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\centerline{\bf BERKELEY-STANFORD COLLOQUIUM}
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\centerline{3:30 p.m., Tuesday, October 31, 2000}
\centerline{At Berkeley}

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\centerline{\sl David Siegmund}
\centerline{\sl Department of Statistics}
\centerline{\sl Stanford University}
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\centerline{\bf Mapping Quantitative Trait Loci}
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The goal of genetic mapping is to locate genes that affect particular traits,
especially genes that affect human susceptibility to particular diseases and
related quantitative\/ traits, e.g., blood pressure and cholesterol level.
Testing markers throughout the genome to identify the relevant genes leads to a
class of irregular statistical problems, where standard large sample theory
does not apply.  In this talk I will describe the general problem of genetic
mapping with special attention to mapping quantitative trait loci (QTL).

(A) Goals

To give a systematic large sample theory for QTL mapping, which 

(i) clarifies the similarities and differences between QTL mapping in
experimental genetics and in humans,

(ii) treats issues of study design of recent interest, e.g., (a) the
comparative value of large pedigrees versus sib pairs,  (b) genotyping only
selected pedigrees, 

and 

(iii) provides a framework to study gene $\times$ gene and gene $\times$
environment interaction.

(B)  Methods

Use (i) the standard components of variance model and a parameterization of the
genetic effects that makes ``linkage parameters'' orthogonal to ``segregation
parameters'' in conjunction with (ii) the framework of local alternatives
employed in large sample statistical theory, in order to obtain explicit
expressions for score statistics and for asymptotic noncentrality parameters,
which can be used to compare the power of different strategies. 

This is joint research with Hsiu-Khuern Tang.

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