Overview
This package contains the MATLAB algorithms used in the paper Heritability and
Genetic Correlations Explained by Common SNPs for Metabolic Syndrome
Traits (see citation below). The main purpose of this paper was to estimate the narrow-
sense heritability (h
2
) for biological traits (phenotypes) and the genetic and residual cor-
relations (r
g(e)
) between them for any number of traits. h
2
is a common measure that
accounts for the fraction of inheritance between parents and offspring due to additive ge-
netic variants. In addition to these measures and by taking advantage of the relationship
between correlation length and pedigree, we estimated the genomic contribution due to
common genetic variants (prevalence of 5% or more in the population) compared to all
genetic variants. The scripts are written for genomic analysis but are not specific to this
type of data and be easily adapted to other data sources. Other measurement matrices and
quantitative outcome variables may be used; though, keep in mind we assume the columns
of both are standard normalized.
The major solver is the restricted maximum Likelihood expectation maximization
scheme (REML EM). These algorithms are designed for the simultaneous estimate of
variances and covariance among any number of traits and is only limited by computa-
tional resources. We emphasize that it is capable of going well beyond a bivariate analysis
using realistic resources as we illustrated in the paper by the simultaneous analysis of
seven Metabolic Syndrome traits. Such simultaneous analysis takes advantage of addi-
tional information to improve estimates, even for the single variance components used to
estimate h
2
. The major implementations are done using four functions: 1) REM LEM,
2) F isherInv, 3) calch2, and 4) calccorr. REM LEM is used to estimate the mean ge-
netic and residual variances, and cross-trait covariances. F isherInv calculates the inverse
Fisher information needed for error estimates.
The script mvlmesim shows an example of a full implementation. For this we include
simulated data with correlated outcome variables. The genZA script also shows how the
genotype matrix is normalized using the vector of minor allele frequencies as written in
the paper.
Note there may be some discrepancy between the variable notation here and what is
written within the actual functions. The notation used here is more consistent with the
general use of these variables. If you want to follow the variables within the functions
then match the variable names by the argument order. In future releases the names will
be consistent.
Credits
The functions REMLEM, REMLEMtrans, F isherInv, and calccorr were originally
written by Carson C Chow and edited by Shashaank Vattikuti. Both authors are from
the Laboratory of Biological Modeling at the National Institutes of Health, NIDDK.
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