Combined linkage and association mapping of quantitative trait Loci with missing completely at random genotype data

In genetics study, the genotypes or phenotypes can be missing due to various reasons. In this paper, the impact of missing genotypes is investigated for high resolution combined linkage and association mapping of quantitative trait loci (QTL). We assume that the genotype data are missing completely at random (MCAR). Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. If the marker genotype is not missing, the model is exactly the same as those of our previous study, i.e., the number of genotype or allele is used as weight to model the effect of the genotype or allele in single marker case. If the marker genotype is missing, the expected number of genotype or allele is used as weight to model the effect of the genotype or allele. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominance effects simultaneously, and the "additive effect model" can only be used to model the additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. The non-centrality parameter approximations of F-test statistics are derived to calculate power and to compare power, which show that the power of the F-tests is reduced due to the missingness. By simulation study, we show that the two models have reasonable type I error rates for a dataset of moderate sample size. However, the type I error rates can be very slightly inflated if all individuals with missing genotypes are removed from analysis. Hence, the proposed method can help to get correct type I error rates although it does not improve power. As a practical example, the method is applied to analyze the angiotensin-1 converting enzyme (ACE) data.