  The prevailing method of analyzing GWAS data is still to test each marker
individually, although from a statistical point of view it is quite obvious
that in case of complex traits such single marker tests are not ideal. Recently
several model selection approaches for GWAS have been suggested, most of them
based on LASSO-type procedures. Here we will discuss an alternative model
selection approach which is based on a modification of the Bayesian Information
Criterion (mBIC2) which was previously shown to have certain asymptotic
optimality properties in terms of minimizing the misclassification error.
Heuristic search strategies are introduced which attempt to find the model
which minimizes mBIC2, and which are efficient enough to allow the analysis of
GWAS data.
  Our approach is implemented in a software package called MOSGWA. Its
performance in case control GWAS is compared with the two algorithms HLASSO and
GWASelect, as well as with single marker tests, where we performed a simulation
study based on real SNP data from the POPRES sample. Our results show that
MOSGWA performs slightly better than HLASSO, whereas according to our
simulations GWASelect does not control the type I error when used to
automatically determine the number of important SNPs. We also reanalyze the
GWAS data from the Wellcome Trust Case-Control Consortium (WTCCC) and compare
the findings of the different procedures.
