The longitudinal variance components (LVC) approach is an extension of the VC approach proposed by Amos . For longitudinal familial data, let Y
)' be a vector of T time point trait values for ki members of the ith family, where Y
' = (Y
, ..., Y
)' for t = 1,..., T. Let E(Y
) = μ + X
β and V
, where defines the direct product of two matrices; G
is a ki × ki matrix of coefficient of relationship between pairs of relatives; Π
is a ki × ki matrix of IBD values for the ith family; I
is a ki × ki identity matrix; and A, B, and C are, respectively, polygenic, major gene, and random environment variance-covariance matrices each of dimension T × T. These matrices are represented by A = (σa.tt'), σa.tt = σ2a.t, B = (σg.tt'), σg.tt = σ2g.t, C = (τg.tt'), τg.tt' = τ2a.t, with their typical elements in the parentheses. We assume Y
follows a multivariate normal distribution. More details about this method can be found in de Andrade et al. .
To test for genetic linkage, we construct a likelihood ratio test. Under the null hypothesis, the major gene parameters, the σg.tt for all t and t', are restricted to be equal to 0. The distribution of the longitudinal test is a mixture of χ2 values . For example, for two time points linkage analysis of an additive genetic effect, the distribution of the bivariate test that the major-gene covariance components are zero is a mixture of 1/4 χ20, 1/2 χ21, and 1/4 χ23.
The longitudinal feature was incorporated in the software ACT  within the module multic, which was used to run the analyses. The longitudinal multipoint linkage analysis was performed only in the concordant five time points from Cohorts 1 and 2. The trait of interest was systolic blood pressure (SBP), and the covariates were age, gender, and body mass index (BMI). Individuals with missing values were eliminated from the analysis.
We used the two-stage procedure described in Levy et al. . This procedure first calculates the within-subject mean BP, and second, uses the sample-wide regressions adjusted for age and BMI, yielding a residual for each subject. Then, these residuals are the traits used in the quantitative linkage analysis. In our analyses, we consider two cases: 1) all subjects in both cohorts regardless of age and 2) only subjects between 25 and 75 years. Each of these analyses was then stratified by time points: 1) using all 21 time points from Cohort 1 and all five time points from Cohort 2 and 2) using only the concordant five time points from Cohorts 1 and 2. After the residuals were obtained, multipoint quantitative linkage analyses were performed for these four different scenarios using SOLAR . We also performed a multipoint quantitative linkage analysis using the average SBP over all measurements for each subject for additional comparison. LOD score values were calculated by dividing the likelihood ratio statistic by 4.6 (2/log e).