Linkage between quantitative trait and marker loci: methods using
all relative pairs
J.M. Olson, E.M. Wijsman
Genetic Epidemiology, 10(2):87-102 (1993)
Abstract
Relative-pair methods for detection of linkage between a
quantitative trait and a marker locus have been proposed by a number
of authors [e.g., Haseman and Elston, Behav Genet 3-19, 1972; Amos
and Elston, Genet Epidemiol 349-360, 1989]. However, development of
tests of significance that combine information from different types
of relative pairs has been hampered by the presence of correlations
between relative pairs from the same pedigree. In this paper, the
methodology of generalized estimating equations is used to provide
an estimate of the robust covariance matrix of the estimates of the
set of relative-pair-type-specific regression parameters. Using this
matrix, an asymptotically most powerful test of linkage which
optimally combines the information contained in the different types
of relative pairs is constructed. This test requires optimal weights
that depend on unknown values of heritability and recombination
fraction to be chosen a priori. However, simulations show that, in
the regions of recombination fraction and heritability of practical
interest, the power of the test does not depend strongly on the
assumptions made when choosing the optimal weights; as a result,
weights that depend only on the number of each type of relative pair
and the variability of the marker identity-by-descent probabilities
work well in practice. In addition, an approximation to the
regression model leads to a simple approach to testing linkage in
which only a single regression parameter is estimated from data
containing different types of relative pairs. The resulting test is
slightly less powerful than the test described above, but its
computational simplicity and lack of dependence on a priori
weighting schemes suggest potential usefulness in large linkage
studies.
Allele-sharing linkage analysis