  The SNPs (Single Nucleotide Polymorphisms) genotyping platforms are of great
value for gene mapping of complex diseases. Nowadays, the high-density of these
molecular markers enables studies of dependence patterns between loci over the
genome, allowing a simultaneous inference of dependence structure and disease
association. In this paper we propose a method based on the theory of variable
range Markov random fields to estimate the extent of dependence among SNPs
allowing variable windows along the genome. The advantage of this method is
that it allows the simultaneous prediction of dependence and independence
regions among SNPs, without restricting a priori the range of dependence. We
introduce an estimator based on the idea of penalized maximum likelihood to
find the conditional dependence neighborhood of each SNP in the sample and we
prove its consistency. We apply our method to autosomal SNPs genotypic data
with unknown phase in the context of case-control association studies. By
examining rheumatoid arthritis data from the Genetic Analysis Workshop 16
(GAW16), we show the utility of the Markov model under variable range
dependence.
