatures. The concept of physiological homeostasis bears some similarity to Waddington's notion of "canalization" [10] although this latter concept is usually applied to growth and developmental homeostasis.
That a breakdown in physiological homeostasis can result in either an increase or decrease in a phenotype — thus increasing the variance — is recognized in the operational definitions of many disorders. For example, among the Diagnostic and Statistical Manual of Mental Disorders (4th ed.) criteria for major depression are the following: a significant decrease
 or
 or
 or
While the preponderance of genetic studies concentrate on the first moment of various phenotypes — and for medical reasons are usually interested in understanding deviantly high (or, rarely, deviantly low) phenotypes — it is reasonable to suppose that the magnitude of an individual's phenotypic variation is to some extent under genetic control [11]. Indeed, recently it has been shown that with respect to shortterm (24hour) variation among hypertensive patients, variability in blood pressure is positively related to organ damage and cardiovascular morbidity [12].
We used the rich longitudinal Framingham Heart Study data to study the genetics of long term variation in SBP. Our findings indicate that there is moderate familial resemblance for the magnitude of the deviation of a person's SBP from his or her unique agerelated trend line. At least three caveats need to be mentioned. First, we restricted our Cohort 1 analysis to individuals with 10 or more measurements. Because this cohort was relatively small, we chose to include all subjects who met the above criterion, regardless of whether they were under treatment for hypertension. Subsequent to the Genetic Analysis Workshop 13, however, we carried out an analysis to determine if there exists a relationship between medication usage and AVGRES. We quantified medication usage as the proportion of SBP assessments where the subject was reported to be medicated. Unexpectedly, there is a strong positive correlation for both cohort 1 (r = 0.51) and Cohort 2 (r = 0.29) in the Framingham Heart Study. This previously unrecognized relationship between the use of hypertension medication and AVGRES is likely to have confounded our linkage analysis in an unknown fashion. Second, we did not adjust the data for body mass index (BMI)a covariate known to show familial resemblance and to affect SBP. Since our phenotype was defined as the average residual from each subject's unique regression line it is unclear what, if any, effect the failure to adjust for BMI had on our results. Third, we did not test whether curvilinear regression would have provided an improved fit compared to simple linear regression. This decision was based on two considerations. First, if for some of the subjects, a quadratic or cubic function were found to fit significantly better than the linear component, its use in a subset of the data would have created a heterogeneous definition of the phenotype. Second, we were aware that the maximum number of available SBP measures on the Cohort 2 subjects was five, and it seemed frivolous to fit a high order function to such meager data.
For the linkage analysis, we chose to analyze the sibship data with two different methods. Although the NP and the EMHE methods are similar, as are all linkage methods, they are not identical. For the data we analyzed, the correlation between the NP and EMHE scores were 0.72 and 0.69 for Cohorts 1 and 2, respectively. Inspection of the quantilequantile (QQ) plots (Fig. 1) reveals that the NP statistic is more conservative than the EMHE statistic. Indeed, 11.6 % and 11.3% of the markers in Cohorts 1 and 2, respectively, are significant at the 0.05 level with EMHE, whereas 6.0% and 7.5% are significant with the NP statistic.
Figure 1. Quantilequantile plots in 5% increments of the linkage statistics for Cohort 1 and Cohort 2
We used the linkage analysis on Cohort 1 to develop hypothesis that could be tested in Cohort 2. Two genomic regions were "replicated" in Cohort 2 using the same statistical method (D5S1456 and D11S2359). An additional two signals were found to be nominally significant by EMHE in Cohort 1 and "replicated" with NP in Cohort 2. Three of these four signals remained nominally significant when extended pedigrees were analyzed.
Acknowledgments
This work was supported in part by the Urologic Research Foundation. Some of the results reported here were obtained by using the program package S.A.G.E., which is supported by U.S. Public Health Resource Grant RR 03655 from the National Center for Research Resources.
References

Levy D, DeStefano AL, Larson MG, O'Donnell CJ, Lifton RP, Gavras H, Cupples LA, Myers RH: Evidence for a gene influencing blood pressure on chromosome 17: genome scan linkage results for longitudinal blood pressure phenotypes in subjects from the Framingham Heart Study.
Hypertension 2000, 36:477483. PubMed Abstract  Publisher Full Text

Dawber TR: The Framingham Study: The Epidemiology of Atherosclerotic Disease.

S.A.G.E.: Statistical Analysis for Genetic Epidemiology, Release 3.1. Department of Epidemiology and Biostatistics, MetroHealth Campus, Case Western Reserve University, Cleveland, OH; 1997.

Kruglyak L, Lander ES: A nonparametric approach for mapping quantitative trait loci.
Genetics 1995, 139:14211428. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Kruglyak L, Lander ES: Complete multipoint sibpair analysis of qualitative and quantitative traits.
Am J Hum Genet 1995, 57:439454. PubMed Abstract  PubMed Central Full Text

Suarez BK, Hodge SE: A simple method to detect linkage for rare recessive diseases: an application to juvenile diabetes.
Clin Genet 1979, 15:126136. PubMed Abstract

Fernandez JR, Etzel C, Beasley TM, Shete S, Amos CI, Allison DB: Improving the power of sib pair quantitative trait loci detection by phenotype winsorization.
Hum Hered 2002, 53:5967. PubMed Abstract  Publisher Full Text

Davis S, Weeks DE: Comparison of nonparametric statistics for detection of linkage in nuclear families: singlemarker evaluation.
Am J Hum Genet 1997, 61:14311444. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Hodge S: The information contained in multiple sibling pairs.
Genet Epidemiol 1984, 1:109122. PubMed Abstract  Publisher Full Text

Coady SA, Jaquish CE, Fabsitz RR, Larson MG, Cupples LA, Myers RH: Genetic variability of adult body mass index: a longitudinal assessment in Framingham families.

Sega R, Corrao G, Bombelli M, Beltrame L, Facchetti R, Grassi G, Ferrario M, Mancia G: Blood pressure variability and organ damage in a general population. Results from the PAMELA study.
Hypertension 2002, 39:710714. PubMed Abstract  Publisher Full Text