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The score statistic
Let yk and yl be the phenotypic values of individuals k and
l, respectively, in a pedigree. It is assumed that there is no
locus-specific dominance effect. Then conditional on the
number of alleles shBMC Genetics 2003, 4 http://www.biomedcentral.com/1471-2156/4/s1/S77
Page 2 of 4
(page number not for citation purposes)
Under the null hypothesis, the segregation parameters are
independent of the linkage parameter [1], a property useful
for deriving the score statistic. Let ni be the number of
individuals in pedigree i and be a
vector of phenotypic values in pedigree i whose mean is
denoted by μi. The mean μi may depend on other covariates
in a linear or nonlinear fashion [5]. Define Σi0 =
(Cov(yik,yil)), , and
where and are the vectors of the probabilities
that IBD = 1 and 2, respectively, for all the relative pairs in
pedigree i. The score statistic, denoted by S, is defined as S
= b2/Var(b) if b > 0; S = 0 otherwise, where b = Σi (πi -
E(πi))t(vi - E(vi)) and, for sibship data, Var(b) =
Var(π)ΣiΣkWang [4] for more discussion on the calculation of b and
Var(b). The score statistic S is asymptotically distributed as
0.5 χ0
2 + 0.5 χ1
2 [1,4]. For sibship data, S is equivalent to
the statistic in [2] that assumes no dominance effect.ared identical by descent (IBD) by k
and l at a putative locus t, we have [4]
where Φkl is the kinship coefficient between individual k
and individual l, is the additive variance due to locus
t, and 1{τ=k} is the indicator function which equals 1 when
τ = k and equals 0 otherwise. The first term, Cov(yk,yl), is
completely determined by the segregation parameters,
such as means, the total additive variance, the total dominance
variance, the variance of environmental effect, etc.
These parameters can be estimated beforehand using phenotypic
data only. The remaining term depends only on
the pedigree structure through Φkl and the linkage parameter
(i.e., ). The hypotheses of interest are
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