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Mathematical Biology seminar
Alun Thomas
Genetic Epidemiology, University of Utah
"Graphical modelling of the joint distribution of alleles at associated
loci. HapGraphs not HapMaps"
September 10, 2003
3:05pm in LCB 225
Pairwise linkage disequilibrium, haplotype blocks and recombination
hot spots provide only a partial description of the patterns of
dependences and independences between the allelic states at proximal
loci. On the gross scale, where recombination and spatial
relationships dominate, the associations can be reasonably described
in these terms. However, on the fine scale of current high density
maps the mutation process is also important and creates associations
between loci which are independent of the physical ordering and which
can not be summarized with pairwise measures of association. Graphical
modeling provides a standard statistical framework for characterizing
precisely this sort of complex stochastic data. While graphical models
are often used in situations where assumptions lead naturally to
specific models, it is less well known that estimation of graphical
models is also a developed field. We show how decomposable graphical
models can be fitted to dense genetic data. The objective function is
the maximized log likelihood for the model penalized by a multiple of
the model's degrees of freedom. Simulated annealing is used to find
good solutions. The great potential of this approach is that
categorical phenotypes can be included in the same analysis and
association with polymorphisms assessed jointly with the inter locus
associations. We illustrate our method and its potential with
phenotypic data on sex, prostate cancer and genotypic data from 25
SNPs in the ELAC2 gene. The results show clear non spatial and non
pairwise dependences.
For more information contact J. Keener, 1-6089
E-mail:
keener@math.utah.edu
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