Biostatistics 1:369-387 (2000)
© 2000 Oxford University Press
Genomic control for association studies: a semiparametric test to detect excess-haplotype sharing
1 Department of Psychiatry, University of
Pittsburgh, Pittsburgh, PA 15213, USA
2 Department of Statistics, Carnegie Mellon
University, Pittsburgh, PA 15213, USAroeder{at}stat.cmu.edu
3 Department of Statistics, Carnegie Mellon
University, Pittsburgh, PA 15213, USA
Individuals who share a disease mutation from a common
ancestor often share alleles at genetic markers adjacent to the
mutation, even if the common ancestor is remote. The alleles at these
adjacent markers, called the haplotype, can be visualized as a string
of realizations of random variables, which may be dependent when
individuals are related in some fashion. Ideally, for a sample of
individuals all having the same (genetic) disease, this
dependence—measured as haplotype-sharing—will be greater
in the vicinity of disease genes than in other regions of the genome.
In this paper we present a semiparametric test for haplotype-sharing.
We begin by developing a model assuming that the ancestral haplotype
is known and thus the extent of haplotype-sharing from a common
ancestor can be determined unambiguously. The amount of overlap at
markers far from the disease is treated as a random variable with an
unknown distribution 
, which we estimate non-parametrically.
Overlap of markers surrounding disease genes are modeled as a mixture
, in which 
is
the fraction of subjects with the disease mutation. Testing for a
disease gene then amounts to testing whether 
. Next we
drop the assumption that the ancestral haplotype is known. To detect
excess clustering of haplotypes, we measure the pairwise overlap of a
set of haplotypes. As in the simpler scenario, this distribution is
modeled as a location-shift mixture. To test the hypothesis we
construct a score test with a simple limiting distribution.
Keywords: Haplotypes; Kernel density estimate; Linkage disequilibrium; Mixture models; Score test
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