Genome-wide association studies (GWAS) comprise a powerful tool for mapping genes of complex traits. However, an inflation of the test statistic can occur because of population substructure or cryptic relatedness, which could cause spurious associations. If information on a large number of genetic markers is available, adjusting the analysis results by using the method of genomic control (GC) is possible. GC was originally proposed to correct the Cochran-Armitage additive trend test. For non-additive models, correction has been shown to depend on allele frequencies. Therefore, usage of GC is limited to situations where allele frequencies of null markers and candidate markers are matched. In this work, we extended the capabilities of the GC method for non-additive models, which allows us to use null markers with arbitrary allele frequencies for GC. Analytical expressions for the inflation of a test statistic describing its dependency on allele frequency and several population parameters were obtained for recessive, dominant, and over-dominant models of inheritance. We proposed a method to estimate these required population parameters. Furthermore, we suggested a GC method based on approximation of the correction coefficient by a polynomial of allele frequency and described procedures to correct the genotypic (two degrees of freedom) test for cases when the model of inheritance is unknown. Statistical properties of the described methods were investigated using simulated and real data. We demonstrated that all considered methods were effective in controlling type 1 error in the presence of genetic substructure. The proposed GC methods can be applied to statistical tests for GWAS with various models of inheritance. All methods developed and tested in this work were implemented using R language as a part of the GenABEL package.
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