On coding genotypes for genetic markers with multiple alleles in genetic association study of quantitative traits

In this study, we will formulate F∞ genetic models under various regression model frameworks and introduce three genotype coding schemes for genetic markers with multiple alleles. Starting from an allele-based modeling strategy, we first describe a regression framework to model the expected genotypic values at given markers. Then, as extension from the biallelic case, we introduce three coding schemes for constructing fully parameterized one-locus F∞ models and discuss the relationships between the model parameters and the expected genotypic values. Next, under a simplified modeling framework for the expected genotypic values, we consider several reduced one-locus F∞ models from the three coding schemes on the estimability and interpretation of their model parameters. Finally, we explore some extensions of the one-locus F∞ models to two loci. Several fully parameterized as well as reduced two-locus F∞ models are addressed.The genotype coding schemes provide different ways to construct F∞ models for association testing of multi-allele genetic markers with quantitative traits. Which coding scheme should be applied depends on how convenient it can provide the statistical inferences on the parameters of our research interests. Based on these F∞ models, the standard regression model fitting tools can be used to estimate and test for various genetic effects through statistical contrasts with the adjustment for environmental factors.Genetic markers with multiple alleles are common phenomena in genetic studies. It is well known that the ABO blood types in human are determined by three alleles at a genetic locus on chromosome 9. Molecular markers such as microsatellites often have multiple alleles. The major histocompatibility complex (MHC), a highly polymorphic genome region that resides on the human chromosome 6, encompasses multiple genes that encode for many human leukocyte antigens (HLA) and play an important role in regulation of the immune responses. Depending on the