Аннотация:
Genetic association studies lead to simultaneous categorical data analysis. The sample for every genetic locus
consists of a contingency table containing the numbers of observed genotype-phenotype combinations. Under
case-control design, the row counts of every table are identical and fixed, while column counts are random. Aim of
the statistical analysis is to test independence of the phenotype and the genotype at every locus.
We present an objective Bayesian methodology for these association tests, utilizing the Bayes factor F_2 proposed
by Good (1976) and Crook and Good (1980). It relies on the conjugacy of Dirichlet and multinomial distributions,
where the hyperprior for the Dirichlet parameter is log-Cauchy. Being based on the likelihood principle, the
Bayesian tests avoid looping over all tables with given marginals. Hence, their computational burden does not
increase with the sample size, in contrast to frequentist exact tests.
Making use of data generated by The Wellcome Trust Case Control Consortium (2007), we illustrate that the
ordering of the Bayes factors shows a good agreement with that of frequentist p-values.
Finally, we deal with specifying prior probabilities for the hypotheses, by taking linkage disequilibrium structure
into account and exploiting the concept of effective numbers of tests (cf. Dickhaus (2014)).
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