### Univariate Approaches

#### Baseline Measure

Baseline measure of CHOL at Exam 1 of both cohorts was used as the dependent variable in variance components model analyses implemented in SOLAR [1]. Total heritability (h^{2}) was estimated as the proportion of the total phenotypic variance due to the additive polygenic variance. SOLAR calculates a LOD score by taking log_{10} of the ratio of the maximum likelihood of a linkage model (containing a quantitative trait loci (QTL) variance and a residual polygenic variance component) to that of a purely polygenic model. The QTL h^{2} was computed as the proportion of the QTL variance to the total phenotypic variance. In multipoint analyses, linkage to adjacent markers was also considered to evaluate the linkage to the current marker using a regression approach [1]. Covariates including gender, age, systolic blood pressure, and height were adjusted for in regression models prior to the heritability and linkage analyses.

#### Summary Measures

In calculating summary measures of the repeated CHOL measurements, we looked at three definitions of the mean by imposing restrictions on the selection of the subjects and their measurements. Definition 1 (D1) required that subjects had CHOL measured for at least three exams. This definition resulted in subjects with a wide range of observations used, from 3 to 15. We were concerned that the different number of exams, and hence different standard error associated with the mean measure, would affect the genetic analysis and explored definitions in which each summary measure was based on a similar number of exams. To obtain, approximately, an equal number of exams for both cohorts, definition 2 (D2) included only the first five exams of both cohorts, and all subjects had to have CHOL measured for at least two exams. For D2, Cohort 1 and 2 members had measures taken at approximately the same age (45 years). To obtain measures taken at approximately the same chronological time in the two cohorts, definition 3 (D3) included only exams 10, 14, 15, and 20 for Cohort 1 and exams 1–5 for Cohort 2, and required all subjects have CHOL measured for at least two exams. A slope of CHOL versus age was computed for each individual satisfying D1. Heritability and linkage analyses were conducted in the same way as for the baseline measure.

### Multivariate Approach

We set up a mixed regression models as follows

*y*_{
ij
}= *X*_{
ij
}β + *g*_{
ij
}+ *r*_{
ij
}+ ε_{
ij
},

where *y*_{
ij
}is the CHOL at the age *j* for subject *i*, *X*_{
ij
}and β are vectors of covariates and coefficients of fixed effects, *g*_{
ij
}and *r*_{
ij
}are subject-specific additive genetic and environmental effects (i.e., repeated measurement effects) respectively, and ε_{
ij
}is the residual environmental effect of subject *i*. To allow age-varying effects, *g* and *r* are modelled by Legendre polynomials similar to the approach in Meyer [2]:

where {α_{
im
}| *m* = 0, ..., *k*_{
A
}- 1} ~ *N*(**0**, ∑_{α}) and {γ_{
im
}| *m* = 0, ..., *k*_{
R
}- 1} ~ *N*(**0**, ∑_{γ}) are random regression coefficients of additive genetic and environmental effects for subjects *i*, φ_{
m
}() is the *m*^{th} Legendre polynomial [3] evaluated at (which is age *j* standardized to the interval [-1,1] by the age range observed in the data), *k*_{
A
}and *k*_{
R
}are the order of the corresponding polynomials. The covariance between two observations of two subjects is then equal to equation (1), assuming *g* and *r* independent of each other,

It can be further simplified by assuming *Cov*(α_{
im
}), α_{
i'l
}= 2Φ_{
ii'
}*Cov*(α_{
m
}), α_{
l
}) and *Cov*(γ_{
im
}, γ_{
i'l )
}= 2δ_{
ii'
}*Cov*(γ_{
m
}, γ_{
l
}), where Φ_{
ii
}, is the kinship coefficient, δ_{ii'}= 1, if *i* = *i*' and 0 otherwise, and , if *i* = *i*' and *j* = *j*', and 0 otherwise. The total h^{2} at a standardized age *t** is therefore

We extended the model to incorporate the effect of a QTL by adding a Legendre polynomial with random coefficients η_{
m
}, *m* = 1, ..., *k*_{
Q
}, ~ *N*(0, ∑_{η}). The covariance contribution from this QTL to equation (1), assuming its independence of *g* and *r*, is , where π_{
ii'
}is the multipoint shared by the two subjects at the QTL. Then the QTL h^{2} due to this locus is

We utilized kinship coefficients and multipoint identity by descent (IBD) computed in SOLAR and read these values into a matrix using SAS/IML. The other parameters

were estimated via a nonlinear maximization procedure NLPQN in SAS/IML [4].

Since computational load increased quickly with the number of observed ages, we divided the 70 distinct ages (ranging from 20 to 93) into five intervals: below age 30, with 10-year increments from age 30 to 60 and greater than 60. Order of polynomials was set as 2 (i.e., *k*_{
A
}= *k*_{
R
}= *k*_{
Q
}= 3) for both polygenic and subject-specific environmental effects and 1 for QTL effects. For those individuals who had more than one exam in an age interval, the average phenotype and covariates measured during that age interval were used in the analyses. Since it was time consuming to carry out genome-wide analyses, we only implemented this analysis at the three linked loci (S7, B30, B32) found in the univariate analyses.