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person-specific environment. The phenotypic variance of the focal trait is
given by
2
p while the relative variance components associated with each
of the structuring matrices are the additive genetic heritability in the host
(h 2 ), and the proportion of phenotypic variance due to random environ-
mental
s
w 2 ). The phenotypic covariance model
essentially captures all of the information necessary for making gross
genetic inferences. It predicts how phenotypically correlated pairs of
individuals will be as a function of their genetic relatedness.
Using a standard maximum likelihood variance estimation method as
implemented in the statistical genetics computer package, SOLAR, 32 we
can estimate the parameters of this model along with any mean effect
parameters (such as covariate effects). In order to estimate this model, we
assume an underlying multivariate density has generated our data which
is obligately violated for traits like worm and egg counts. We therefore
typically perform direct inverse Gaussian transformations on all pheno-
types prior to analysis. Even after such transformation, these traits are not
exactly normal. However, prior analyses have shown that as long as
kurtosis is not excessive, the maximum likelihood analyses provide valid
results. 33
Using this approach, we can test to see whether a host genetic compo-
nent is necessary to explain the observed phenotypic covariances among
individuals. Likelihood ratio tests (LRT) are formed as twice the difference
in ln likelihoods. Because of boundary conditions (variances must be
greater than or equal to zero), the resultant test statistics are distributed as
mixtures of chi-square distributions. For example, when comparing
a model that includes host genetic factors and random environmental
factors with a baseline model only including random environmental
factors (i.e. h 2
factors (e 2
h 2
¼
1
0), the LRT is distributed as a 50:50 mixture of a point mass
at zero and a chi-square distribution with 1 degree of freedom.
¼
IDENTIFYING SPECIFIC GENES RESPONSIBLE
FOR HERITABILITY OF
ASCARIS
BURDEN
The basic knowledge that host genetic factors are involved in the
observed distribution of Ascaris burden is of limited immediate trans-
lational value. The most important reason for doing host genetic analysis
is to identify the actual causal genes underlying human variation in
disease risk. Knowledge of causal genes (and their causal sequence
variants) can provide new windows into understanding disease and can
directly provide novel drug targets. How does one go about localizing
and identifying these causal genetic factors that ultimately determine
heritability? Many recent advances in analysis of human quantitative
traits have been made in the context of genetically complex diseases. 34,35
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