  For the vast majority of genome wide association studies (GWAS) published so
far, statistical analysis was performed by testing markers individually. In
this article we present some elementary statistical considerations which
clearly show that in case of complex traits the approach based on multiple
regression or generalized linear models is preferable to multiple testing. We
introduce a model selection approach to GWAS based on modifications of Bayesian
Information Criterion (BIC) and develop some simple search strategies to deal
with the huge number of potential models. Comprehensive simulations based on
real SNP data confirm that model selection has larger power than multiple
testing to detect causal SNPs in complex models. On the other hand multiple
testing has substantial problems with proper ranking of causal SNPs and tends
to detect a certain number of false positive SNPs, which are not linked to any
of the causal mutations. We show that this behavior is typical in GWAS for
complex traits and can be explained by an aggregated influence of many small
random sample correlations between genotypes of a SNP under investigation and
other causal SNPs. We believe that our findings at least partially explain
problems with low power and nonreplicability of results in many real data GWAS.
Finally, we discuss the advantages of our model selection approach in the
context of real data analysis, where we consider publicly available gene
expression data as traits for individuals from the HapMap project.
