A new variance component parameter was introduced into a standard pedigree-based variance component model
, where
is the phenotypic covariance matrix,
is the total phenotypic variance,
,
, and
respectively represent the proportion of
that can be attributed to the residual additive effect of polygenes, the gene pathway-specific variation, and a random environmental effect. Several critical structuring kernels are employed to model the covariances between individuals:
is the expected or theoretical kinship matrix integrated over the genome,
is the empirically estimated pathway-specific kinship matrix (the PSGRM), and
is the identity matrix. Such kernel-based approaches for summarizing the effects of multiple genetic variants have been proposed decades previously [
9] and has grown in popularity recently [
10,
11] Maximum likelihood estimates (assuming a multivariate normal probability density) and LRTs of the
parameter were obtained using an extension of the
polygenic command in SOLAR independently for each gene pathway [
11]. The significance of each gene pathways variance component estimate was obtained from a LRT against the null model
. Because the variance component
is tested on its boundary, the LRT statistic is distributed as a 50:50 mixture of a 1-degree-of-freedom chi-square and a point of mass zero [
12] although this is conservative [
13]. For both models, we calculated the heritability of systolic blood pressure using the first simulated phenotypic replicate. We used sex, age, and smoking status as covariates in our model. To control for possible population stratification, we also included as covariates the first 5 genetic principal components calculated from a subset of ~29,000 low, mutual, linkage disequilibrium (LD) SNPs from the GAW18 GWAS data. Those principal components are responsible for 5% of the trait's total variance and were calculated in 117 founder samples using routine
prcomp in R [
14] and were then projected to the rest of the genotyped pedigree so as to not incorrectly capture systematic pedigree information.