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Genome-wide association studies (GWAS) aim to assess relationships between single nucleotide polymorphisms (SNPs) and diseases. They are one of the most popular problems in genetics, and have some peculiarities given the large number of SNPs compared to the number of subjects in the study. Individuals might not be independent, especially in animal breeding studies or genetic diseases in isolated populations with highly inbred individuals. We propose a family-based GWAS model in a two-stage approach comprising a dimension reduction and a subsequent model selection. The first stage, in which the genetic relatedness between the subjects is taken into account, selects the promising SNPs. The second stage uses Bayes factors for comparison among all candidate models and a random search strategy for exploring the space of all the regression models in a fully Bayesian approach. A simulation study shows that our approach is superior to Bayesian lasso for model selection in this setting. We also illustrate its performance in a study on Beta-thalassemia disorder in an isolated population from Sardinia. Supplementary Material describing the implementation of the method proposed in this article is available online.