Abstract
An ANOVA type general multi-allele (GMA) model was proposed in Wang (2014) on analysis of variance components for quantitative trait loci or genetic markers with phased or unphased genotypes. In this study, by applying the GMA model, we further examine estimation of the genetic variance components for genetic markers with unphased genotypes based on a random sample from a study population. In one locus and two loci cases, we first derive the least square estimates (LSE) of model parameters in fitting the GMA model. Then we construct estimators of the genetic variance components for one marker locus in a Hardy-Weinberg disequilibrium population and two marker loci in an equilibrium population. Meanwhile, we explore the difference between the classical general linear model (GLM) and GMA based approaches in association analysis of genetic markers with quantitative traits. We show that the GMA model can retain the same partition on the genetic variance components as the traditional Fisher's ANOVA model, while the GLM cannot. We clarify that the standard F-statistics based on the partial reductions in sums of squares from GLM for testing the fixed allelic effects could be inadequate for testing the existence of the variance component when allelic interactions are present. We point out that the GMA model can reduce the confounding between the allelic effects and allelic interactions at least for independent alleles. As a result, the GMA model could be more beneficial than GLM for detecting allelic interactions.
Highlights
There are two different ways in assessing the statistical association of a categorical variable with a continuous outcome
By applying the general multi-allele (GMA) model, we further examine estimation of genetic variance components for genetic markers with unphased genotypes from a random sample of individuals in a study population
We show that the GMA models can provide the same partition on the genetic variance components as the original Fisher’s analysis of variance (ANOVA) models but the general linear model (GLM) cannot
Summary
There are two different ways in assessing the statistical association of a categorical variable with a continuous outcome. We can either make a direct comparison of the group means among groups defined by the categorical variable or assess the variation that the categorical variable may contribute to the total variance of the continuous outcome The former approach is usually conducted via fitting a general linear model (GLM) with or without an adjustment for other covariates. We derive the LSE of model parameters in fitting the GMA model and develop estimators of the variance components for two genetic markers in an equilibrium population In both one locus and two loci cases, we explore the difference between the GLM and GMA in association analysis of genetic markers. The performance in model selection between using GLM and GMA models is examined
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